Nabil Mr

Génie Industriel

Cmp Augusto

Vincent Mr

Stéphane Pr

Pierre Badel

Pr

Flavien Balbo

Jean-François Bassereau

PR Batton-Hubert Mireille

Michel Ma

Alberto Carlos

Moreno-Camacho

ABSI

Keywords: sustainable supply chain, supply chain network design, sustainable development policy, optimization, sustainability assessment, dairy supply chain sustainable supply chain, supply chain network design, sustainable development policy, optimization, sustainability assessment, dairy supply chain

In the following lines, I would like to express my deepest gratitude to all those who have contributed one way or another to the completion of this thesis. May God bless you to a greater extent than my heart may wish.

First, sincere thanks to my advisors, professors Anicia, Natacha, and Jairo. I would like to them for their patience, understanding, and constant disposition to contribute to this work from their different research fields. The variety of their approaches enrich this work and my knowledge of sustainability in operations. I value the

vi List of Tables Table 1.

Abstract

This work addresses the research problem of quantitative support for decision-making in sustainable supply chain network design (SSCND). We first identify the common key indicators utilized to assess sustainability in supply chain design applications. We propose both (i) a single-objective and (ii) a multiobjective modeling approaches to deal with environmental and social criteria to the design of a supply chain network from a company perspective. Considering a broader perspective of sustainability in supply chains, the unit of analysis is extended from a company perspective to consider a wide-industry perspective for the sector. We specifically consider the effects of policy application on encompassing the sector towards sustainable development and its impacts in the supply network structure.

The purpose of this work is to propose an efficient assessment procedure for the joint assessment of economic, environmental, and social performance for the design or redesign of supply chain network. A mathematical formulation considering the evolution of the supply chain and the construction of capacities in the long term is presented. To this regard, we define sustainability objectives according to the current conditions of the sector and the country. We compare the supply chain structure changes over a time horizon following an ex-ante sustainability assessment approach. Moreover, sustainability key performance indicators are chosen considering current sustainability challenges of the sector. The performance of the model is tested with an application in the dairy industry in a developing-economy country. It illustrates the utility of the model to evaluate national mitigation and adaptation activities in the design of supply chain networks. The need of setting targets when measuring sustainability in the supply chain field is highlighted.

Results offer meaningful decision support to policymakers in evaluating implementation of policies and actions, and in the definition of strategical paths towards sustainability.

xi

Résumé

Cette thèse s'inscrit dans les recherches sur l'aide quantitative à la prise de décision dans la conception de réseaux de chaînes d'approvisionnement durables (SSCND). Dans un premier temp, nous identifions les indicateurs clés communs utilisés dans des publications scientifiques pour évaluer la durabilité dans les applications de conception de chaînes d'approvisionnement. Nous proposons ensuite (i) une approche de modélisation à objectif unique et (ii) une approche de modélisation multi-objectifs pour inclure les critères environnementaux et sociaux dans la conception d'un réseau de chaîne d'approvisionnement du point de vue de l'entreprise. En considérant la perspective plus large de la durabilité dans les chaînes d'approvisionnement, l'unité d'analyse est étendue d'une perspective d'entreprise pour considérer l'ensemble d'une filière au sein des différentes régions d'un pays donné. En particulier, nous étudions les effets de la mise en oeuvre des politiques de développement durable sur la structure du réseau d'approvisionnement pour l'industrie laitière en Colombie.

Introduction (en français)

En 1987, la publication "Notre avenir à tous" de la Commission mondiale sur l'environnement et le développement des Nations unies a ouvert, au niveau mondial, le débat sur le développement durable et la durabilité (CMED, 1987). À ce moment-là, le document définissait le développement durable comme "un développement qui répond aux besoins du présent sans compromettre la capacité des générations futures à répondre à leurs propres besoins." Selon [START_REF] Ferrer | Sustainability : What Does it Mean for the Operations Manager[END_REF], la simplicité de cette définition et son caractère inspirant ont permis l'utilisation généralisée de ce concept par les universitaires, les praticiens et les contextes politiques. De légères variations de cette définition sont couramment utilisées pour définir la durabilité. Par exemple, l'appropriation du concept de développement durable dans le milieu des affaires a conduit John Elkington à inventer le terme Triple Bottom Line (TBL) [START_REF] Elkington | Towards the Sustainable Corporation: Win-Win-Win Business Strategies for Sustainable Development[END_REF][START_REF] Elkington | Enter the triple bottom line. The Triple Bottom Line: Does It All Add Up[END_REF]. L'auteur souligne comment les stratégies durables peuvent bénéficier simultanément aux entreprises et aux clients, ainsi qu'à l'environnement, ce qui incite les entreprises à comptabiliser leurs gains et leurs pertes non seulement en termes économiques, mais aussi en termes environnementaux et sociaux.

Comme indiqué par [START_REF] Allaoui | Sustainable agro-food supply chain design using two-stage hybrid multi-objective decision-making approach[END_REF], les décisions concernant l'emplacement des installations, la détermination de la capacité, la sélection de la technologie, la sélection du mode de transport qui sont, entre autres, impliquées dans le problème de conception de réseau de chaîne d'approvisionnement correspondent à l'une des principales décisions au niveau stratégique ayant un impact sur la performance économique, environnementale et sociale d'une chaîne d'approvisionnement à long terme. Par exemple, d'une part, la construction d'une usine de fabrication dans une région spécifique peut générer de nouvelles opportunités de travail, promouvoir le développement de l'infrastructure routière, déclencher l'arrivée d'habitants dans la région et encourager le développement de services sociaux. D'autre part, elle peut menacer l'écosystème de la région, en raison de la consommation d'eau, de l'utilisation des terres, de la pollution, de l'élimination des déchets et, d'une manière générale, de la pression accrue sur les ressources naturelles et les services sociaux, ce qui a des répercussions sur l'environnement et entraîne une diminution du bien-être social.

En raison de la multiplicité des contextes et des caractéristiques de l'environnement des entreprises, des marchés et des parties prenantes, le problème de l'évaluation de la performance de durabilité d'un réseau de chaînes d'approvisionnement ne peut pas être abordé de manière générique [START_REF] Brandenburg | Quantitative models for sustainable supply chain management: Developments and directions[END_REF]. Pour le dire autrement, puisque les défis du développement durable ne sont pas les mêmes pour toutes les industries, il apparait fondamental de développer des études personnalisées considérant les particularités de l'industrie et de son territoire. Par exemple, la consommation d'eau peut ne pas être aussi pertinente dans le secteur bancaire que dans les systèmes alimentaires. ,De plus, tous les secteurs d'activités n'ont pas fait l'objet de la même attention dans la littérature scientifique. Par exemple [START_REF] Grant | Sustainable Logistics and Supply Chain Management: Principles and practices for sustainable operations and management[END_REF], ont montré que, dans la littérature, il existe de nombreuses études développées dans les cas de l'industrie manufacturière, tandis que le secteur agricole a reçu moins d'attention, malgré les caractéristiques sociales documentées des moyens de subsistance des agriculteurs et xiii la contribution représentative du secteur dans les émissions totales de gaz à effet de serre (GES) au niveau mondial.

Dans de nombreux pays, notamment dans les pays en développement, le secteur agroalimentaire joue un rôle essentiel dans l'économie en étant un contributeur important au produit intérieur brut (PIB) [START_REF] Gebresenbet | Logistics and Supply Chains in Agriculture and Food[END_REF] et il constitue un agent essentiel du développement économique, social et environnemental durable des communautés rurales [START_REF] Naik | Challenges of creating sustainable agri-retail supply chains[END_REF]. Selon la Banque mondiale, ce secteur représentait près d'un tiers du PIB mondial en 2014 (World Bank Group, 2015). De plus, en raison de la croissance démographique, des progrès des transports, des technologies de l'information et de la communication, le secteur agricole a connu un taux de croissance annuel de plus de 6% au cours de la dernière décennie, et sa production devrait être multipliée par deux d'ici 2050 [START_REF] Fao | Climate Change and The Global Dairy Cattle sector -The role of the dairy sector in a low-carbon future[END_REF]. Dans son sens le plus large, l'industrie agricole comprend un large ensemble de procédures et services connexes, dans lequel les ressources naturelles sont utilisées pour produire des produits de base tels que les aliments, les fibres, les carburants et les produits forestiers, entre autres. Plus précisément, les chaînes d'approvisionnement agroalimentaires comprennent une série d'activités allant de la production à la distribution pour amener les produits agricoles de la ferme au marché. Les chaînes d'approvisionnement agroalimentaires ont des impacts environnementaux spécifiques qui influent sur l'atteinte des limites planétaires, telles que les émissions de gaz à effet de serre, l'impact sur la biodiversité, le changement d'utilisation des sols, la consommation d'eau, les effets sur les cycles du phosphore et de l'azote (Boutaud et Gondran, 2020), l'élimination des déchets, le développement social, entre autres, qui deviennent des facteurs pertinents dans la configuration du réseau.

En fonction de ces considérations, ce travail présente un modèle intégré pour évaluer les dimensions économiques, environnementales et sociales, tout en tenant compte des politiques sectorielles et nationales en matière d'environnement et de développement. Au lieu d'avoir une perspective de chaîne d'approvisionnement d'entreprise, le modèle est destiné à travailler dans la macro localisation des capacités dans une perspective de large industrie. Le présent travail envisage plusieurs approches de formulation pour traiter la conception de la chaîne d'approvisionnement lorsque les facteurs environnementaux et sociaux sont pris en compte dans le processus de prise de décision. Il explore les formulations à objectif unique et multi-objectifs. Le travail souligne l'impact des critères de durabilité sur la structure de la chaîne d'approvisionnement, et discute de la nécessité de définir des objectifs pour évaluer la durabilité au niveau de la chaîne d'approvisionnement. Enfin, il présente un modèle mathématique visant à effectuer une xiv évaluation ex ante de la durabilité au niveau de l'ensemble de la filière pour la définition de la structure de la chaîne d'approvisionnement, dans le cadre du développement de politiques ou d'actions. Le modèle représente la structure de la chaîne d'approvisionnement, au cours de l'horizon temporel jusqu'à ce qu'elle atteigne les objectifs spécifiés à atteindre. Bien que le modèle puisse être appliqué à plusieurs secteurs, ce travail présente un cas spécifique pour l'industrie laitière en Colombie.

La structure du document

Cette thèse est organisée en huit chapitres comme présenté dans la Figure 0.1. Le chapitre 1 énonce notre problèmatique de recherche, les objectifs de la recherche et décrit la méthodologie de l'étude. Le chapitre 2 présente la revue de la littérature, la réflexion, les paramètres d'évaluation de la durabilité, les approches de solutions et les applications. Le chapitre 3 présente un modèle de programmation linéaire en nombres entiers mixtes (MILP) avec une approche de solution axée sur les dimensions. Ici, trois objectifs différents portant sur les dimensions économiques, environnementales et sociales sont évalués pour comparer l'impact sur la structure du réseau lorsque la décision est guidée par un seul critère d'évaluation. Les résultats montrent comment la structure du réseau affecte les facteurs économiques, environnementaux et sociaux. Ils montrent également comment les préférences dans une dimension représentent des compromis dans les deux autres ou au moins dans l'une d'entre elles. Le chapitre 4 présente une approche de modélisation multi-objectifs pour la conception de chaînes d'approvisionnement durables. Contrairement à d'autres approches dans lesquelles les préférences du décideur sont incluses, ce chapitre présente une approche de programmation d'objectifs de Chebyshev sans préférence. Au lieu d'attribuer des pondérations à chaque objectif ou de limiter leur aggravation, l'approche xv de Chebyshev estime la meilleure solution possible en minimisant la distance maximale à la solution idéale pour chaque objectif. L'idée derrière cette approche était d'inclure les critères dans une modélisation mathématique en évitant d'adopter une mentalité de compromis ou une approche de durabilité faible.

Le chapitre 5 présente une description générale de l'étude de cas et de son importance dans le contexte écologique et le développement social du pays. Il présente également une définition de la durabilité pour le secteur à partir de laquelle les indicateurs de durabilité proposés sont dérivés. Le chapitre 6 présente un modèle mathématique pour la conception d'une chaîne d'approvisionnement dans une perspective industrielle large, tout en considérant l'exécution de politiques et d'actions. Au lieu de considérer des objectifs multiples, l'approche considère le temps nécessaire pour atteindre des valeurs définies pour un ensemble d'indicateurs clés dans les trois dimensions de la durabilité. La performance du modèle est évaluée à l'aide d'une étude de cas dans l'industrie laitière de la Colombie au chapitre 7. Les résultats du modèle sont utiles pour la définition des capacités et de la localisation des installations de production, de transformation et de distribution, dans tout le pays. Les conclusions et les perspectives de recherche sur le lien entre la durabilité et la conception de la chaîne d'approvisionnement sont discutées au chapitre 8.

Les conclusions

Cette thèse aborde le problème de la conception d'un réseau de chaînes d'approvisionnement en tenant compte des facteurs sociaux, environnementaux et économiques. Pour traiter ce problème, différentes approches de modélisation sont proposées au cours du développement du projet. En effet, cette thèse explore des approches de modélisation mono-objectif et multi-objectifs, en utilisant des indicateurs individuels et composites pour représenter les critères de durabilité au niveau de la chaîne d'approvisionnement et discuter de leurs applications, opportunités et défauts. Contrairement à d'autres études sur le sujet, qui se concentrent principalement sur le développement d'algorithmes efficaces sur le plan informatique, ce travail est en outre centré sur la discussion de la durabilité et du lien entre la gestion de la chaîne d'approvisionnement et l'évaluation de la durabilité. En particulier, ce travail s'intéresse spécialement à l'évaluation de la durabilité dans les décisions stratégiques de la chaîne d'approvisionnement sous l'application de politiques.

Reconnaissant le lien entre le développement durable et l'évaluation de la durabilité, cette thèse commence par présenter une revue sur le problème de conception de réseaux de chaînes d'approvisionnement, avec un intérêt intentionnel pour la compilation des métriques incluses dans le problème à traiter avec des critères économiques, environnementaux et sociaux. Le travail a été principalement axé sur l'évaluation des indicateurs utilisés dans l'application réelle du problème de conception de réseaux. La revue présente les critères les plus courants utilisés pour représenter les différentes catégories dans les trois dimensions de la durabilité. En bref, elle identifie la performance financière comme étant la catégorie la plus prédominante dans la gestion de la chaîne d'approvisionnement pour évaluer la durabilité au niveau économique, la pollution atmosphérique dans la dimension environnementale, et dans la dimension sociale, les catégories les plus influentes sont les conditions de travail et le développement social.

Ce travail considère l'évaluation de la durabilité au niveau de la chaîne d'approvisionnement sous deux angles différents. D'une part, il considère une vision de la durabilité de l'entreprise au niveau de l'optimisation de la planification de l'approvisionnement. Dans le chapitre 3, nous présentons une approche xvi axée sur les dimensions, un MILP pour la conception d'un réseau de chaîne d'approvisionnement générique. Le modèle est résolu en considérant trois objectifs différents, un pour chaque dimension de la durabilité.

Les résultats montrent l'effet des critères de décision sur la structure de la chaîne d'approvisionnement. Il est utile de reconnaître la capacité d'amélioration de la chaîne d'approvisionnement en calculant des valeurs idéales pour chaque dimension considérée. En outre, il expose l'impossibilité de les atteindre toutes en même temps en raison de la nature conflictuelle des objectifs. Le chapitre 4 présente une approche multiobjectifs pour traiter l'inclusion synchronisée des critères de durabilité. Nous discutons des différentes approches multi-objectifs dans la littérature académique et de leurs façons de traiter les préférences des décideurs. En outre, nous discutons de certaines lacunes liées à l'absence d'objectifs définis pour chaque dimension de l'évaluation de la durabilité. Le modèle est résolu à l'aide d'une approche de programmation par objectifs de type Tchebychev. L'approche de la solution sans préférence a conduit à une solution faisable sans établir de préférences biaisées sur les objectifs. Mais, plus important encore, elle ouvre la discussion sur les objectifs et l'horizon temporel en considérant le développement durable dans les chaînes d'approvisionnement.

D'autre part, ce travail aborde la durabilité dans une perspective industrielle au sens large. Ce travail discute de la nécessité d'une vision holistique de la durabilité dans les décisions à long terme au niveau de la chaîne d'approvisionnement, étant donné que les efforts séparés et individuels des entreprises pourraient ne pas entraîner la réduction des émissions qui est nécessaire pour atteindre les engagements nationaux et mondiaux en matière de changement climatique et de développement durable. Par conséquent, ce travail contribue à la définition d'un modèle d'évaluation ex ante de la durabilité pour la conception du réseau d'approvisionnement dans le secteur laitier en Colombie présenté au chapitre 6. Le modèle multi-période traite de la méga-localisation des installations de production, de transformation et de distribution pour atteindre un ensemble d'objectifs de durabilité sous l'application de politiques et d'actions. Contrairement aux travaux antérieurs adoptant une recherche de compromis sur les performances économiques, environnementales et sociales, le modèle vise à atteindre un objectif défini pour les indicateurs clés définis dans chaque dimension de la durabilité, en modifiant la structure de la chaîne d'approvisionnement sur un horizon temporel. En tant qu'aspect novateur de la modélisation, l'évaluation inclut l'utilisation des terres pour les activités agricoles et leur transformation en pratiques durables.

Cette thèse contribue à la discussion sur l'évaluation de la durabilité et sur la nécessité d'établir des objectifs de durabilité lors de la prise de décisions relatives à la gestion de la chaîne d'approvisionnement, en particulier lors de la conception de la chaîne d'approvisionnement. Comme indiqué par [START_REF] Pope | Conceptualising sustainability assessment[END_REF], l'évaluation de la durabilité nécessite un concept de durabilité bien défini.

Les efforts risquent d'échouer à présenter des solutions alternatives lorsque les objectifs ne sont pas définis. À cet égard, ce travail souligne la pertinence de l'évaluation des améliorations dans un contexte où les cibles ou les objectifs souhaités sont discutés. En outre, il examine la définition des indicateurs clés de performance de la durabilité en fonction de ce que la durabilité signifie pour les parties prenantes dans le cas d'étude spécifique présenté ici. , 1987). To that moment, the document defined sustainable development as "development that meets the needs of the present without compromising the ability of future generations to meet their own needs." In accordance with [START_REF] Ferrer | Sustainability : What Does it Mean for the Operations Manager[END_REF], the simplicity of this definition and its inspirational character have permitted the widespread use of that concept by academics, practitioners, and political contexts. Slight variations of this definition are commonly used to define sustainability. For instance, Kannegiesser & Günther (2014) refers a definition of sustainability in the business context that was previously presented by the International Institute for Sustainable Development (IISD) as "-adopting business strategies and activities that meet the needs of the enterprise and its stakeholders today while protecting, sustaining and enhancing the human and natural resources that will be needed in the future." However, as pointed out by [START_REF] Bryceson | Agrifood Chains as Complex Systems and the Role of Informality in Their Sustainability in Small Scale Societies[END_REF], the concept of sustainability has way different meanings when it is addressed by environmentalists, business managers, social scientists, and other fields [START_REF] Daly | Sustainable Development-Definitions, Principles, Policies[END_REF]. There are so many definitions that it is necessary to define the concept in every context it is used.

For instance, the appropriation of the sustainable development concept in the business environment took John Elkington to coin the term Triple Bottom Line (TBL) [START_REF] Elkington | Towards the Sustainable Corporation: Win-Win-Win Business Strategies for Sustainable Development[END_REF][START_REF] Elkington | Enter the triple bottom line. The Triple Bottom Line: Does It All Add Up[END_REF]. The author emphasizes how sustainable strategies may benefit companies and customers simultaneously and the environment, motivating companies to account for its gain and losses in economic terms and to measure their gains and losses in environmental and social terms. Over the last years, the TBL concept has rapidly spread out in the supply chain management research field as reflected in the increasing number of papers addressing sustainability in general supply chain management. It addresses issues at operational, tactical and strategical level, such as sourcing, production, inventory, transportation management, and network design [START_REF] Anvari | The facility location problem from the perspective of triple bottom line accounting of sustainability[END_REF][START_REF] Devika | Designing a sustainable closed-loop supply chain network based on triple bottom line approach: A comparison of metaheuristics hybridization techniques[END_REF][START_REF] Montoya-Torres | Designing sustainable supply chains based on the Triple Bottom Line approach[END_REF][START_REF] Moreno-Camacho | Sustainability metrics for real case applications of the supply chain network design problem: A systematic literature review[END_REF][START_REF] Mota | Supply chain design and planning accounting for the Triple Bottom Line[END_REF].

Decisions related to location, capacity, operation technology of facilities, and transportation mode are involved in the supply chain network design problem (SCND). It corresponds to one of the most determining decision at strategic level. As stated by [START_REF] Allaoui | Sustainable agro-food supply chain design using two-stage hybrid multi-objective decision-making approach[END_REF], these decision affect economic performane of the company. Also, they have a larger impact on the company's environmental and social performance in the long term. For instance, on one hand, the construction of a manufacturing plant in a specific region can generate new labor opportunities, promote the development of road infrastructure, trigger the arrival of inhabitants into the region and encourage the development of social services facilities. On another hand, it might result in a threat to the region's ecosystem, due to consumption of water, use of land, pollution, waste disposal, and in general, amplified pressure on natural resources and social services, which results in environmental impacts and decreasing of social well-being.

Supply chain network design problem has received increasing attention over the last decades, as shown by multiples review on this issue [START_REF] Barbosa-Póvoa | Opportunities and challenges in sustainable supply chain: An operations research perspective[END_REF][START_REF] Bubicz | Incorporating social aspects in sustainable supply chains: Trends and future directions[END_REF][START_REF] Eskandarpour | Sustainable supply chain network design: An optimization-oriented review[END_REF][START_REF] Xu | The Design of Green Supply Chains under Carbon Policies: A Literature Review of Quantitative Models[END_REF]. Having the current complexity of worldwide production-distribution network, sustainable development is not narrowed to a focal company perspective. Instead, a holistic view of the entire network is needed. Consequently, action planning having impact on financial resources, natural resources and stakeholders involves each actor in the supply chain, from the initial producers of raw material to the enduser customers, to design or redesign their processes [START_REF] Montoya-Torres | Conceptual framework for measuring carbon footprint in supply chains[END_REF][START_REF] Touboulic | Theories in sustainable supply chain management: a structured literature review[END_REF][START_REF] Wolff | Detecting unsustainable pressures exerted on biodiversity by a company. Application to the food portfolio of a retailer[END_REF]. Moreover, due to the multiplicity of contexts and characteristics of businesses environment, markets, and stakeholders, the problem of assessing sustainability performance of a supply chain network cannot be addressed in a generic way [START_REF] Brandenburg | Quantitative models for sustainable supply chain management: Developments and directions[END_REF]. To put it differently, since challenges to sustainable development are not equal in every industry, it results fundamental to develop customized studies considering the particularities of the industry and its territory. For instance, water consumption might not be that relevant in banking as it is for food systems.

In this regard, it is observed that bioenergy is one of the sectors receiving more interest from academics. Notably, most of the case studies published in academic literature focus on the "biomass to bioenergy" industry, which links the agricultural and the industrial sectors seeking to partially replace fossil fuels by more sustainable energy sources [START_REF] Eskandarpour | Sustainable supply chain network design: An optimization-oriented review[END_REF]. Findings of these research highlight that most of the studies focus on generic environmental impacts coming from the distribution process and facilities location, but factors in both environmental and social dimensions in the agricultural sector are scarcely involved into the decision-making process. Indeed, [START_REF] Grant | Sustainable Logistics and Supply Chain Management: Principles and practices for sustainable operations and management[END_REF] stated that, in the literature, there are numerous studies developed in the manufacturing industry , while the agricultural sector has received less attention. Despite the documented social characteristics of farm livelihood and the representative contribution of the sector in the total greenhouse gas (GHG) emissions at global level.

In many countries, especially in developing countries, agri-food sector plays an essential role in the economy by being a significant contributor to gross domestic product (GDP) [START_REF] Gebresenbet | Logistics and Supply Chains in Agriculture and Food[END_REF].

It constitutes an essential agent in the economic, social and environmentally sustainable development of rural communities [START_REF] Naik | Challenges of creating sustainable agri-retail supply chains[END_REF]. According to the World Bank, this sector accounted for almost one-third of global GDP in 2014 (World Bank Group, 2015). Moreover, due to population growth, advances in transport, information, and communication technology, the agricultural sector has an annual growth rate of over 6% during the last decade. Its production is expected to twofold by 2050 [START_REF] Fao | Climate Change and The Global Dairy Cattle sector -The role of the dairy sector in a low-carbon future[END_REF]. The sector is especially important in Latin America and the Caribbean region. It represents 14.1% of total generated employees in the region in 2018 (OECD/FAO, 2019), meanwhile in the European Union it accounted about 4.4% of total employment by 2017 (Eurostat, 2019). Despite the economic growth of agri-food sector in the last years, rural areas still tending to lag in social and economic conditions. For instance, according to the European Comission (2007), incomes in rural areas are near 20% lower than in urban areas, and rural areas present higher unemployment rates. Agri-food sector also plays a significant role in the environment. Agriculture, forestry and land-use change account for 25% of GHG emissions. Part of the solution to climate change is therefore in the mitigation in the agriculture sector.

In its broadest sense, the agricultural industry comprises a width set of procedures and its related services. Natural resources are used to produce commodities such as food, fiber, fuels, and forest products, among others. Specifically, agri-food supply chains comprise a series of activities from production to distribution to bring farm products from farms to markets. There are unique characteristics of agri-food supply chains affecting sustainability such as soil use change, water consumption, effects on the phosphorus and nitrogen cycles, waste disposal, and social development. These become relevant factors at determining location for production facilities and en up affecting the configuration of network.

At this far, three aspects stand out on the SCND research field. First, although sustainability assessment claims for a holistic view of the supply chain, it focuses sometimes on downstream operations and impacts coming from upstream suppliers might be sidelined, especially when agricultural activities occur at this level. This phenomenon might lead to superficial solutions with low impacts in supply chain sustainability. Second, most works consider a focal corporate sustainability perspective; wide-industry approaches to sustainable development are scarce. Recent studies have suggested that incremental environmental improvements carried out by individual companies may be inadequate to contend with global environmental issues. In this regard, public organizations are called to be the connecting points between the sustainable development goals and corporate supply chain management strategies, to bring global aspirations into regional and local contexts [START_REF] Paletta | A Step-by-Step Process towards an Evolutionary Policy Encouraging the Adoption of Sustainable Business Models[END_REF].

Last but not least, surprisingly, few studies consider goals and targets at defining sustainable alternative solutions [START_REF] Robert | What is Sustainable Development? Goals, Indicators, Values, and Practice[END_REF]. Most of the works focus on developing models to the design of more ecofriendly or socio-friendly structures. Although clearly the new yielded solution represents an improvement compared with the first state, no further analyses are done to confirm that the new solution meets some requirements in the context to be considered sustainable. Therefore, an integrated perspective of supply chain design is needed. In order to assess sustainability criteria into the SC, (i) suitable metrics for the three dimensions of sustainability must be appropriately defined; (ii) it is required the definition of sustainability objectives and indicators to compare performance from different configurations; and (iii) suitable models need to be developed to optimize the multi-dimensional performance of sustainable supply chains [START_REF] Beske-Janssen | 20 Years of Performance Measurement in Sustainable Supply Chain Management -What Has Been Achieved? Supply Chain Management[END_REF].

According to these considerations, this work presents an integrated model to assess economic, environmental, and social dimensions, while considering environmental and development sectorial and national policies. Instead of having a corporate supply chain perspective, the model is intended to work in the macro location of capacities in a wide-industry perspective. The present work considers multiple formulation approaches to deal with supply chain design when environmental and social factors are considered into the decision-making process. It explores single-objective and multi-objectives formulations. The work highlights the impact of sustainability criteria on supply chain structure and discuss the urge to define targets at assessing sustainability at supple chain level. Finally, it presents a mathematical model useful to carry out an ex-ante sustainability assessment at the wide industry level to define the supply chain structure, under development of policies or actions. The model defines the evolution of the supply chain structure during the time-horizon until it reaches the specified targets. Although the model could be applied to several sectors, this work presents a specific case in the dairy industry in Colombia.

This work contributes to developing mathematical models to the design of supply chain network structures under the evaluation of policies or actions. Moreover, it presents a way to define targets for assessing The main objective of the review is to identify both, the common indicators to assess sustainability in supply chain design in different sectors, and how they can be assessed [START_REF] Moreno-Camacho | Sustainability metrics for real case applications of the supply chain network design problem: A systematic literature review[END_REF]. The review was also useful to confirm that the lowest attention has been given to the agricultural sector. Therefore the definition of specific metrics for agricultural sector needed deeper inquire. Remaining two questions were:

(iii) How can these metrics or performance indexes be involved in analytical models to better decisionmaking in the supply chain network design problem? and

(iv) What are the differences in outcomes when sustainability metrics are involved in the design of a supply chain network?

Models in Operations Research dealing with sustainability might be classified as single-objective models and multi-objectives models. Those two approaches were addressed in this thesis. Chapter 3 presents a mixed-integer linear programming (MILP) model with a dimension-driven solution approach. Here, three different objectives addressing economic, environmental, and social dimensions are evaluated to compare the impact on the network structure when the decision is guided by only one evaluation criterion. The results show how network structure affects economic, environmental and social factors. It also shows how preferences in one dimension represent compromises in the remaining two or at least one of them. From this work, new questions arise, for instance, facing different configurations, which one is sustainable? how to define targets to these criteria? among others.

Classical approach to the inclusion of preferences in mathematical model is addressed by multi-objective optimization. Chapter 4 presents a multi-objective modeling approach to sustainable supply chain design.

Unlike other approaches where decision-maker preferences are included, this chapter presents a nonpreference Chebyshev goal programming approach. Instead of receiving weights to each objective or to limit worsening to them, Chebyshev approach calculates the best possible solution at minimizing the maximum distance to the ideal solution for each objective. The idea behind the approach was to include the criteria into a mathematical modeling avoiding adopting a trade-off mentality or a weak sustainability approach. As mentioned by [START_REF] Elkington | [END_REF], TBL term might get misinterpreted by early adopters, as long as, instead of encouraging business to track and manage economic social and environmental value added, application fell short by adopting a trade-mentality, considering it as an accounting tool. Here new questions came out: how long it takes to get from the initial structure of the supply chain to the new recommended structure? Is it a sustainable configuration? Isolated improvements by one company are enough to reach sustainable development? Other questions related to measurement methodologies appeared as well, for example: what are the advantages or disadvantages of using composite criteria to assess sustainability? Or how to define challenging enough and realistic targets for assessing sustainable development?

Going forward from that point, represented a challenge to bring to this work insights and perspectives of sustainability from other several disciplines. For example, to give a satisfactory answer to question (i) and (ii), a specific research of criteria for assessing sustainability in agriculture was carried out. At that point, the inspiring work of (de [START_REF] De Olde | Assessing sustainability at farm-level: Lessons learned from a comparison of tools in practice[END_REF] takes us to a completely new world in which we were introduced to a full variety of sustainability assessment tools, including the efforts of [START_REF] Bélanger | DELTA: An Integrated Indicator-Based Self-Assessment Tool for the Evaluation of Dairy Farms Sustainability in Quebec, Canada[END_REF][START_REF] Djekic | Environmental life-cycle assessment of various dairy products[END_REF][START_REF] Elsaesser | Quantifying sustainability of dairy farms with the DAIRYMAN sustainability-index[END_REF][START_REF] Grenz | RISE-a method for assessing the sustainability of agricultural production at farm level[END_REF][START_REF] Lebacq | Sustainability indicators for livestock farming. A review[END_REF][START_REF] Paracchini | A diagnostic system to assess sustainability at a farm level: The SOSTARE model[END_REF][START_REF] Van Calker | Development and application of a multi-attribute sustainability function for Dutch dairy farming systems[END_REF][START_REF] Van Cauwenbergh | SAFE-A hierarchical framework for assessing the sustainability of agricultural systems[END_REF][START_REF] Zahm | Assessing farm sustainability with the IDEA method -from the concept of agriculture sustainability to case studies on farms[END_REF]. The influence of these works is reflected in (United Nations, 2015). For more details the interested reader is referred to the NDC Registry, hosted in https://www4.unfccc.int/sites/NDCStaging/Pages/Home.aspx.

The NDC's time horizon is compatible with the proposed Agenda for Sustainable Development but more important it is useful to determine a framework for the definition of goals in the seeking of sustainable development. Based on this, Chapter 6 presents a mathematical model to the design of a supply chain with a wide-industry perspective, while considering the execution or policies and actions. Instead of considering multiple objectives, the approach considers the required time to reach defined values for a set of key indicators in the three dimensions of sustainability. The performance of the model is evaluated using a case study in the dairy industry of Colombia in Chapter 7. The model results are useful to the definition of capacities and location for production, processing, and distribution facilities throughout the country. To close this thesis, conclusions and further research on the link between sustainability and supply chain design are discussed in Chapter 8.

Methodology approach

In general terms, several types of research methodologies are available: qualitative, quantitative and mixed, this last combining the two previous ones [START_REF] Gómez | Introducción a la metodología de la investigación científica[END_REF]. The present research work is a quantitative study that involves collecting and qualitative data analysis to answer the research question and the analysis of results to describe and explain part of the problem under study. This research can also be classified as descriptive-explanatory. It is descriptive because it identifies relevant aspects of the research universe, pointing out alternatives that promote the enhancement of decision-making processes for the actors involved in the design of a sustainable supply chains through the implementation of a practical methodology for its design and the evaluation of economic, social and environmental indicators.

Descriptive research works on realities, aiming at the description, registration, analysis, and interpretation of the current nature of a process or phenomenon to provide a correct interpretation [START_REF] Rodriguez Moguel | Metodología de la Investigación[END_REF]. This research aims to characterize the problem of sustainable design of supply chains in the agrifood sector, the impact of these indicators on the chain's strategic decisions, and, based on these descriptions, a solution model is proposed. Based on the latter, this study is also explanatory since it explains the variables and parameters that intervene in the problem, under a strategic approach for the design of logistics chains.

This research provides new insights for the solution of this problem at considering public policies and national development targets in the definition of supply chain structures. Finally, the objective is that future research on the subject will allow the concepts and approaches formulated in the new approach proposed in this work to be deepened. It is worth noting that this research is not intended to study the social behaviors, attitudes, beliefs, ways of thinking and acting of a group or collectivity. The approaches made to the developed model to support the decision making process in the design of sustainable supply chains will not be related to individual beings (e.g., administrative staff, clients, etc.), but to the technical aspects associated with the design of the chain and its impact at strategic level on decision making and on the economic, social and environmental indicators evaluated.

analysis in specific research processes mainly of exploratory type, in which the variables are still unknown and the phenomenon studied is not fully understood, facilitating the case study to reach a higher level of understanding [START_REF] Voss | Case research in operations management[END_REF].

Overview of publication outputs

The outputs of this research have been presented at three international conferences, two works have been published and two more are submitted to review in academic journals by the time this manuscript was written. Table 1.1 gives an overview of publications and presentations, and their link with the different chapters of this manuscript. The current chapter presents a review of academic literature related to sustainable supply chain network design (SSCND). It includes a review of modeling strategies and solution methods for decision making when the three pilar of sustainability, or at least two of them, are considered in order to define the location of facilities within a supply network (e.g., economy and environment). Besides, it presents a report of metrics and sustainability assessment tools included in analytical methods for supply chain design.

Considering the object of study of the present work, a particular emphasis is placed on reviewing methodologies for measuring sustainability in the agricultural sector.

Supply chain network design

Supply chain network design (SCND) encompasses multiple decisions at the tactical and strategic levels in the supply chain management context. Indeed, as is stated by [START_REF] Eskandarpour | Sustainable supply chain network design: An optimization-oriented review[END_REF][START_REF] Pourhejazy | The new generation of operations research methods in supply chain optimization: A review[END_REF], different disciplines such as management, logistics, and Operations Research are interrelated with in this topic, which presents a challenge to consolidate and synthesize a definition for the field. Figure 2.2 presents a framework of the problems addressed within the SCND field at different decision levels and corresponding with different activities in the supply chain.

In the scientific literature, SCND is often understood as part of the supply chain planning process at the strategic level. Mainly, decisions aiming to shape the structure of the distribution network, such as determining the number of tiers, the number of facilities at each tier, their geographical location, their capacity, and technology, as well as determining the flow of material from one location to another.

According to [START_REF] Govindan | Supply chain network design under uncertainty: A comprehensive review and future research directions[END_REF][START_REF] Mangiaracina | Distribution network design: a literature review and a research agenda[END_REF], SCND also comprises the definition of strategic policies concerning inventory and transportation modes. Indeed, during the last decades, SCND has been one of the most active application fields of Operation Research and the Management Sciences [START_REF] Barbosa-Povoa | How To Design and Plan Sustainable Supply Chains Through Optimization Models?[END_REF][START_REF] Calleja | Methodological approaches to supply chain design[END_REF][START_REF] Garcia | Supply chain design and optimization: Challenges and opportunities[END_REF]. Even though the design of an entirely new network is not very frequent, the redesign of existent supply chains, as a consequence of political decisions, new suppliers, and new technologies, pose the same challenges.

Usually, in the classical literature of Supply Chain Management (SCM), the problem of determining the structure of the network of a supply chain is addressed from an economic perspective. Models frequently establish the minimum total operational cost as a decision criterion; meanwhile, the objective of profit maximization has received less attention [START_REF] Mangiaracina | Distribution network design: a literature review and a research agenda[END_REF]. However, over the last few years, with the growing global concern about environmental and social impacts derived from supply chain operations, both practitioners and academics have seen the need to incorporate additional factors allowing a broader assessment of the supply chain in the three dimensions of sustainability.

Figure 2.2. Supply chain network design activities by decision level [START_REF] Manzini | Supply chain and network design, management and optimization: From facility location to vehicle routing[END_REF] In fact, during the last decades, the integration of the triple-bottom-line (TBL) dimension in classical Operations Management problems has attracted an increasing number of researchers and practitioners, making sustainability one of the most active supply chain management topics. This fact is reflected by the growing number of original papers addressing this issue like in [START_REF] Ansari | A state-of-art literature review reflecting 15 years of focus on sustainable supply chain management[END_REF][START_REF] Gupta | Sustainable supply chain management: Review and research opportunities[END_REF][START_REF] Rajeev | Evolution of sustainability in supply chain management: A literature review[END_REF][START_REF] Seuring | From a literature review to a conceptual framework for sustainable supply chain management[END_REF][START_REF] Touboulic | Theories in sustainable supply chain management: a structured literature review[END_REF] and also, by the increasing number of review papers aiming to synthesize the progress in the area [START_REF] Ansari | A state-of-art literature review reflecting 15 years of focus on sustainable supply chain management[END_REF][START_REF] Carter | Mapping the Path Forward for Sustainable Supply Chain Management: A Review of Reviews[END_REF][START_REF] Rajeev | Evolution of sustainability in supply chain management: A literature review[END_REF].

Sustainable supply Chain Network Design

During the last three decades, the problem of designing sustainable supply chains has become an issue of growing interest to the scientific community, which is reflected in the number of published articles related to the subject [START_REF] Eskandarpour | Sustainable supply chain network design: An optimization-oriented review[END_REF][START_REF] Moreno-Camacho | Sustainability metrics for real case applications of the supply chain network design problem: A systematic literature review[END_REF]. Classical operation research costdriven models were extended to consider environmental factors in objectives, constraints, or parameters, in relation with the involved decisions (i.e., facility location, transport mode selection, technology selection, among others), making ways to what is known as Green Supply Chain Network Design (GSCND) [START_REF] Eskandarpour | A large neighborhood search heuristic for supply chain network design[END_REF][START_REF] Xu | The Design of Green Supply Chains under Carbon Policies: A Literature Review of Quantitative Models[END_REF]. [START_REF] Eskandarpour | Sustainable supply chain network design: An optimization-oriented review[END_REF], present a comprehensive literature review, analyzing 87 papers, published from 1990 to 2014, addressing the design of sustainable supply chains, with particular emphasis on the optimization methods used to solve the problem. Noteworthy, about 70% of the reviewed papers were published after 2009. That review highlights the way in which environmental assessment has progressively gone from partial evaluation of environmental impacts from one or more operations in supply chain (i.e., manufacturing, inventory, transportation, etc.) to a more comprehensive methodologies like carbon footprint and life cycle assessment (LCA) and its inclusion in classical optimization techniques from the field of Operations Research. As stated by [START_REF] Blass | Same Supply Chain, Different Models: Integrating Perspectives from Life Cycle Assessment and Supply Chain Management[END_REF], there is a potential to build bridges between the industrial ecology and the Operation Management / Research communities, while the latter increasingly converge around sustainable supply chains.

On the other hand, previous reviews on sustainable supply chain design also mention how factors assessing the performance of the supply chain on the social dimension has been included in a less extent [START_REF] Bubicz | Incorporating social aspects in sustainable supply chains: Trends and future directions[END_REF][START_REF] Eskandarpour | Sustainable supply chain network design: An optimization-oriented review[END_REF][START_REF] Moreno-Camacho | Sustainability metrics for real case applications of the supply chain network design problem: A systematic literature review[END_REF]. Certainly, corporate social responsibility performance is one of the essential assessment challenges in the context of supply chain, however, it is occasionally misinterpreted. Sometimes, corporate social responsibility is linked with the fact of companies spending great amount of money in charity or other sort of philanthropic activities, but in accordance with [START_REF] Grant | Sustainable Logistics and Supply Chain Management: Principles and practices for sustainable operations and management[END_REF], this is not necessarily related. In fact [START_REF] Carroll | A Three-Dimensional Conceptual Model of Corporate Performance[END_REF], affirms that corporate social responsibility integrates four not mutually exclusive categories, namely, economic, legal, ethical, and discretionary responsibilities of business to society. These categories are useful to conceptualize the key issues in social performance. First, companies are called to be profitable as the basic economic unit in the society. Second, it is expected of companies to operate within the framework of legal requirements and regulations. The third category encompasses for additional ethical behaviors on companies, which are above law, but nevertheless are expected by the society. Finally, voluntary activities in which companies assume a role of helping society, which not imperative, nor legally imposed, nor generally expected in an ethical sense either.

From a quantitative point of view, the aforementioned presents a significant challenge to the evaluation of social performance in the supply chain context, in particular, at the long-term level where supply chain network decisions are framed. Although some economic and environmental criteria can be modeled as a cost function (e.g., carbon footprint emissions, production, and transportation costs, etc.), some environmental and social issues cannot be represented merely as a cost or flow function. Indeed, some crucial issues are qualitatively defined (e.g., public responsibility, respect of human rights, etc.) and may not be transformed as a quantitative function. Not surprisingly, the complexity of representing social conditions through numerical indicators, the lack of consensus on the accurate criteria for its evaluation, the lack of appropriate methods to measure social performance at supply chain level, and the scarcity of available data are the most relevant reasons for the late development of social assessment [START_REF] Bubicz | Incorporating social aspects in sustainable supply chains: Trends and future directions[END_REF][START_REF] Eriksson | Elements affecting social responsibility in supply chains[END_REF][START_REF] Popovic | Quantitative indicators for social sustainability assessment of supply chains[END_REF].

Nevertheless, there is an increasing concern of evaluating social impacts to harmonize practices ensuring social equity, ecosystems protection, and economic development as is reflected on recent publications [START_REF] Messmann | How to quantify social impacts in strategic supply chain optimization: State of the art[END_REF]. As the concern for developing and managing sustainable supply chains grows, indicators and assessment tools for social and environmental performance acquire great prominence. The following section presents an extensive review on sustainability indicators in strategic supply chain optimization.

Sustainability indicators for supply chain optimization

Considering the growing interest in involving environmental and social factors into analytical decisionmaking models at supply chain context, there are at least two elements worth to highlight. On the one hand, sustainability indicators depend heavily on available data and their possibility of being represented as an element of the model. On the other hand, sustainability assessment tools offer a methodology to quantify or assess these indicators. The current subsection presents a review of the most common sustainability indicators in supply chain network design formulations.

Sustainability has a measurable character in the supply chain context that matches the concepts of efficiency and effectiveness. It involves that sustainability is not just an external standard to satisfy requirements from stakeholders (effectivity). It must also consider internal standard accomplishment to ensure the profitability and continuity of business (efficiency). Sustainability addresses the balance of economic, environmental and social objectives. According to [START_REF] Taticchi | Performance measurement of sustainable supply chains[END_REF], the notion of balance in performance measurements of sustainability implies the necessity of using different metrics and perspectives that tied together provide a holistic view of the organization. Hence, the use of metrics constitutes an important element to determine efficiency and effectiveness and letting to compare between competing alternative solutions [START_REF] Dekker | Operations Research for green logistics -An overview of aspects, issues, contributions and challenges[END_REF][START_REF] Hervani | Performance measurement for green supply chain management[END_REF].

Additionally, the sustainability term presupposes a behavior that reaches a steady state wherein established parameters for each dimension of sustainability (i.e., economic, environmental, and social) can be kept in the long term (Kannegiesser & Günther, 2014). It is not by coincidence that academics have become increasingly interested in sustainability assessment regarding decisions at the strategic level of the supply chain. Indeed, these decisions have considerable impacts in the long-term, and define action boundaries in the tactical and operational decision levels [START_REF] Barbosa-Póvoa | Opportunities and challenges in sustainable supply chain: An operations research perspective[END_REF].

According to [START_REF] Stindt | How Transdisciplinarity Can Help to Improve Operations Research on Sustainable Supply Chains-A Transdisciplinary Modeling Framework[END_REF], assessing sustainability in the supply chain field requires multidisciplinary teams, as the approach extends beyond economic consideration to include ecological and social factors, which the management researchers are often unfamiliar with. In this sense transdisciplinary research is encouraged, however, the integration between SCM models and social and environmental sciences is weak, affecting the quality of the proposed models. The operations research (OR) methods commonly used to address problems in SCND can often be criticized for their shortcomings in fieldwork [START_REF] Stindt | How Transdisciplinarity Can Help to Improve Operations Research on Sustainable Supply Chains-A Transdisciplinary Modeling Framework[END_REF]. In some cases, the selection of the metrics is too generic and does not response to the challenges faced by the specific industry under study; in the economic, environmental, or social dimensions. This leads to a lack of holistic understanding and shortcomings in the abstraction and its consequent modeling of real-world problems [START_REF] Stindt | A generic planning approach for sustainable supply chain management -How to integrate concepts and methods to address the issues of sustainability[END_REF]. Hence, the usefulness of these works as support for decision making in real applications is often compromised.

Results presented in this section are part of the review paper published in [START_REF] Moreno-Camacho | Sustainability metrics for real case applications of the supply chain network design problem: A systematic literature review[END_REF].

The review was intended to respond to the following questions:

i. What are the common economic, environmental, and social criteria considered in applied cases of design or redesign of supply chain networks? ii.

What solution methods are employed to deal with the problem? iii.

What real cases are described in the scientific literature?

The work uses an existent framework proposed by Chardine-Baumann & Botta-Genoulaz (2014) to classify sustainability assessment indicators for supply chain network design. Figure 2.3 presents the model composed of fifteen sustainable fields, five fields for each dimension (i.e., economy, environment, and society), each of them is linked to one of the main challenges faces for companies to reach sustainability. A total of 113 papers were considered in the analysis and the results are presented below. From the review of the studies, it can be concluded that the evaluation of the economic dimension focuses primarily on the financial performance category. Although this dimension attends for several different fields, other fields such as reliability, responsiveness and flexibility has received little attention.

Three main indicators appear to be related to the economic dimension: minimization of total cost, maximization of profit (MP), and maximization of net present value (NPV). The last is common when the problem considers an evaluation over multiple time periods, while the first two appear in both multiple and single periods evaluation. This condition is not a minor detail as the sustainability may be not seen as a stationary assessment in one point of time but as a kept state over time.

In line with decisions in the design of the supply network, facility location, and transportation cost are the most common components of the cost. These cost drivers appear in 62% and 53% of the reviewed papers, respectively. Other drivers of the cost include production, purchasing and holding costs, with 41%, 37% y 26%, respectively. About 16% of the studies include fix and variable operational costs, while the cost caused by carbon emissions is present in about 12% of the works. Taxation over carbon emissions is one of the worldwide initiatives aiming at reducing GHG emissions in both developed and developing countries by encouraging the investment on cleaner technologies (Xu, Pokharel, et al., 2017). The most usual carbon policies include carbon cap, carbon emission tax and carbon cap and trade [START_REF] Jin | The impact of carbon policies on supply chain design and logistics of a major retailer[END_REF]. The carbon cap policy has not a direct affection over the cost since it determines a threshold over the number of allowable emissions to a company. Meanwhile, carbon tax emissions and carbon cap and trade, enact a relation of substitution between economic and environmental resources. Notably, from the 13 papers covering carbon cost, only [START_REF] Rezaee | Green supply chain network design with stochastic demand and carbon price[END_REF] state an existing relation; not necessarily linear, but positive between the green design of the chain and both carbon price and budget availability. This conclusion might open new ways in the design of effective policies for reducing emissions and consumption of natural resources.

Environmental indicators

Life cycle assessment (LCA) methodologies offer a complete approach to the evaluation of environmental impacts through the whole supply chain, however, sometimes due to methodological, technical, or informative barriers an LCA analysis is not possible or would be to costly. Indeed, most of the works opt for partial evaluation considering the more challenging activities in the supply chains.

An analysis of the assessment of environmental performance within the five fields listed in the used framework is presented below. The Environmental management field evaluates the impacts derived from the environmental certification owned by the company, in compliance with the environmental regulation within a specific sector, as well as the number of resources invested in environmental protection. The last one is readily convertible into a cost driver, while the others correspond to a qualitative measure, seldom included into the SCND problem, but broadly evaluated within the partner selection problem.

One of the most significant impacts caused by the company operations comes from the use of raw or recycled material, water and energy in the surrounding area, those factors are grouped in the use of resources field. For instance, Feitó-Cespón et al. ( 2017) consider the environmental impact of using waste material instead of virgin raw material in a plastic recycling supply chain.

Water consumption appears frequently (for example in [START_REF] Anvari | The facility location problem from the perspective of triple bottom line accounting of sustainability[END_REF] 2017). The last one highligthes the relationship with the adopted process technology.

Energy consumption from production process is also considered often as in [START_REF] Azadeh | Evolutionary multiobjective optimization of environmental indicators of integrated crude oil supply chain under uncertainty[END_REF], or from warehouses activities in [START_REF] Colicchia | Eco-efficient supply chain networks: Development of a design framework and application to a real case study[END_REF]. [START_REF] Miranda-Ackerman | A green supply chain network design framework for the processed food industry: Application to the orange juice agrofood cluster[END_REF] considers energy consumption depending of the selection of processing technology. [START_REF] Zhalechian | Sustainable design of a closed-loop location-routing-inventory supply chain network under mixed uncertainty[END_REF] consider the waste of energy derived of waiting time for vehicles to be unloaded at collection centers in a reverse supply chain. [START_REF] Accorsi | The land-network problem: Ecosystem carbon balance in planning sustainable agro-food supply chains[END_REF] address the design of an agri-food supply chain in which the total amount of energy used in transport and production would be smaller than the amount of energy produced by renewable sources such as solar fields or wind farms in an agri-food supply chain.

The pollution field has been broadly covered, especially for the air pollution sub-field. Although, there are multiple sources of contamination along the supply chain, our review shows that, most of the works focus on GHG emissions assessment at Scope 1 or Scope 2. As defined by the Greenhouse Gas (GHG) Protocol. Scope 1 embodies direct emissions from owned or controlled sources (e.g., company vehicles and company facilities). Scope 2 comprehends indirect emissions from the generation of purchased electricity, steam, heating, and cooling consumed by the company. Finally, Scope 3 includes all others indirect emissions that occur in the supply chain the company belongs to. Figure 2.5 presents a graphic view of the sources of emissions included at every scope.

Figure 2.5. GHG emissions scopes Source: Greenhouse Gas Protocol Hence, CO2 emissions from transportation activities and facilities operation are the more frequent sources, considered in real cases. This is not surprising, since transport sector, including the movement of people and goods produces around 20% of global energy-related CO2 emissions, approximately 80% of them originating from road transportation [START_REF] Sims | Transport[END_REF]. Contribution of CO2 emissions for transportation activities are generally expressed as a product of the distance and the emission factor of fuel consumption. More sophisticated methodologies to calculate CO2 emissions for transportation activities are possible but unconventional on the papers dealing with the SCND problem. [START_REF] Rajkumar | Automotive Closed Loop Supply Chain With Uncertainty[END_REF], calculate CO2 emissions as a function of the capacity in weight used of the truck transporting the product between the different echelons. Additionally, in (C. Chen et al., 2017), the authors include factors affecting the vehicle emissions depending on vehicle type and shape, road conditions and regional climate. A sensibility analysis let them conclude about the importance of road conditions over environmental impact what might result in a critical point for establishing sustainable supply chains in some developing countries suffering from lack of appropriate highways for both freight transportation and passenger transportation.

Operation of industrial facilities is the second most-common factor used to measure environmental impact in the supply chain design. In accordance with [START_REF] Sims | Transport[END_REF], facilities operation also contributes to about 28% of global energy-related GHG emissions and is therefore a significant factor. At industrial facilities, GHG direct emissions come mainly from production process involving combustion of fossil fuel for power or heat. GHG indirect emissions are the result of energy consumption of power industrial buildings and equipment. Emissions from industrial facilities deteriorate air quality with several polluting compounds. Several types of atmospheric pollutions can be observed, for example:

 Photochemical air pollution, for instance, is related to the emissions of different types of gas such as VOC or NOx, that interact with the oxygen of the air to produce ozone, which is a strongly reactive and it is the cause of several health issues, such as asthma.  The release of sulphuric or nitrous oxides may generate acid rains.  The release of CFC gases contributes to the erosion of the ozone layer.  The release of greenhouse gases (GHG) contributes to climate change, which is today one of the most studied issues of air pollution

According to [START_REF] Fischedick | Industry[END_REF] more than 80% of total emissions correspond to CO2, about 8% to methane, other compounds including hydrofluorocarbons, perfluorocarbons, nitrous oxide and Sulphur hexafluoride constitute the remaining approximate 10% percentage. Global warming potential values relatives to CO2 permit to convert emissions of different compounds into equivalent CO2 units (CO2 eq.) to standardize the unit of measure.

The most common factor to quantify the environmental impact of industrial facilities is direct emissions from manufacturing process. Some authors also consider emissions from others buildings such as warehouses, recollection centers, dismantling centers, and so on in [START_REF] Aalirezaei | Designing a sustainable recovery network for waste from electrical and electronic equipment using a genetic algorithm[END_REF][START_REF] Brandenburg | Low carbon supply chain configuration for a new product -A goal programming approach[END_REF][START_REF] Ghaderi | A multi-objective robust possibilistic programming approach to sustainable switchgrass-based bioethanol supply chain network design[END_REF][START_REF] Govindan | Bi-objective integrating sustainable order allocation and sustainable supply chain network strategic design with stochastic demand using a novel robust hybrid multi-objective metaheuristic[END_REF]Govindan, Jha, et al., 2016). Carbon footprint, as defined by [START_REF] Wiedmann | A Definition of Carbon Footprint[END_REF], as the total amount of carbon emissions that is directly and indirectly caused by an activity is less extended and addressed, among others by [START_REF] Accorsi | The land-network problem: Ecosystem carbon balance in planning sustainable agro-food supply chains[END_REF][START_REF] Azadeh | Evolutionary multiobjective optimization of environmental indicators of integrated crude oil supply chain under uncertainty[END_REF]. Furthermore, as an own feature of the SCND problem, some studies consider not just emissions at the operational phase but also the emission caused during the construction process or preoperational phase, air pollution as a result of construction of facilities is considered in [START_REF] Anvari | The facility location problem from the perspective of triple bottom line accounting of sustainability[END_REF] and [START_REF] Arampantzi | A new model for designing sustainable supply chain networks and its application to a global manufacturer[END_REF].

Pollutant emissions related to materials are studied in [START_REF] Zhou | The Impacts of Carbon Tariff on Green Supply Chain Design[END_REF]. In this work, a computer manufacturing company has the possibility to choose between different modules to assemble a piece of equipment. The purchase decision is supposed to be characterized not only by the difference in the cost of the different modules but also by the amount of emissions derived from the product during the assembly stage and during its useful life.

Pollution caused by raw materials acquisition or use of final products are less frequently studied (Kannegiesser et al., 2014). Additionally, since most of the studies focus on a single company rather than a holistic view of the sector, GHG emissions generated by suppliers is fewer considered. Figure 2.6 presents the number of studies considering GHG emissions using partial assessment.

Additionally, water pollution and land pollution are scarcely studied in real applications of the SCND problem. [START_REF] Anvari | The facility location problem from the perspective of triple bottom line accounting of sustainability[END_REF] consider this factor in relation with the waste generated during construction of the facilities, they consider a sensitive waste factor to the location due to a location with a higher population, and higher aquifers level are more sensitive to waste. [START_REF] Chávez | Towards a comprehensive model of a biofuel supply chain optimization from coffee crop residues[END_REF] evaluate the positive effect of using agricultural waste from coffee crops to produce biofuel avoiding dumping these wastes into the water sources. Besides, other types of pollution like noise, smells, visual pollution, vibrations, and radiations do not take part in the environmental impact assessment of the design of supply chains. Finally, no papers were found attending to the consideration in the Dangerousness field. Meanwhile, in the last field Natural environment, just two papers include considerations over promotion and protection of biodiversity. [START_REF] Accorsi | The land-network problem: Ecosystem carbon balance in planning sustainable agro-food supply chains[END_REF], consider the use of land in a rural region, including a reforestation activity. The authors calculate the number of hectares of land devoted to planting trees, in such a way that ensure a zero-carbon emissions operation in a food supply chain, emissions associated with cultivation and logistics activities must be equated to emissions captured by the forest. [START_REF] Izadikhah | A new preference voting method for sustainable location planning using geographic information system and data envelopment analysis[END_REF], consider a biodiversity factor, calculated like the loss of species caused by building a new facility in the candidate zone.

Social indicators

The current section presents the findings regarding the different categories in the social dimension . In the sub-field work conditions, employment is the most frequent social indicator used in at measuring social performance at supply chain level. The total number of jobs created is considered by most authors, with small adjustments. [START_REF] Miret | Design of bioethanol green supply chain: Comparison between first and second generation biomass concerning economic, environmental and social criteria[END_REF], evaluate the social benefit of the total number of created jobs. They use an approach to estimate not only the direct jobs created in the transformation echelon but also the indirect and induced jobs created through the whole set of activities in the life cycle of the product. [START_REF] Anvari | The facility location problem from the perspective of triple bottom line accounting of sustainability[END_REF], [START_REF] Arampantzi | A new model for designing sustainable supply chain networks and its application to a global manufacturer[END_REF], [START_REF] Ghaderi | A multi-objective robust possibilistic programming approach to sustainable switchgrass-based bioethanol supply chain network design[END_REF] Another factor considered in the working condition field is health and safety of employees. As an example, [START_REF] Ghaderi | A multi-objective robust possibilistic programming approach to sustainable switchgrass-based bioethanol supply chain network design[END_REF] uses the total number of lost days by year caused by injuries to establish an indicator for employee's health, the number of occurred injuries during a period time is related to the selection of technology at each facility. [START_REF] Aalirezaei | Designing a sustainable recovery network for waste from electrical and electronic equipment using a genetic algorithm[END_REF] addressing the design of a reverse supply chain for waste from electrical and electronic equipment, introduce a parameter quantifying the damage caused to workers at the collection centers, due to the exposition to hazardous substances. Other aspects related to working conditions as employee satisfaction and stability are addressed in [START_REF] Arampantzi | A new model for designing sustainable supply chain networks and its application to a global manufacturer[END_REF]. The authors study both idle time and dismissals to serve as indicators.

Suppliers

Regarding societal commitment, the main factor that is considered is wealth creation and social progress within host countries, by increasing their gross domestic product (GDP). In this case, regions with lower economic development have priority for the location of new facilities. This condition is considered in [START_REF] Anvari | The facility location problem from the perspective of triple bottom line accounting of sustainability[END_REF][START_REF] Arampantzi | A new model for designing sustainable supply chain networks and its application to a global manufacturer[END_REF]Babazadeh, Razmi, Rabbani, & Pishvaee, 2017;[START_REF] Ghaderi | A multi-objective robust possibilistic programming approach to sustainable switchgrass-based bioethanol supply chain network design[END_REF][START_REF] Mota | Supply chain design and planning accounting for the Triple Bottom Line[END_REF][START_REF] Varsei | Sustainable supply chain network design: A case of the wine industry in Australia[END_REF][START_REF] Zahiri | Toward an integrated sustainable-resilient supply chain: A pharmaceutical case study[END_REF][START_REF] Zhalechian | Sustainable design of a closed-loop location-routing-inventory supply chain network under mixed uncertainty[END_REF]. According to [START_REF] Anvari | The facility location problem from the perspective of triple bottom line accounting of sustainability[END_REF], this consideration promotes fair distribution of development through the regions and, along with creating jobs in regions with higher unemployment rates, helps reduce immigration and its potential consequences. However, location in less developed areas considerably affects environmental and economic objectives due to the increase in the distance between production and consumer sites, the lack of environmental and social regulation, and the scarcity of skilled workforce.

Regarding the same field, [START_REF] Anvari | The facility location problem from the perspective of triple bottom line accounting of sustainability[END_REF] introduce other conditions affecting community development such as security level, medical facility access, and educational level at facility location region. Security at the location is crucial for the operations of the company and the habitat of the employees. Besides, access to medical services and education offers workers and their families favorable conditions for settling in the area and provides the company with the opportunity to find skilled workers and deal with staff turnover.

The field customer issues groups together all the actions carried out by the company and the effects they have on the consumer. For instance, since some products may have health impacts on consumers, companies are responsible for providing safe products. That condition is considered by [START_REF] Ghaderi | A multi-objective robust possibilistic programming approach to sustainable switchgrass-based bioethanol supply chain network design[END_REF] and L. [START_REF] Zhu | Sustainable Logistics Network Modeling for Enterprise Supply Chain[END_REF]. The authors consider the number of hazardous products going out of the production line based on the production technology. Besides, in some works, demand satisfaction is used as an indicator of social performance because the deprivation of some products could impact the consumer. This condition is evaluated in [START_REF] Anvari | The facility location problem from the perspective of triple bottom line accounting of sustainability[END_REF], [START_REF] Ashfari | Facility location decisions within integrated forward/reverse logistics under uncertainty[END_REF][START_REF] Ashfari | Facility location decisions within integrated forward/reverse logistics under uncertainty[END_REF][START_REF] Feitó-Cespón | Redesign of a sustainable reverse supply chain under uncertainty: A case study[END_REF]. Y. [START_REF] Zhang | Robust Optimization on Regional WCOfor-Biodiesel Supply Chain under Supply and Demand Uncertainties[END_REF] use a similar approach in a reverse supply chain for recovering waste cooking oil in China. Authors argue that to satisfy the demand helps to reduce the illegal trade of edible oil in this country, representing a tremendous social benefit.

Inclusion of sustainability factors in the design of supply chains deals with the evaluation of new criteria and essentially it works with the existence of conflicting objectives. The academic literature presents several modeling approaches and solution techniques to deal with the evaluation of environmental and social criteria into the SCND. These models are usually based on classical location-allocation facilities models to which are added, either new objectives or additional constraints to address the assessment of performance of environmental and social dimensions. A description of these approaches is presented in the following section.

Sustainable supply chain design modeling approaches

From an Operations Research perspective, SCND comprises the definition of optimal location and capacity of the facilities at each level of the network, it also allows to define the flow of materials among facilities. The use of mathematical programming-based methodologies is widespread.

Single objective formulations

This type of formulation usually considers an economical objective and defines constraints to the fulfillment of the defined sustainability criteria. This approach enriches the conventional SCND model by adding constraints for the social and the environmental dimension. For instance, declaring a cap in the total amount of GHG emissions or defining a minimum number of created jobs. This approach keeps the focus on logistics operations in the supply chain, while integrating new concerns into the decision process [START_REF] Eskandarpour | Sustainable supply chain network design: An optimization-oriented review[END_REF].

Frequently, under this modeling approach, environmental impacts caused through the chain are monetized under a carbon-taxes schemes. Taxation over carbon emissions is one of the worldwide initiatives aiming at reducing GHG emissions in both developed and developing countries (Xu, Pokharel, et al., 2017). The most usual carbon policies include carbon cap, carbon emission tax and carbon cap and trade [START_REF] Jin | The impact of carbon policies on supply chain design and logistics of a major retailer[END_REF]. On the one hand, a carbon cap policy has not a direct impact over the cost since, it determines a threshold over the number of allowable emissions to a company. In terms of the model, it is expressed as an additional constraint. On the other hand, carbon tax emissions and carbon cap and trade schemes, enact a relation of substitution between economic and environmental resources. In this case the emission cost is an additional driven for the total cost.

As an example, [START_REF] Almansoori | Design of optimization model for a hydrogen supply chain under emission constraints -A case study of Germany[END_REF] address the design of a hydrogen supply chain network considering both carbon emission cap and carbon emission taxes as a strategy to promote CO2 emissions reductions. Xu, Elomri, et al. (2017) work in the design of a reverse supply chain for solid waste recycling considering a carbon emission cap. [START_REF] Accorsi | The land-network problem: Ecosystem carbon balance in planning sustainable agro-food supply chains[END_REF] propose a single objective model considering a zero-carbon supply chain for the design of a regional potato supply chain. The model ensures that total emission caused by crop and logistics activities in the food supply chain are offset by tree planting and its potential for carbon sequestration. [START_REF] Quddus | Sustainable network design for multi-purpose pellet processing depots under biomass supply uncertainty[END_REF] include a carbon trading mechanism that allow decision makers to sell or buy carbon credits while monitoring emissions from supply chain. D. [START_REF] Zhang | Green supply chain network design with economies of scale and environmental concerns[END_REF] and [START_REF] Zhou | The Impacts of Carbon Tariff on Green Supply Chain Design[END_REF] present an analysis on the structure of a supply chain considering different tariffs on carbon taxes. The authors conclude that carbon tax ratio influences the structure of the supply chain and the allocation of demand as well.

Multi-objective formulations

A second optimization strategy to deal with sustainability assessment in SCND is Multi-objective optimization (MOO). Under this approach, it is assumed the existence of multiple conflicting sustainability objectives. Generally, the model contains one objective for each evaluated dimension of sustainability. Broadly speaking, economic objectives consist of a summation of cost from strategical and tactical decisions. Environmental objectives quantify the environmental impact in the network; in some cases, it is expressed like sums of the equivalent CO2 emissions generated from production and transportation activities when a partial scope evaluation is considered. Other works using LCA-based approach consider the sum of environmental impacts through the entire product life cycle to construct an environmental objective function.

Additionally, since social assessment might involves several factors with different measurement units, objective functions for the social dimension are frequently constructed as a linear weighting of the deviation from optimal value of each factor assessed as in [START_REF] Anvari | The facility location problem from the perspective of triple bottom line accounting of sustainability[END_REF] and [START_REF] Zahiri | Toward an integrated sustainable-resilient supply chain: A pharmaceutical case study[END_REF]. As an example [START_REF] Zahiri | Toward an integrated sustainable-resilient supply chain: A pharmaceutical case study[END_REF] consider two social objectives in only one objective function. It evaluates total created job opportunities and economic development at the same time. The use of this sort of compound criteria might lead to overcompensation among the factors. The poor performance of one factor is masked by the outstanding performance of another factor.

Depending on the solution approach either a priori or a posteriori method can be utilized. Regarding a posteriori methods, both exact and heuristic methods are utilized to define the set of non-dominated solutions that represent the set of "optimal" candidate solutions [START_REF] Marler | Survey of multi-objective optimization methods for engineering[END_REF]. The most widely used generation methods remain the weighted metric method as in [START_REF] Afshari | Multi-objective optimisation of facility location decisions within integrated forward / reverse logistics under uncertainty[END_REF], C. Chen et al. ( 2017) [START_REF] Colicchia | Eco-efficient supply chain networks: Development of a design framework and application to a real case study[END_REF] and Govindan, Jha, et al. (2016) and the ε-constraint method as in [START_REF] Anvari | The facility location problem from the perspective of triple bottom line accounting of sustainability[END_REF], [START_REF] Arampantzi | A new model for designing sustainable supply chain networks and its application to a global manufacturer[END_REF][START_REF] Feitó-Cespón | Redesign of a sustainable reverse supply chain under uncertainty: A case study[END_REF] and [START_REF] Varsei | Sustainable supply chain network design: A case of the wine industry in Australia[END_REF].

Evolutionary algorithms for multi-objective optimization appears in [START_REF] Afshari | Multi-objective optimisation of facility location decisions within integrated forward / reverse logistics under uncertainty[END_REF], [START_REF] Azadeh | Evolutionary multiobjective optimization of environmental indicators of integrated crude oil supply chain under uncertainty[END_REF] and [START_REF] Miranda-Ackerman | A green supply chain network design framework for the processed food industry: Application to the orange juice agrofood cluster[END_REF]. Hence, the decision maker is provided with a set of equally optimal solutions to select from them the one what best suits.

Time to sustainability formulation

Finally, one of the most recently developed strategies to deal with sustainability assessment within the SCND context is the Time to sustainability (TTS) approach. It might be defined as a single objective formulation, however, unlike the previous formulation the main objective does not account for money but for time. In this regard the model accounts for the number of periods of time (e.g., years) until every sustainability indicator reaches an acceptable pre-defined value. This approach was firstly introduced in (Kannegiesser & Günther, 2014), where an application for the European automotive sector is presented (Kannegiesser et al., 2014).

TTS optimization strategy overcomes the drawback of multi-objective optimization models since the weighting of objectives is not required. It means that the decision maker is not faced with defining relative preferences of conflicting objectives. Furthermore, considering the time dimension confers to sustainability a dynamic character, based on the observation that in the long-term, conflicting objectives often reach an acceptable steady state due to technological advances and regulations of external conditions. Variants of the TTS approach are presented in [START_REF] Kannegiesser | The time-to-sustainability optimization strategy for sustainable supply network design[END_REF]. These new variants overperform the basic TTS approach previously mentioned in respect to the validity of results and the computational time. To the best of our knowledge, the TTS optimization strategy has been scarcely studied into the academic literature despite its advantages, originality, relevance and flexibility to deal with several different sustainability metrics in parallel.

Deterministic and non-deterministic considerations

In real scenarios of the supply chain, decisions are rarely made under certainty. Moreover, since SCND problem implies long-term decisions, there are multiples parameters that might change across the time.

Several works in the literature incorporate uncertainty into their modeling approach. We found demand to be the most common uncertain parameter considered 13 papers out of 77 address it. Five works consider uncertainty in supply: including papers considering uncertainty in harvest rate for biofuel conversion.

Uncertainty on recycled products rate as the number of units recovered from the market in a closed-loop supply chain scenario is addressed in four papers. Finally, other non-deterministic parameters included corresponding to production and transportation costs and facilities capacity. Table 2.1 presents a list of some recent works addressing sustainable supply chain design classified by modeling characteristics. [START_REF] Accorsi | The land-network problem: Ecosystem carbon balance in planning sustainable agro-food supply chains[END_REF][START_REF] Almansoori | Design of optimization model for a hydrogen supply chain under emission constraints -A case study of Germany[END_REF][START_REF] Babazadeh | Robust Optimization Method to Green Biomass-to-Bioenergy Systems under Deep Uncertainty[END_REF][START_REF] Clavijo Buritica | Designing a sustainable supply network by using mathematical programming: a case of fish industry[END_REF][START_REF] Costa | A decisional simulation-optimization framework for sustainable facility location of a biodiesel plant in Colombia[END_REF][START_REF] Duarte | Biofuel supply chain design from Coffee Cut Stem under environmental analysis[END_REF][START_REF] Galvez | Reverse logistics network design for a biogas plant: An approach based on MILP optimization and Analytical Hierarchical Process (AHP)[END_REF][START_REF] Izadikhah | A new preference voting method for sustainable location planning using geographic information system and data envelopment analysis[END_REF][START_REF] Mohd Idris | Spatial optimisation of oil palm biomass co-firing for emissions reduction in coal-fired power plant[END_REF]Varsei et al., 2017;[START_REF] Zhang | Green supply chain network design with economies of scale and environmental concerns[END_REF][START_REF] Zhou | The Impacts of Carbon Tariff on Green Supply Chain Design[END_REF][START_REF] Zohal | Developing an ant colony approach for green closed-loop supply chain network design: a case study in gold industry[END_REF] Eco + Soc (Babazadeh, Razmi, Rabbani, et al., 2017)

Stochastic

Eco + Env [START_REF] Ahn | Economic optimization of integrated network for utility supply and carbon dioxide mitigation with multi-site and multi-period demand uncertainties[END_REF][START_REF] Fahimnia | Greening versus resilience: A supply chain design perspective[END_REF][START_REF] Ghelichi | A stochastic programming approach toward optimal design and planning of an integrated green biodiesel supply chain network under uncertainty: A case study[END_REF][START_REF] Quddus | Sustainable network design for multi-purpose pellet processing depots under biomass supply uncertainty[END_REF][START_REF] Rezaee | Green supply chain network design with stochastic demand and carbon price[END_REF][START_REF] Saif | Cold supply chain design with environmental considerations: A simulation-optimization approach[END_REF]Xu, Elomri, et al., 2017)

Multiple objectives

Deterministic

Eco + Env (Cambero et al., 2016;C. Chen et al., 2017C. Chen et al., , 2018;;[START_REF] Chen | A particle swarm approach for optimizing a multi-stage closed loop supply chain for the solar cell industry[END_REF][START_REF] Colicchia | Eco-efficient supply chain networks: Development of a design framework and application to a real case study[END_REF][START_REF] Domínguez-García | Optimal planning for the supply chain of biofuels for aviation in Mexico[END_REF][START_REF] Fang | Design of green cold chain networks for imported fresh agri-products in belt and road development[END_REF][START_REF] Gao | Shale Gas Supply Chain Design and Operations toward Better Economic and Life Cycle Environmental Performance: MINLP Model and Global Optimization Algorithm[END_REF]Govindan, Garg, et al., 2016;[START_REF] Kuo | Design and Analysis of Supply Chain Networks with Low Carbon Emissions[END_REF][START_REF] Miranda-Ackerman | A green supply chain network design framework for the processed food industry: Application to the orange juice agrofood cluster[END_REF][START_REF] Murillo-Alvarado | Multi-objective optimization of the supply chain of biofuels from residues of the tequila industry in Mexico[END_REF][START_REF] Nodooshan | Environmental and Economic Optimization of Algal Biofuel Supply Chain with Multiple Technological Pathways[END_REF][START_REF] Palacio | A decision-making model to design a sustainable container depot logistic network: the case of the Port of Valencia[END_REF][START_REF] Tang | The design of a sustainable location-routing-inventory model considering consumer environmental behavior[END_REF][START_REF] Urata | Global supply chain network design and Asian analysis with material-based carbon emissions and tax[END_REF] Eco + Env + Soc [START_REF] Aalirezaei | Designing a sustainable recovery network for waste from electrical and electronic equipment using a genetic algorithm[END_REF][START_REF] Anvari | The facility location problem from the perspective of triple bottom line accounting of sustainability[END_REF][START_REF] Arampantzi | A new model for designing sustainable supply chain networks and its application to a global manufacturer[END_REF][START_REF] Awad-Nunez | How Should the Sustainability of the Location of Dry Ports Be Measured? a Proposed Methodology Using Bayesian Networks and Multi-Criteria Decision Analysis[END_REF]Cambero & Sowlati, 2016;[START_REF] Chávez | Towards a comprehensive model of a biofuel supply chain optimization from coffee crop residues[END_REF]Govindan, Jha, et al., 2016;[START_REF] Jafari | Sustainable supply chain design with water environmental impacts and justice-oriented employment considerations: A case study in textile industry[END_REF]X Jiang et al., 2018;[START_REF] Kesharwani | Biofuel supply chain optimal design considering economic, environmental, and societal aspects towards sustainability[END_REF][START_REF] Miret | Design of bioethanol green supply chain: Comparison between first and second generation biomass concerning economic, environmental and social criteria[END_REF][START_REF] Mota | Supply chain design and planning accounting for the Triple Bottom Line[END_REF][START_REF] Rabbani | Developing a sustainable supply chain optimization model for switchgrass-based bioenergy production: A case study[END_REF][START_REF] Roni | A multi-objective, hub-and-spoke model to design and manage biofuel supply chains[END_REF][START_REF] Varsei | Sustainable supply chain network design: A case of the wine industry in Australia[END_REF][START_REF] Zhu | Sustainable Logistics Network Modeling for Enterprise Supply Chain[END_REF] Stochastic Eco + Env [START_REF] Asadi | A bi-objective stochastic location-inventoryrouting model for microalgae-based biofuel supply chain[END_REF][START_REF] Azadeh | Evolutionary multiobjective optimization of environmental indicators of integrated crude oil supply chain under uncertainty[END_REF][START_REF] Brandenburg | Low carbon supply chain configuration for a new product -A goal programming approach[END_REF][START_REF] Ebrahimi | A stochastic multi-objective location-allocation-routing problem for tire supply chain considering sustainability aspects and quantity discounts[END_REF][START_REF] Fahimnia | Marrying supply chain sustainability and resilience: A match made in heaven[END_REF][START_REF] Fazli-Khalaf | A robust fuzzy stochastic programming model for the design of a reliable green closed-loop supply chain network[END_REF][START_REF] Gargalo | Optimal Design and Planning of Glycerol-Based Biorefinery Supply Chains under Uncertainty[END_REF][START_REF] Govindan | Bi-objective integrating sustainable order allocation and sustainable supply chain network strategic design with stochastic demand using a novel robust hybrid multi-objective metaheuristic[END_REF][START_REF] Khorasani | The development of a green supply chain dual-objective facility by considering different levels of uncertainty[END_REF][START_REF] Rahmani Ahranjani | Closed loop supply chain network design for the paper industry: A multi-objective stochastic robust approach[END_REF][START_REF] Rajkumar | Automotive Closed Loop Supply Chain With Uncertainty[END_REF][START_REF] Tosarkani | A possibilistic solution to configure a battery closed-loop supply chain: Multi-objective approach[END_REF][START_REF] Yılmaz Balaman | Network design and technology management for waste to energy production: An integrated optimization framework under the principles of circular economy[END_REF][START_REF] Zeballos | Integrating decisions of product and closed-loop supply chain design under uncertain return flows[END_REF] Eco + Soc [START_REF] Afshari | Multi-objective optimisation of facility location decisions within integrated forward / reverse logistics under uncertainty[END_REF] Eco + Env + Soc [START_REF] Fattahi | A multi-stage stochastic program for the sustainable design of biofuel supply chain networks under biomass supply uncertainty and disruption risk: A real-life case study[END_REF][START_REF] Feitó-Cespón | Redesign of a sustainable reverse supply chain under uncertainty: A case study[END_REF][START_REF] Ghaderi | A multi-objective robust possibilistic programming approach to sustainable switchgrass-based bioethanol supply chain network design[END_REF][START_REF] Jabbarzadeh | Resilient and sustainable supply chain design: sustainability analysis under disruption risks[END_REF]Mota, Gomes, et al., 2018;[START_REF] Mousavi Ahranjani | Hybrid Multiobjective Robust Possibilistic Programming Approach to a Sustainable Bioethanol Supply Chain Network Design[END_REF][START_REF] Osmani | Multi-period stochastic optimization of a sustainable multi-feedstock second generation bioethanol supply chain -A logistic case study in Midwestern United States[END_REF][START_REF] Zahiri | Toward an integrated sustainable-resilient supply chain: A pharmaceutical case study[END_REF][START_REF] Zhalechian | Sustainable design of a closed-loop location-routing-inventory supply chain network under mixed uncertainty[END_REF][START_REF] Zhang | Robust Optimization on Regional WCOfor-Biodiesel Supply Chain under Supply and Demand Uncertainties[END_REF] Eco (Economic criteria), Env (Environmental criteria), Soc (Social criteria)

Applications

The current section presents an analysis regarding the origin and the industrial context of the studies in the review. The goal of the section is to classify and discuss the published works from 2015 to 2018 according to their application area or economic sector and the continent where the case study took place. The classification per country has been intentionally divided into OECD and non-OECD countries, since OECD countries promote the adoption of sustainable energy policies, economic growth, prosperity, and sustainable development. The classification aims to identify a relation between these national policies and the study on sustainability at supply chain level.

According to the U.S. Mission to the OECD, the 37 countries belonging to the organization account for near to 63% of the world gross domestic product (GDP), more than 75% of global trade, are home of about 20% of the population of the world and represent more than half of global energy consumption (U.S Mission, n.a). In 1990, emissions of CO2 from OECD countries represented more than 50% of global emissions, but because of the increasing global concern about environmental protection, these economies have made efforts to control and reduce the number of emissions from their industrial activities and nowadays their emissions represent about 38% percent of global emissions of CO2. However, as mentioned by [START_REF] Wiedmann | Environmental and social footprints of international trade[END_REF], this number, rather than a better environmental performance, might represent a burden shift from developed countries to developing ones. This situation is partially evidenced by the high number of cases addressing sustainable supply chains in developing economies in non-OECD countries as shown in Globalization has brought significant changes in supply chains networks, leading to geographical separation of production and consumption zones [START_REF] Wiedmann | Environmental and social footprints of international trade[END_REF]. Over the last decades, an increasing offshoring strategy has taken place among manufacturing companies; low labor costs are often the primary reason for companies to relocate their operations, considerations like lesser environmental taxes and the advantages of economies of scale in high volume production result being sensible factors for companies to move their operations abroad. The industrialization process of these regions results in a change of the scale of environmental and social impacts.

In the 1990's, China was the preferred destination to relocate operations from companies, the movement to other countries in South Asia, Africa, and Latin America took place after (Xuemei Jiang & Green, 2017). Figure 2.7. Number of studies per continent shows that about 60% of the total studies addressing sustainability in the SCND problem are cases from Asia, being Iran, China, and India the countries with the highest contributions. The rising concern about sustainable development in China and India is influenced by the accelerated growth in both production and consumption emissions because of the industrialization process. In 2017 while on the one hand some of the OECD members countries experienced decreases in their total amount of energy-related CO2 emissions, including the United States, the United Kingdom, Japan, and Mexico, on the other hand, Asian economies accounted for two-thirds of the global increase in carbon emissions, with China and India being the countries with the most significant growth (IEA, 2017).

As pointed out by (Babazadeh, Razmi, Pishvaee, et al., 2017) the high number of applied cases in Iran is due to the national concern for fuel production and its consequences for environment and society. Iran has an abundant source of fossil fuels and is one of the biggest exporters of crude oil around the world. However, due to the emissions caused by extraction and processing, some cities deal with serious issues having negative impacts on environmental and socially unsustainable development. Air quality causes affectations such as skin and respiratory diseases, acid rain, and unacceptable living conditions in these cities. For this reason, state entities have increased budgets for the promotion of alternatives biofuels, which has yielded to new research in biomass supply chain design, which apparently has contributed with the mentioned results.

Surprisingly, from the review, no study cases addressing sustainable supply chain design were found in African countries. [START_REF] Makan | Sustainable supply chain initiatives in reducing greenhouse gas emission within the road freight industry[END_REF] address the implementation of sustainable transport management practices for South African road freight transport. The work identifies that the main drivers to the adoption of sustainable activities include pressure from consumers and brand protection, pressure from top management and cost saving and revenue. Additionally, they point out some of the main barriers to its adoption that involve lack of government support, lack of understanding of the cost and insufficient manpower. Similar conclusions are yielded by [START_REF] Agyemang | Evaluating barriers to green supply chain redesign and implementation of related practices in the West Africa cashew industry[END_REF] who also mention initial implementation cost of green practices, difficulties to assess environmental sustainability performance, and lack of integrated management information and traceability systems as a barrier to the redesign of green supply chains mainly in West African countries.

Regarding the sector of application, manufacturing of electronic components and production of energy from biomass are the most represented sectors applying sustainability criteria in the SCND and partner selection decision. Notably, most of the cases studied focus on the bioenergy sector, which links the agricultural and the industrial sectors seeking for partially replacing of fossil fuels for more sustainable energy sources. However, most of the studies focus on generic environmental impacts coming from the distribution process and facilities location, but factors in both, environmental and social dimensions in the agricultural sector are scarcely involved into the decision-making process. Indeed, [START_REF] Grant | Sustainable Logistics and Supply Chain Management: Principles and practices for sustainable operations and management[END_REF], stated that, in the literature, there are numerous studies developed in manufacturing industry cases, while the agricultural sector has received less attention, despite the known social characteristics of its participants in the first tier (i.e., farmers) and the representative contribution that it sectors made to the total GHG emissions at global level.

As far as the electronic component market is concerned, the treatment or disposal of electronic components at the end of life is one of the most significant threats affecting its sustainable development. The European directive on waste electrical and electronic equipment (WEEE Directive) and the Restriction of Use of Certain Hazardous Substances (RoHS Directive) have been promoting the creation of schemes that involve safe and responsible collection, recovery and recycling procedures for all types of electronic waste. Studies addressing sustainability in this sector often used an approach of closed loop supply chain. The total environmental impact from raw materials, assembly, and production process, recovery and disposal are evaluated, usually, through quantification of CO2 equivalent emissions, or directly by the calculation of produced waste [START_REF] Anvari | The facility location problem from the perspective of triple bottom line accounting of sustainability[END_REF].

The automotive and fashion sectors have gained increasing interest respect to the results in [START_REF] Eskandarpour | Sustainable supply chain network design: An optimization-oriented review[END_REF]. The textile industry is a high water consumption sector [START_REF] Jafari | Sustainable supply chain design with water environmental impacts and justice-oriented employment considerations: A case study in textile industry[END_REF] and energy intensive [START_REF] Fahimnia | Marrying supply chain sustainability and resilience: A match made in heaven[END_REF], hence, those criteria are usually evaluated in this context. Finally, sector such as construction, information, and communication technology, and e-commerce present a low frequency of applied cases, although the sectors are getting increasing attention from media and civil society. Table 2.2 presents a summary of the classification of studies by sector. As displayed in Table 2.2 agricultural supply chains have been received little attention, despite of the notorious convergence of sustainability issues in the sector. For instance, it is well known that the advancement of agri-food industry deals with insurance viability and competitiveness while promoting good environmental practices and improve livelihood and economic conditions in rural areas. The next section is devoted to explaining the characteristics of agri-food supply chains and its relationship with sustainable development as part of the description of the study subject of this work.

Sustainability in Agri-food supply chains

Broadly speaking, agricultural industry comprises a width set of procedures and its related services, wherein natural resources are used to produce commodities such as food, fiber, fuels, and forest products, among others. Specifically, agri-food supply chains comprise a series of activities from production to distribution to bring farm products from farm to market [START_REF] Tsolakis | Agrifood supply chain management: A comprehensive hierarchical decision-making framework and a critical taxonomy[END_REF]. According the characteristics of the product these can be classified in supply chains for fresh agricultural products or supply chains for processed food products [START_REF] Naik | Challenges of creating sustainable agri-retail supply chains[END_REF]. According to [START_REF] Tsolakis | Agrifood supply chain management: A comprehensive hierarchical decision-making framework and a critical taxonomy[END_REF], agri-food supply chains are differentiated from other types of chains, due to the short life-cycle of goods, the seasonality in harvesting and production operations, the high product differentiation, the specific requirements in transportation, storage conditions and material recycling, the need to comply local and international legislation and regulations regarding food safety and public health, as well as environmental conditions.

In many countries, especially in developing countries, agri-food sector plays an essential role in the economy by being a significant contributor to GDP [START_REF] Gebresenbet | Logistics and Supply Chains in Agriculture and Food[END_REF] and it constitutes an essential agent in the economic, social and environmentally sustainable development of rural communities [START_REF] Naik | Challenges of creating sustainable agri-retail supply chains[END_REF]. According to the World Bank, this sector accounted for almost one-third of the global GDP in 2014. Moreover, due to population growth, advances in transport, information and communication technology, the agricultural sector has an annual growth rate of over 6% during the last decade, and its production will be twofold by 2050 [START_REF] Fao | Climate Change and The Global Dairy Cattle sector -The role of the dairy sector in a low-carbon future[END_REF]. The sector is especially important in Latin America and the Caribbean region where it represents the 14.1% of total generated employees in the region in 2018 (OECD/FAO, 2019), meanwhile in the European Union it accounted about 4.4% of total employment by 2017 (Eurostat, 2019).

Despite the economic growth of agri-food sector in the last years, rural areas, where it takes place, still tending to lag as regards in social and economic conditions. For instance, according to the European Comission (2007), incomes in rural areas is near 20% lower than in urban areas, and rural areas present higher unemployment rates. Agri-food sector also plays a significant role in the environment. Agriculture, forestry, and land-use change that account for 25% of greenhouse gas emissions. Sustainability in the food industry is an issue receiving increasing attention in the last years since growing population generates an enormous pressure in food supply [START_REF] Rohmer | Sustainable supply chain design in the food system with dietary considerations: A multi-objective analysis[END_REF]. The current consumption behavior affects agroecological resources, food security, and health, representing a critical issue for both consumers and producers [START_REF] Naik | Challenges of creating sustainable agri-retail supply chains[END_REF].

There are unique characteristics of agri-food supply chains affecting sustainability such as soil use change, water consumption, effects on the phosphorus and nitrogen cycles, waste disposal, social development, among others, that become relevant factors within the configuration of the network. For example, in order to reduce the wastes generated along the agri-food supply chain, as an indirect approach to address the environmental impact, (Caicedo Solano, García Llinás, & Montoya-Torres, 2020) proposed an innovative framework to couple Lean Thinking principles with Operations Research techniques. This framework was later validated by (Caicedo Solano, García Llinás, Montoya-Torres, et al., 2020). Moreover, one of the significant social issues affecting sustainability in the sector, is the practical exclusion of primary suppliers in the chain. Due to the scarcity of resources and limited access to information, smallholders might be unable to adopt sustainable practices. The situation is even worst in developing countries where the lack of access to technology threatens the productivity and competitivity of small farmers.

The issue has been recently addressed by some authors. For instance [START_REF] Accorsi | The land-network problem: Ecosystem carbon balance in planning sustainable agro-food supply chains[END_REF] developed a linear programming model to the design of a zero-emission supply chain with an application in the potato farming context. The model considers a land-use assessment for the location of crops, processing facilities, warehouses, forests, and renewable energy production fields. Overall emissions associated with crops and logistics activities are compensated by the planting of forests and the use of renewable energies. [START_REF] Clavijo Buritica | Designing a sustainable supply network by using mathematical programming: a case of fish industry[END_REF] propose an optimization model for the design of the supply network of the fish industry. The authors present a single objective model including a penalty cost over the production of fat waters, and organic solid waste at fish farms. Miranda-Ackerman, Azzaro-Pantel, and Aguilar-Lasserre (2017) present a non-linear multi-objective model for the green supply chain network design of orange juice. The environmental objective calculates the CO2 equivalent emissions generated by the orchard production, pasteurization process, bottling, and transportation activities. The model considers four agricultural practices according to the intensity of the use of agrochemicals, as well as a set of different processing and bottling technologies, which differ in the associated environmental impacts. The authors present a genetic algorithm and a multicriteria decision-making tool to solve the model. [START_REF] Fang | Design of green cold chain networks for imported fresh agri-products in belt and road development[END_REF], address the design of a cold supply chain network for transportation of fresh products to China from ports to retailers. The environmental objective aims to minimize the amount of CO2e emissions from distribution centers operations and freight transportations activities, while to the economic pillar considers minimization of total costs.

Conclusions

This chapter presented a review of the academic literature addressing sustainability and its link with supply chain network design. The review presented a particular focus on metrics and modelling approaches. Moreover, a classification regarding sectors and countries of application is done. The review highlighted how researchers in the supply chain management field have paid more attention to economic and environmental criteria, than to social criteria. However, there is an increasing interest on dealing with the three dimensions of sustainability with fairness, therefore, in the incremental inclusion of criteria, social dimension has becoming a relevant topic. The design of the whole supply chain network is a critical decision in supply chain management. For example, decisions regarding the number, location, and capacity of facilities, the selection of suppliers and transportation modes, the allocation of demand, etc. have a strategic impact on economic, as well as in environmental and social performance.

In this regard, the economic dimension is still mainly represented by criteria in the financial performance field. Although some authors highlight the dynamical approach of sustainability and the need of inversion in the long-term to reach steady state in sustainable development, the Net present value (NPV) objective have been used in a lesser extent [START_REF] Barbosa-Póvoa | Opportunities and challenges in sustainable supply chain: An operations research perspective[END_REF][START_REF] Kannegiesser | The time-to-sustainability optimization strategy for sustainable supply network design[END_REF]. Opportunities exist to propose solution methodologies evaluating sustainability in the long term and its impacts on monetary flow, as investment is required to reach sustainable development.

Regarding the environmental dimension, air pollution remains the most common criterion at assessing environmental impacts. Since the energy sector and the transport sector are greatest contributors to GHG emissions in developing economies, most of the studies addressing supply chain network design focus on the partial evaluation of direct emissions coming from operation facilities and transportation activities, even in studies involving agricultural activities. This consideration might be reevaluated at assessing agricultural supply chains in which the greater contribution to environmental impacts is caused by production activities at farms.

Regarding the sector of application, several advances have been made in bioenergy and electronic component sectors, to assess environmental and social performance at the strategic level of supply chain planning, mostly because of regulatory framework in these sectors. There are multiple opportunities to research on agricultural applications, they start to gain an essential place in the literature, considering the period of study from 2015 to 2018. Since, different crops required different growing times, different level of water, different harvesting techniques, and different consideration of distribution also, as in the case of the cold chain. Besides, there are valuable opportunities for further research in the agricultural and food, automotive, industrial and textile sectors due to their own characteristics of high-water consumption and labor-intensive activities. It is even more crucial because with the globalization, environmental and social footprint spread out affecting, mainly, population of developing countries.

Finally, we can mention that lack of comprehensive supply chain design criteria might drives into partial solution with low impacts on supply chain sustainability. Therefore, a holistic perspective of supply chain is required to assess sustainability at supply chain level. In this regard, it is required to work in at least three paths. First, the definition of suitable indicators for the three dimensions of sustainability, ensuring the availability of data to measure them. Second, the definition of sustainability objectives to compare performance from different configurations and desirable states in the future. Last but not least, the construction of suitable models to optimize the multi-dimensional performance of sustainable supply chains [START_REF] Beske-Janssen | 20 Years of Performance Measurement in Sustainable Supply Chain Management -What Has Been Achieved? Supply Chain Management[END_REF]. The following chapters will be devoted to present different approaches to deal with sustainability issues for supply chain design from a modeling perspective.

Literature review

Although the definition of sustainable development and sustainability involves several aspects, evidenced by the multidisciplinarity of concepts included in the sustainable development goals (SDG's) (UN General Assembly & United Nations, 2015), sometimes, in the context of supply chain design decisions, at managerial level, this complexity is reduced to the evaluation of a single objective. As stated by [START_REF] Eskandarpour | Sustainable supply chain network design: An optimization-oriented review[END_REF] this approach keeps the focus on logistics operations, while integrate new features into decision making process.

As far as modeling techniques are concerned, the use of multicriteria evaluation techniques is widespread to the selection of suppliers as well as to the definition of potential locations that meet a selected set of criteria that respond mostly to environmental requirements. For instance, Galvez, Rakotondranaivo, Morel, former is usually measured through quantification of GHG emissions as a tacit agreement on its relationship with climate change. While to the social dimension, there is no complete agreement in what must be measured, however, most of the factors are related with working conditions, particularly, employment and health and safety [START_REF] Moreno-Camacho | Sustainability metrics for real case applications of the supply chain network design problem: A systematic literature review[END_REF]. In this regard, two different approaches are utilized in the related literature. On the one hand the use of environmental and social constraints, establishing upper or lower bounds to the key indicators within each dimension as appropriate. For example, Xu et al., (2017) deal with the design of a multi-national reverse supply chain to collect waste, considering emissions through the chain regarding the flows of solid waste products. To solve the problem a MILP robust technique is employed considering a cap on the number of emissions. Multiple values for the cap are tested in separate computation experiments. Results show higher values on the emission cap are related with lower total costs and slight changes on network structure. Mainly, lower values on cap emissions promotes performance of inner local activities discouraging international transport of waste.

On the other hand, a second approach to consider sustainability criteria within optimization models is related to monetarization of ecological impacts. This assumption of interchangeability among economical and natural resources is, according to Feitó-Cespón, Sarache, Piedra-Jimenez, & Cespón-Castro ( 2017), a branch of neoclassical environmental economics, which grounds that natural resources can be utilized and replaced with no limits as long as it provides human society with a wide array of functions and services.

The idea of weak sustainability has been discussed widely within the scientific community, debating the relationship between well-being and nature, and the compensability through monetary values. For more on this regard the interested reader might find useful the work of [START_REF] Ang | Beyond the Environmentalist's Paradox and the Debate on Weak versus Strong Sustainability[END_REF][START_REF] Biely | The idea of weak sustainability is illegitimate[END_REF][START_REF] Davies | Appraising Weak and Strong Sustainability: Searching for a Middle Ground[END_REF]. Here the review is limited to the description of the approach in the sustainable supply chain field rather than state a position on the issue.

For instance, Clavijo Buritica, Escobar, & Triana Sánchez (2017), address the problem of designing a supply chain to the fish industry. The authors consider an economic objective which include monetary penalties for the yield of surplus waste at fish farms and fish production centers, since waste discharge might pollute natural water sources. Other authors work on supply chain design under carbon emission policies, which involve penalties on GHG emissions. [START_REF] Duarte | Biofuel supply chain design from Coffee Cut Stem under environmental analysis[END_REF] propose a single objective model to the design of a biodiesel supply chain considering a cost over the undesirable ecological effects caused by CO2 eq. emissions at biomass growth and pre-treatment activities, biofuel processing and material transportation through different levels. Three scenarios are evaluated considering different CO2 emission cost. As expected, higher CO2 prices are related with lower economic benefits. Moreover, with the data associated to the case study evaluated, variation in CO2 prices does not end up modifying supply chain network structure. For instance, Zhou, Gong, Huang, & Peters (2017) consider a global supply chain in which carbon tariffs are imposed over products coming from countries with no carbon regulations to regulated countries. According to the results, higher carbon tariffs instead of motivating appropriation of cleaner technologies in non-regulated countries end up discouraging exports to countries where carbon tariffs are imposed. Interestingly, non-regulated countries are encouraged to adopt cleaner technologies when local production in regulated countries is not enough to meet the internal demand. [START_REF] Almansoori | Design of optimization model for a hydrogen supply chain under emission constraints -A case study of Germany[END_REF] address the problem of designing a network to the supply of hydrogen under emission constraints. The authors evaluate carbon cap as well as carbon tax policies separately, while consider CO2 emissions coming from hydrogen plants and hydrogen distribution activities. The authors claim that regarding the structure of the supply chain the effect of carbon tax is equivalent to the implementation of a carbon target, although allocation of demand may have slight variations.

That said, the aim of the effort on this first chapter is to analyze how does environmental and social criteria affect the structure of the supply chain. Putting it differently, which is the impact of considering environmental and social key indicators in the location of facilities within classical optimization techniques for SCND. Therefore, the current chapter present a driven dimension analysis to the definition of a supply chain network, key indicators are selected in the three categories of sustainability and then three single objectives problems are solved to compare the yielded results.

Problem statement

This chapter addresses with the design of a supply chain when the decision concerning selection of suppliers, allocation of manufacturing and distribution facilities and transportation mode selection are guided considering different criteria from economic, environmental, and social dimensions, separately. The supply chain is composed of suppliers, manufacturers, warehouses, and retailers.

Formally speaking, we consider a forward supply chain, where a set of suppliers 𝑆 with endless capacity, deliver raw material to a set of production facilities or manufacturers 𝑀 with fixed and known capacity, who are the producers. Manufactured goods are delivered to a set of capacitated warehouses 𝐷 who meets a set of demand points or retailers 𝑅. Additionally, we consider the possibility to choose among a set of automation technologies 𝑇 in each one of the actives production facilities. Finally, to transport final goods from warehouse to retailers. We consider the possibility of use both, a conventional fuel vehicles fleet and electrical vehicles fleet. We consider each unit moving from a node to another one, incurring thus in a unitary transportation cost and generate an amount of CO2 emissions during this trajectory. Each active manufacturer might operate equipped with a chosen technology, which is related with the number of jobs offered at the facility. Moreover, technology level decision has an impact on the environmental dimension due to by-products and related CO2 emissions from production process. It is assumed that high automation levels are related with lower levels of greenhouse gas emissions due use energy efficiency, operational efficiency enhancement, and reduction of processing waste. However, it is also related to lower hand-work demand what causes low job offers and low impact in social development.

Regarding the warehouses, we consider handling product within warehouses as a source of CO2 emissions, mainly derived from energy consumption during its transit through facilities. Besides, it is considered selection of a supplier causes a positive social impact due to the economical activation in the region. To this purpose each supplier is associated with a social sustainability factor 𝜑 𝑠 representing social features and its impacts in equity, population, health among others as is proposed in [START_REF] Hutchins | An exploration of measures of social sustainability and their application to supply chain decisions[END_REF].

In this sense, supplier in less developed regions get higher 𝜑 𝑠 since labor offering and economic involvement of this region are expected to represent higher benefits. Finally, there is a decision regarding the type fleet to use in the distribution of products from warehouses to retailers. The use of an electrical fleet has a reduction on the emissions caused by transporting but implies a greater cost than the use of conventional fuel vehicles.

The evaluated features have impacts into each one of the three dimensions of sustainability deemed. Hence, the definition of a network structure lead by each one of the evaluated dimensions might derive in several differences, since there are expected trade-offs between the key indicators. For instance, economic performance is negatively impacted by the number of suppliers and the use of electric vehicle fleet to final distribution. However, these conditions improve social and environmental performance, respectively. On the other hand, environmental performance is negatively impacted when a high number of suppliers is considered, due to spread transportation activities. The number of production facilities and technology decisions have opposite effects, regarding social and environmental dimension, and clearly these decision affect economic performance. Lastly, although the number of warehouses in operation and the use of electric fleet has non evaluated contribution to social performance it affects environmental and economic performance.

Mathematical model

The current section presents the proposed Mixed-Integer Linear Programming (MILP) model to deal with the problem described above. Definition of sets, variables, parameters, constraints, and the different objective functions to be evaluated on the mathematical are as follows:

Sets

Constraints

Then, the classical equations to ensure meet demand, capacity limitation and flow equilibrium in the supply chain network are presented.

Capacity facility constraint

∑ 𝑥 𝑠𝑚 ≤ 𝐺 * 𝜆 𝑠 𝑚 ∀ 𝑠 (1) ∑ 𝑥 𝑠𝑚 ≥ 𝑚𝑠𝑢𝑝 𝑠 * 𝜆 𝑠 𝑚 ∀ 𝑠 (2) ∑ 𝑥 𝑠𝑚 ≥ ∑ 𝛿 𝑚𝑡 𝑡 𝑠 ∀ 𝑚 (3) ∑ 𝑦 𝑚𝑡𝑑 ≤ 𝑐𝑎 𝑚𝑡 * 𝛿 𝑚𝑡 𝑑 ∀ 𝑚, 𝑡 (4)
∑ 𝑦 𝑚𝑡𝑑 ≥ 𝑚𝑜𝑓 𝑚 * 𝑐𝑎 𝑚𝑡 * 𝛿 𝑚𝑡 𝑑 ∀ 𝑚, 𝑡 (5) ∑ 𝑤 𝑑𝑓𝑟 ≤ 𝑐𝑎 𝑑 * 𝛾 𝑑 𝑟,𝑓 ∀ 𝑑 (6)
Demand and equilibrium flow constraints

∑ 𝑤 𝑑𝑓𝑟 = 𝑑𝑒𝑚 𝑟 ∀ 𝑟 𝑑,𝑓 (7)
∑ 𝑥 𝑠𝑚 = ∑ 𝑦 𝑚𝑡𝑑 ∀ 𝑚

In the formulation above, constraints (1) and ( 2) ensure that only an active supplier can send units of material raw. An active supplier refers a supplier that has been selected to be part of the supply chain providing manufacturers with raw material. Equations (3) ensures units coming from suppliers are delivered only to manufacturers in operation, avoiding extra open facilities in the case where the total number of jobs is maximized. Equations ( 4) and ( 5) define upper and lower boundaries for production quantity at manufacturing facilities, respectively. Both equations, (4) and ( 5) are necessary to avoid excess of open production facilities in the case where the total number of job opportunities is maximized. In fact, to avoid unrealistic results when social performance guides the configuration of the network, a minimum operational efficiency index is fixed in equation ( 5). It ensures that an open manufacturer facility must produce at least a fixed quantity of units to validate hiring workers. That might be understood as a minimum productive performance at manufacturers. Equation ( 6) allows warehouses to cater retailers according to its capacity. Constraint (7) warrants demand for each retailer is satisfied. Equations ( 8) and ( 9) ensure the material flow balance between suppliers and manufacturers and between manufacturers and warehouses, respectively. Constraint (10) at most one automation level can be assigned to each manufacturing plant. Lastly, the description of decision variables is given at constraints ( 11) and ( 12).

Objective functions

To assess the dimensions of sustainability (i.e., economic, environmental, and social) three different objectives were proposed. The first objective (𝑍 1 ) is to minimize the total cost of supply chain operation as a measure of the economic performance. Equation ( 13) shows how this cost is calculated, including the fixed cost to operate several production facilities and warehouses as well as the variables cost for the total amount of raw material transported between the suppliers and the manufacturers and the goods produced and transported towards retailers.

𝑍

Total number of CO2 emissions during material forward flow throughout the supply chain was selected as indicator to define the network structure from an environmental perspective. The sum of the total amount of metric tons of CO2 derivate from the raw material and final products transportation, the CO2 emissions caused by production process in production facility with a specific technology and the emission from a warehouse open is shown in the Equation ( 14). Worth to point out, features of reverse logistics or closedloop supply chain are not addressed in this objective.

𝑍 2 = ∑ 𝑒 𝑠𝑚 * 𝑥 𝑠𝑚 𝑠,𝑚 + ∑ (𝑒 𝑚𝑑 + 𝑒𝑝 𝑚𝑡 ) * 𝑦 𝑚𝑡𝑑 𝑚,𝑡,𝑑 + ∑ 𝑒 𝑑𝑟 * 𝑤 𝑑𝑓𝑟 𝑑,𝑓,𝑟 (14)
For the social perspective assessment two factors have been selected and expressed in a composite indicator, particularly total amount of job opportunities created by manufacturer 𝑚 using technology 𝑡 and social impact caused by supplier's selection 𝑠. In this case, the proposed metrics have different dimensions, with the objective to join them together in an only one expression, a scalarization method was applied [START_REF] Ehrgott | Mutiobjective Programming[END_REF]. For each one of the metrics in the social dimension the range of its function is calculated (i.e., the maximum and the minimum possible values when each metric is evaluated separately). Let 𝑖 the index for the metrics, let 𝑀𝑎𝑥 𝑖 and 𝑀𝑖𝑛 𝑖 the maximum and the minimum value of the metric 𝑖, respectively, calculated separately. It should be noted that in this case the optimal value for the metric 𝑖 (i.e., 𝑂𝑝𝑡 𝑖 ) corresponds to 𝑀𝑎𝑥 𝑖 value for both factors, since the objective is to generate the higher social impact through hiring the highest number of employees and promoting business with suppliers in less developed regions causing the highest possible impact.

For each one of the two proposed measures regarding the social performance a value 𝑏 𝑖 is calculated, as is shown in equation ( 15). 𝑏 𝑖 represents the deviation of the measure value 𝑖 (i.e.,𝑣 𝑖 ), from its optimal value.

𝑏 𝑖 = |𝑂𝑝𝑡 𝑖 -𝑣 𝑖 | 𝑀𝑎𝑥 𝑖 -𝑀𝑖𝑛 𝑖 ; 𝑤𝑖𝑡ℎ 0 ≤ 𝑏 𝑖 ≤ 1 (15)
Then, the objective consists of to minimize the bias of the metrics values respect to its optimal value in the expression (16).

𝑀𝑖𝑛 𝑍 3 = ∑ 𝑏 𝑖 𝑖 (16)
The model aims to find the best possible configuration of supply chain network that optimizes each one of the proposed economic, environmental, and social performance measures, separately. To identify differences in the structure network when the decision is clearly biased by one of the dimensions of sustainability. Nevertheless, in any case, the model ensures to meet minimum productivity requirements, in a competitive context to avoid unrealistic outcomes.

Results

To test the performance of the proposed model a dataset is constructed considering probability distributions to the scenario presented in (Montoya-Torres, 2015) for the design of a supply chain in a high-variety production environment. The model considers the existence of 30 potential suppliers, 20 manufacturing facilities, 30 warehouses and 15 retailers. This section presents the results of the numerical example. All experimental tests were conducted on a personal computer with an Intel Core i5 4200U processor, 1.60 GHz with 8.00 GB of RAM. The proposed model was programed using GAMS and solved using the mixedinteger programming solver ILOG CPLEX 12.2. Not analysis is considered over computational times, there are not relevant differences interesting to point them out.

During the analysis, the best possible supply chain structure was found evaluating the economic, environmental, and social performance, separately. As it was explained before, the two proposed metrics to evaluate social impact into the supply chain have not the same measure units, consequently a normalization procedure was carried out for those metrics as presented above. The minimum and the maximum possible value (i.e., range of function for each metric) is shown in Table 3.1. So, the minimum number of created opportunities jobs is 272 jobs and maximum 461 jobs, the scenario in which the manual process is favored at every in-operation manufacturer. Finally, the indicator to social sustainability supplier assessment has a minimum value of 0.307 and a maximum value of 4.656 in the case the great number of suppliers are chosen to increase the social impact to the supply chain. As shown in Figure 3.1 when the decision is based solely on the economic criteria the network is composed by four suppliers (black circles in external circumference), four manufacturing facilities (black squares), all of them with the highest automation level and ten distribution centers (DC's) (black triangles in the internal square),to meet the demand of the fifteen retailers. Besides, the total demand is dispatched using conventional fuel fleet. A total number of 272 jobs offers are generated and 4 suppliers participate into the chain. Since less developed areas are usually located far away from market regions, representing higher transportation costs, suppliers in remote areas are barely considered to be part of the supply chain structure.

In the case, when the decision is guided by the environmental criteria four suppliers are chosen, four manufacturing facilities are opened, same number as in the previous case, with the highest automation level. Four DC's are selected to deal with the demand. Unlike the previous case, all goods are delivered using the electric fleet. The total cost increase about 33% meanwhile the emissions of CO2 reduced near to 51%, showing the existent trade-offs between these competing objectives. As mentioned before suppliers in remote areas are neglected to be part of the supply chain, since transportation of raw material from those to manufacturer plants imply a considerable increase on carbon emissions. This condition results particularly important in developing countries where rural road infrastructure usually is in poor conditions. This particular feature and its impacts on sustainability development, particularly in environmental performance have been addressed in Chen, Hu, Gan, & Qiu (2017).

Finally, the last case when social criteria determine the structure of the network, the number of suppliers increases up to seven. Job offers are promoted by a higher number of manufacturing facilities, six in this case, all of them equipped with the lowest automation level, leading to a manpower intensive production system. In this case the number of DC's opened is fourteen and the distribution of products use both, conventional and electric fleet in a relation 3 to 1, approximately. The total cost is almost the double respect to the first scenario and the environmental impact caused by the supply chain is also the worst. The total amount of emissions is almost three times compared with the best scenario. The hiring rate in the social decision-based scenario is about 65% greater than the same metric in the first scenario.

Is worthy to note that the previous results show the best performance of the supply chain of each one of the dimensions of sustainability. However, the definition of what must be a sustainable supply chain is not necessarily related to one of these extreme points. Clearly, is not possible to obtain the best of the three scenarios at the same time. However, the dynamic condition of sustainable development must lead to the companies in the supply chain to establish acceptable interval of operations for each one of the evaluated criteria. Supply chain design as key element on the strategic decision level of supply chain management must deal with dynamic decisions impacting the evolution of the chain in the oncoming time.

Furthermore, to change from one configuration to another great investments are required. For instance, to change from a conventional fuel fleet to an electrical fleet, required either, replacement of a full fleet of trucks or development of a third-party logistics who oversee the distribution. In fact, this decision is rarely assumed for one period to another. In this sense separate evaluation of sustainability criteria is useful to determine current limits of operation and as well to define limits to the acceptable intervals of operation.

Conclusions

This chapter present the first effort during the research process to evaluate the differences in the supply chain network structure, when the decision is guided by each one of the dimensions of sustainability, separately. Results show how the structure changes in relation with the assessed criteria, pointing out the trade-off interactions between the objectives of sustainability in the supply chain field context.

Moreover, it presents a starting discussion about sustainable considerations at supply chain level. Further of establishing a result the separate performance assessment is useful to identify acceptable levels of operations in each one of the dimensions of sustainability, bringing into the focus the notion of dynamic in the sustainability concept. Since achieving optimum for one objective requires compromise of other objectives, it is required to establish acceptable values to every key indicator to consider a solution as sustainable. An additional interesting point related to supply chain structure is the required time to move towards a more sustainable structure. It is more evident when addressing sustainability assessment on existent supply chain networks or at facing disruptive technologies. The current chapter presents a multi-objective optimization model to the design of a supply chain network.

The chapter starts by presenting a brief literature review on multi objective optimization model to sustainable supply chain network, features and solution techniques. It highlights the role of decision maker preferences on sustainable supply chain design context. Unlike the model presented in the previous chapter, here, indicators of sustainability are evaluated at the same time to establish the location of production and warehouses facilities. The problem deals with the existence of conflictive objectives, therefore a Multi objective Optimization (MOO) technique is used to solve it. The analysis of the results opens the discussion regarding the need of defining objectives at assessing sustainability and presents an initial approach to it.

Multi-Objective Optimization

As mentioned in previous chapters SSCND bring economic, environmental, and social aspects into the spotlight, while considering strategical decisions for companies such as facilities location, technology production selection, supplier selection, demand allocation and transportation modes, among others.

Although some environmental and social factors can be expressed in economic terms such as taxes over GHG emissions [START_REF] Zakeri | Carbon pricing versus emissions trading: A supply chain planning perspective[END_REF], or investment in community development programs. Other environmental, and especially some social factors, are not easily represented through a cost function, neither desired to be. As a result, the definition of a sustainable supply chain network from the operational research perspective becomes a Multi-Objective Optimization Problem (MOOP), and the modeling approach also becomes difficult, involving tradeoffs between conflicting objectives (Mota, Carvalho, et al., 2018). Indeed, as reported by [START_REF] Eskandarpour | Sustainable supply chain network design: An optimization-oriented review[END_REF][START_REF] Moreno-Camacho | Sustainability metrics for real case applications of the supply chain network design problem: A systematic literature review[END_REF] about three-quarters of the works addressing sustainable supply chain rely on multi-objective approaches. Nevertheless, having social dimension received less attention, many of the works focus on bi-objective models considering economic and environmental performance assessment.

Most of the works consider the existence of conflicting objectives in the pursuit of financial performance and environmental compliance. For instance, environmental impacts caused during both the construction and the operation phase of facilities, might include, discharges of solid wastes, water flows pollution, and noise and air pollution. Additionally, [START_REF] Anvari | The facility location problem from the perspective of triple bottom line accounting of sustainability[END_REF] recognized the antagonistic relation between environmental and social performances at the location of industrial facilities. Considering that the economic growth that boosts social development is regularly performed at the expense of natural resources. For instance, the construction of a new production plant in a specific region might represent job opportunities for its inhabitants, but also promotes the migration into the region, adding pressure on general community services such, hospitals, or schools, among others. As a matter of fact, the existence of conflicting objectives is a basic assumption for multi objective optimization. Otherwise, if all objectives improve and worsen under the same conditions, then the problem might be easily reduced to the consideration of a unique objective.

Formally, a multi objective optimization problem (MOP) is defined as:

𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒 {𝑓 1 (𝑥), 𝑓 2 (𝑥), … , 𝑓 𝑘 (𝑥)} 𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 𝑥 ∈ 𝑆
Where 𝑘 ≥ 2 is the number of objectives and 𝑥 ∈ ℝ 𝑛 is a n-position vector containing the values for the decision variables to be determined in the problem. 𝑆 ⊂ ℝ 𝑛 is the set of feasible solutions implicitly determined by the set of constraints. Unlike single-objective optimization, where it is possible to determine between any given pair of solutions if one is better than the other, in multi-objective optimization there does not exist a straightforward method to determine if a solution is better than other. Different approaches to rank solutions are considered in the scientific literature [START_REF] Bouyssou | Outranking Methods[END_REF][START_REF] Li | An Ontology of Preference-Based Multiobjective Metaheuristics[END_REF]. In this regard, the Pareto dominance relation is the most commonly adopted method in multi-objective optimization to compare between a set of solutions [START_REF] Jaimes | An Introduction to Multiobjective Optimization Techniques[END_REF]. By definition, let 𝑥 ∈ ℝ 𝑛 be a vector with i coordinates 𝑖 ∈ {1, … , 𝑛}, measuring positive attributes of a company such as, profit, service level, environmental benefits, among others. We say that vector 𝑥 Pareto-dominates a vector 𝑦 ∈ ℝ 𝑛 ; denoted by 𝑥 ≺ 𝑝𝑎𝑟𝑒𝑡𝑜 𝑦, if an only if 𝑥 𝑖 ≧ 𝑦 𝑖 for all coordinates i, with strict inequality for at least one coordinate.

Conversely, if coordinates represent negative or "bad" attributes, for instance, cost, defective products, pollution, layoffs, etc., vector 𝑥 Pareto-dominates a vector 𝑦 if and only if 𝑥 𝑖 ≦ 𝑦 𝑖 for all coordinates of i, with strict inequality for at least one coordinate. Moreover, a solution vector 𝑥 is Pareto optimal if there does not exist, in a given set of alternatives, a vector 𝑦 such that 𝑦 ≺ 𝑝𝑎𝑟𝑒𝑡𝑜 𝑥 [START_REF] Voorneveld | Characterization of Pareto dominance[END_REF].

By virtue of the below definition of optimality, multi-objective optimization techniques usually find several trade-off solutions. In a variable space these vectors are referred as Pareto optimal decision vectors, while in objective space, are called Pareto optimal front (POF) (López [START_REF] Jaimes | An Introduction to Multiobjective Optimization Techniques[END_REF]. Nevertheless, in practice, only one solution must be selected for implementation. For instance, having different cities for the location of facilities, only one point will be selected to establish it. Formally, two solution vectors belonging to the POF are equivalent, one is as good as the other, and it requires the involvement of a decision-maker, who provides subjective preference information to choose the best solution in a particular instance of the problem [START_REF] Kaliszewski | Multiple Criteria Decision Making by Multiobjective Optimization[END_REF]. Therefore, multi-objective problems might be understood as the combination of both, finding a set of Pareto optimal solutions and decision-making.

Mathematical programming techniques are classified considering how and when preferences from decisionmaker are included into the searching procedure. Generally speaking, four approaches are considered in the literature, namely, non-preference, a priori, a posteriori, and interactive methods. Broadly speaking, in non-preference techniques, it is considered the decision-maker to not have specific assumption non bias on the solution. Therefore, after receiving the solution the decision-maker can make the choice to accept or reject it. One of the most common methods belonging to this category is the method of global criterion. For this method, the MOP is transformed into a single objective defined as:

𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒 (∑|𝑓 𝑖 (𝑥) -𝑧 𝑖 * | 𝑝 𝑘 𝑖=1 ) 1 𝑝 𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 𝑥 ∈ 𝑆
Where 𝑧 𝑖 * is the ideal solution for the objective i, and k represents the number of objectives. The reached solution strongly stands on the value of p. Although the method yields a unique solution, different Pareto optimal solution could be calculated changing the value of p.

A priori methods for the solution of multi-objective optimization model entails the definition of preferences of the decision maker prior to the searching process. The preferences can be asked as a weight or relative importance of the objectives or as desired values for each objective. To this category belong approaches such as goal programming and lexicographic method. An example of the former is presented in [START_REF] Miret | Design of bioethanol green supply chain: Comparison between first and second generation biomass concerning economic, environmental and social criteria[END_REF] to the design of a bioethanol green supply chain. The authors consider total operational costs, environmental costs, and total jobs as indicators for each sustainability dimension. The resultant MOP is solved using a weighted goal programming. It is emphasized the advantages of using this type of methodologies in problems such as SCND which contains a large number of binary variables, and the POF may contain a very few numbers of optimal solutions. According to [START_REF] Miret | Design of bioethanol green supply chain: Comparison between first and second generation biomass concerning economic, environmental and social criteria[END_REF] in this type of problem, goal programming approach guides the problem within a bounded interval, limits the computational time, by avoiding the generation of complex research tree with no promising solutions, and ineluctably returns a feasible solution. [START_REF] Nayeri | Multi-objective fuzzy robust optimization approach to sustainable closed-loop supply chain network design[END_REF] consider the design of a closed-loop supply chain network to the production and distribution of water tanks under uncertainty conditions. The authors consider total cost for the economic dimension, CO2, and asbestos emission for environmental dimension, and for the social dimension a composite indicator including jobs opportunities and lost working days caused by injuries during the establishment of facilities. A Goal programming method is utilized to solve the model while the preferences of decision-maker are included as desirable values between the range given by worst and best possible value to each objective.

In [START_REF] Isaloo | Optimizing a robust bi-objective supply chain network considering environmental aspects: a case study in plastic injection industry[END_REF] the authors present a comparison between non-preference and a priori methods to the design of a supply chain network for a plastic company. Total operational costs and environmental impacts are employed to address two sustainability dimensions. The results show the advantages of the weighted goal programming at reaching best solution with slightly higher computational times. Although a priori methods are intended to provide a unique solution to the decision-maker, several a priori methods, like weighted goal programming could be utilized to construct a pareto optimal front by solving multiple problems varying the weights. This method is also used in [START_REF] Vafaei | Designing a sustainable multi-channel supply chain distribution network: A case study[END_REF] at designing the distribution network for an e-commerce, considering economic, environmental and social criteria.

Regarding a posteriori methods, the decision-maker is involved after the MOP is solved. In this case a set of equally optimal solutions (POF) is generated, and the decision maker may choose the one that suits the best his or her preferences. Different methods might be employed to obtain a representative set of Pareto optimal solutions such as weighted sum method, epsilon constraint method, evolutionary multi-objective algorithms, among others. Indeed, the weighted sum method and the ε-constraint method are among the most common methods used to address SSCND. Weighted sum entails selecting a set of non-negative scalars, and strictly positive for at least one objective weights 𝑤 𝑖 , to compose a unique objective function combining all the objectives in the problem, such that ∑ 𝑤 𝑖 = 1 𝑘 𝑖=1

, where 𝑘 represent the number of objectives. The transformed objective function become a linear combination of the different objectives, and the set of Pareto optimal solutions can be generated by parametrically varying the weights 𝑤 𝑖 in the objective function.

For instance, [START_REF] Afshari | Multi-objective optimisation of facility location decisions within integrated forward / reverse logistics under uncertainty[END_REF] present a weighted sum method to the design of a closed-loop supply chain under uncertainty. The authors consider customer satisfaction and supply chain total cost as objectives to evaluate social and economic dimensions, respectively. [START_REF] Colicchia | Eco-efficient supply chain networks: Development of a design framework and application to a real case study[END_REF] address the selection of transit points and the allocation of demand for a chocolate manufacturer, considering environmental impacts coming from transportation and warehousing activities. [START_REF] Wang | Supply chain network optimization with consideration of raw material and final product substitutions driven by price and carbon emissions[END_REF] consider a bi-objective nonlinear programming model to the design of a supply chain, where different raw material might be selected, according to its purchase price, production cost and carbon emissions. In their work, profit maximization and carbon emissions minimization are considered in a weighted sum method. One of the most mentioned shortcomings of this method is its inability to deal with non-convex regions, in which the method shortfall at enumerates all the non-dominated solutions in the POF [START_REF] Collette | Multiobjective Optimization[END_REF].

A second method frequently employed to provide a representative set of the Pareto front, and which overcome the difficulty of nonconvexity is the ε-constraint method and its variations. In the ε-constraint method only one objective is optimized using the remaining objectives functions as a constraint in the model [START_REF] Mavrotas | Effective implementation of the ε-constraint method in Multi-Objective Mathematical Programming problems[END_REF]. Parametrical variation in the right side of the constrained objective functions leads to obtain the efficient solutions of the problem. In particular, [START_REF] Murillo-Alvarado | Multi-objective optimization of the supply chain of biofuels from residues of the tequila industry in Mexico[END_REF] propose an εconstraint method to design a biorefinery supply chain based on residues of the tequila industry in Mexico. The authors consider simultaneously economic and environmental objectives. Total profit is the chosen indicator in the financial performance category, while environmental impacts associated with transportation and production activities are measured in Eco-Indicator points using the Eco-Indicator 99 method. [START_REF] Cambero | Economic and life cycle environmental optimization of forest-based biorefinery supply chains for bioenergy and biofuel production[END_REF] address the design of a bioenergy fuel supply chain considering economic as well as environmental impacts. Net present value (NPV) is used to calculate economic performance and the environmental objective aims to maximize GHG emission savings with the introduction of a biorefinery supply chain. To put it differently to maximize the difference in the total amount of GHG emissions between a baseline scenario with no biorefinery and an alternative scenario where forest and wood residues are harnessed to the operation of a biorefinery for the production of biofuels and energy. In the model, forest mill, biorefinery operations, biomass and biofuel transportation, and energy generation are considered to calculate CO2 equivalent emissions (CO2eq.). They used an augmented ε-constraint method to solve the problem. Same method is employed in Cambero & Sowlati (2016), the authors present an extension of the biorefinery supply chain network design, mentioned above, to consider social aspects. Here, social benefit is associated with the creation of new different types of jobs, including managers, supervisors, operators, truck drivers, among others. It considers unemployment rate by region and type of job. Other examples of ε-constraint method to solve sustainable supply chain design in different sectors are as follows, wine industry [START_REF] Varsei | Sustainable supply chain network design: A case of the wine industry in Australia[END_REF], biofuels [START_REF] Gargalo | Optimal Design and Planning of Glycerol-Based Biorefinery Supply Chains under Uncertainty[END_REF][START_REF] Nodooshan | Environmental and Economic Optimization of Algal Biofuel Supply Chain with Multiple Technological Pathways[END_REF][START_REF] Osmani | Multi-period stochastic optimization of a sustainable multi-feedstock second generation bioethanol supply chain -A logistic case study in Midwestern United States[END_REF][START_REF] Rabbani | Developing a sustainable supply chain optimization model for switchgrass-based bioenergy production: A case study[END_REF], home appliances [START_REF] Urata | Global supply chain network design and Asian analysis with material-based carbon emissions and tax[END_REF], and agricultural products [START_REF] Fang | Design of green cold chain networks for imported fresh agri-products in belt and road development[END_REF].

Multi-objective evolutionary algorithms (MOEAs) are nature inspired algorithms using population-based approach to construct a representative set of the POF for a specific problem. There at least to main objectives for evolutionary algorithms, to obtain a set of solution as close as possible to the POF and to find a set diverse enough to represent the complete POF. [START_REF] Asadi | A bi-objective stochastic location-inventoryrouting model for microalgae-based biofuel supply chain[END_REF] propose a bi-objective model for the design of a biofuel supply chain. In the model, the minimization of costs and impacts via CO2e emission are considered to the performance in the economic and the environmental dimension, respectively. The authors compared the performance of Multi-Objective Particle Swarm Optimization (MOPSO) and the Non-Sorting Genetic Algorithm (NSGA-II) to solve this problem. In fact, evolutionary algorithms have gained attention in the SSCND context. [START_REF] Miranda-Ackerman | A green supply chain network design framework for the processed food industry: Application to the orange juice agrofood cluster[END_REF] present a genetic algorithm to the design of an orange juice supply chain, considering GHG emissions.

Finally, in the fourth category interactive methods, here, the preferences of the decision-maker are iteratively considered through the searching process. A typical interactive method starts with an initial pareto optimal solution, the preferences from the decision-maker are included to generate new Pareto optimal solutions in each step. The process will finish in a non-infinite number of steps or as a satisfying solution was found, what occurs first. An example of this type of procedure is presented in Govindan, Jha, & Garg (2016). The authors deal with the design of a closed-loop supply chain for the electrical manufacturing industry. The economic dimension is evaluated through the maximization of profits. The saved costs by the recovery activities and the cost of CO2e emissions are accounted for the environmental dimension. Finally, the social pillar is represented by a weighted sum of social indicators, including economic welfare and growth, extended producer responsibility, and employment. The proposed algorithm determines aspirational level of each objective by solving three different problems. Then a new objective function is constructed using a weighted sum of the deviations from the ideal solution to each objective. The solutions are presented to the decision-maker who decides either to stop the process and select one of the alternative solutions or to evaluate a new set of weights according to his or her preferences.

As presented below are multiple the approaches to deal with multiple objectives at assessing environmental and social performance in classics formulation of SCND. However, in the context of sustainability at supply chain level, there are some inherent problems related to the application of a priori and a posteriori methods. First, there is a difficulty of selecting the weights to cope with problems of scale, since the objectives have different magnitudes (monetary units, GHG emissions, Eco-points, lost days, jobs, and so on) [START_REF] Ehrgott | Mutiobjective Programming[END_REF]. Second, for a priori methods, it is expected from the decision maker to have some knowledge about the interdependencies of the objectives and the feasible objectives values [START_REF] Hartikainen | Constructing a Pareto front approximation for decision making[END_REF]. However, sustainability encompasses a broad set of requirements, many of them outside of the scope of classic business decisions, and the expected results coming from the appropriation of sustainable practices might be difficult to estimate. Therefore, there is no certainty in the accurate selection of weights by the decision maker. Third, the visualization of the set of Pareto optimal solutions is not easy when the problem considers three or more objectives. Additionally, the selection of one option when a large set of solutions is displayed becomes a tough task even more when the trade-off between the conflicting objectives is not well understood [START_REF] Khan | A Trade-off Analysis of Economic and Environmental Aspects of a Disruption Based Closed-Loop Supply Chain Network[END_REF]. Last but not least, sustainability assessment is deeply linked with the definition of explicit goals, determined targets at seeking sustainable development.

That being said, the current chapter presents a non-preference method to the solution of MOP to the design of a supply chain network, considering economic, environmental and social criteria. Unlike a priori or a posteriori methods where the intervention of the decision-maker has a high influence on the final solution, by defining preferences over conflicting objectives. The solution method here utilized aims to minimize the maximum undesirable deviations from the best possible performance of the supply chain at every assessed dimension. The main purpose of the study is to identify the highest potential improvements achieved by the supply chain structure, while considering no bias or preferences among the objectives.

Problem statement

Generally speaking, this chapter addresses the design of a single-period, four-level supply chain, including production sites, processing plants, distribution centers, and retailers, as shown in Figure 4.1. The model aims to determine the optimal location and capacity of processing and distribution facilities, to choose the suppliers from a set of potential candidates, to determine transportation modes among facilities, and finally, to define the quantity of product that goes from one facility to another, in order to satisfy the demand of a product in a set of regions. Variable costs are related to the total volume of production at the corresponding facility. In our study only road transportation is available. However, given the plurality of road conditions to access farms, distribution centers in small villages, or retailers in downtown, etc., different types of trucks are considered. It is assumed that a restricted set of suitable transportation modes has been identified a priori for each supplier and retailer, considering the road characteristics. For instance, due to road conditions, such as road width, freight weight restrictions and so on, some suppliers, collection centers or retailers might present restrictions to the use of certain types of trucks. The model considers three types of trucks, namely, light truck, medium truck, and heavy truck, all conditioned for the transport of refrigerated freight and differentiated by different load capacities and consumption of fuel. The transportation cost is assumed linear in function to the quantity carried and the covered distance to each type of truck. GHG emissions are calculated by multiplying the consumption of fuel by its correspondent emission factor.

The supply chain configuration considers economic, environmental, and social factors. To evaluate the economic performance, the objective aims to minimize the total network costs, including facilities location costs, procurement costs, processing costs, and transportation costs. The environmental dimension is evaluated through the quantification of CO2e emissions coming from production and transportation activities. Finally, the social objective is to maximize the social impact caused by the creation of employees at processing facilities and economy development through the inclusion of local suppliers. Priority has been given to less developed regions both, for the selection of suppliers and the installation of processing plants.

Mathematical formulation

The current section introduces the mixed-integer programming model to the design of the supply chain. The following sets are defined in constructing the mathematical model: a set of suppliers S, we also define a set of potential locations to install processing plants P, a set of potential zones to locate distribution centers D, a set of retailers R, a set of available transportation types, from farmers to processing plants M and from processing plants to distribution centers and retailers T. Moreover, Finally, CP and CD are the sets containing capacity options for processing plants P and distribution centers D, respectively. We define the following decision variables and parameters as well.

Decision variables

Objective functions

Assessment of impacts in social and environmental and economic dimensions are included as separate objectives in the model. The first objective equation (1) presents the total operational costs of the supply chain. This cost is the sum of opening facilities cost (i.e., processing plants and distribution centers), purchasing cost, production cost at processing plants and cost of transportation between facilities.

𝑍 1 = ∑ 𝐿𝐶 𝑐𝑝 *
The objective at the environmental dimension (𝑧 2 )focuses on the pollution caused by the production process and transportation. Equation ( 2) calculates CO2e emissions emitted from transportation activities at the different tiers and the emissions coming from the processing at production plants.

𝑍 2 = ∑ 𝐸𝑚𝑓𝑐 *
In the model two different factors represent the social dimension. The first one, to maximize the social benefit associated with the generation of employment in the zone of located processing plants. The second one, to maximize the social benefit associated with the selection of local suppliers. These two objectives are evaluated together in a normalized equation (3). The denominator of each term in the equation is a sum of parameters representing the maximum possible value to obtain. For instance, ∑ 𝜑 𝑠 𝑠∈𝑆 , corresponds to the sum of add value factor for all regions of suppliers 𝑠 ∈ 𝑆, so each term in (3) becomes in a percentage respect to an upper bound of it itself.

𝑍 3 = ∑ 𝑈𝑟 𝑝 * 𝑦 𝑝𝑐𝑝 𝑝∈𝑃,𝑐𝑝∈𝐶𝑃 ∑ 𝑈𝑟 𝑝 𝑝∈𝑃 + ∑ 𝜑 𝑠 𝑠∈𝑆 * 𝑦 𝑠 ∑ 𝜑 𝑠 𝑠∈𝑆 (3)

Constraints

Demand and flow conservation constraints

Equation (4) ensures that the retailer's demand is met. Equations ( 5) and ( 6) guarantee the flow balance at processing plants and distribution centers, respectively, by equating the total inputs and outputs at each type of facility. To avoid unrealistic results when considering the social dimension, equations (4), ( 5) and ( 6) are defined as equalities. As an example, if demand is not established as an equality, the model in the third scenario could lead to an overflow production seeking to create a large number of employees, resulting in an unrealistic operation. Constraints ( 10) and ( 11) ensure the delivery of raw milk and processed products only in available vehicles according to the restriction of access for each supplier and retailer, respectively.

∑ 𝑥

Operational constraints

Addressing environmental and social assessment without operational conditions aspects would drive into not realistic solutions [START_REF] Brandenburg | Low carbon supply chain configuration for a new product -A goal programming approach[END_REF]. Moreover, one of the critical factors in the social field of corporations is to be profitable; a profitable company is able to offer stable working conditions, contributes to the development of the region while satisfying the demand in the market. Hence, this model considers some minimal operational requirements expressed in the following constraints.

∑ 𝑥 𝑝𝑑𝑡 𝑑∈𝐷,𝑡∈𝑇 ≥ ∑ 𝐶𝑀 𝑐𝑝 * 𝑦 𝑝𝑐𝑝 * 𝑀𝑢𝑝 𝑐𝑝∈𝐶𝑃 ∀ 𝑝 ∈ 𝑃 (12) ∑ 𝑥 𝑝𝑑𝑡 𝑑∈𝐷 ≥ ∑ 𝐶𝐷𝐶 𝑐𝑑 * 𝑦 𝑑𝑐𝑑 * 𝑀𝑢𝑑𝑐 𝑐𝑑∈𝐶𝐷 ∀ 𝑑 ∈ 𝐷 (13) ∑ 𝑦 𝑝𝑐𝑝 𝑐𝑝∈𝐶𝑃 ≤ 1 ∀ 𝑝 ∈ 𝑃 (14) ∑ 𝑦 𝑑𝑐𝑑 𝑐𝑝∈𝐶𝑃 ≤ 1 ∀ 𝑑 ∈ 𝐷 (15)
To avoid the creation of employees on idle processing plants, constraint (12) ensures that an open processing plant is used at least at its minimum balance capacity. In the dairy sector processing plants used to be constructed with a recognized overcapacity to attend fluctuations in the processing of raw milk in rainy months. Use a plant at partially capacity might be acceptable. Same way, constraint (13) imposes a minimum use of the capacity for open distribution centers. Constraints ( 14) and ( 15) limit to one the number of processing plants or distribution centers open at each selected region, respectively.

Solution approach

For the solution of the multi-objective optimization problem (MOP) defined in the previous subsection, a Chebyshev goal programming is proposed to find a balance between the accomplishment of the objectives. Chebyshev goal programming can be considered as a specific form of the weighted goal programming [START_REF] Thill | Spatial Multicriteria Decision Making and Analysis: A Geographic Information Sciences Approach[END_REF]. A set of single goal optimization problems are solved to arrive at the best and worst possible values of each objective. The best values are then used as the upper bounds or the aspiration levels for the objectives. The objective becomes one of minimizing the differences from those aspirational levels, so the solution obtained minimizes the worst unwanted deviation from any single goal [START_REF] Ghufran | Optimum multivariate stratified double sampling design: Chebyshev's Goal Programming approach[END_REF]. To apply the Chebyshev goal programming approach to the solution of the MOP, a new set of constraints need to be added ( 16). Let 𝛰 be the value of an element of the set of the multiple objectives to be evaluated, 𝑂 ∈ {𝑧 1 , 𝑧 2 , 𝑧 3 }, and let 𝑛 𝑂 and 𝑝 𝑂 be the negative and positive deviation of the objective 𝑂 from its target value 𝑂 𝑡𝑎𝑟𝑔𝑒𝑡 , then:

𝛰 + 𝑛 𝑜 -𝑝 𝑜 = 𝑂 𝑡𝑎𝑟𝑔𝑒𝑡 ∀𝛰 ∈ {𝑍1, 𝑍2, 𝑍3} (16)
The Chebyshev goal programming variation aims to minimize the maximum undesirable deviations from the defined target for any single objective. In our specific case, since both economic and environmental objectives correspond to a minimization function, favorable variations are undesirable for these objectives, while a negative deviation is undesirable for the social objective. Let 𝑍 1 * , 𝑍 2 * , 𝑍 3 * be the ideal values for the economic, environmental, and social values, respectively, and let 𝑝 𝑍1 , 𝑝 𝑍2 , and 𝑛 𝑍3 the undesirable deviations for each objective. For instance, as a rise in the total cost is an undesirable result to the economic dimension the positive deviation appears in the relation. While 𝑛 𝑍3 appears in the equation related to the social objective since here a negative deviation represents a low social impact. Finally, let λ be a scalar representing the percentage deviation of each objective to the intended solution. Therefore, constraints ( 17)-( 19) are added to the model, and (20) become the new objective function to be addressed.

𝑝 𝑍1 Z 1 * ≤ 𝜆 (17) 𝑝 𝑍2 Z 2 * ≤ 𝜆 (18) 𝑛 𝑍3 Z 3 * ≤ 𝜆 (19)
𝑚𝑖𝑛 𝜆 (20)

Case study

The case described in this section is based on a realistic supply chain aiming to serve the demand for milk and dairy products in the central region of Colombia. Economic, environmental, and social data for the case study were obtained with Colombian data through sectoral entities, previous studies from governmental agencies, and sustainable reports of milk processing industries when possible. Regarding investment cost for the construction of new facilities, production plants or warehouses, it is estimated by considering the price of similar facilities that is already built. The milk processing plant in Santa Marta (Colombia) with a capacity 20 million liters/year and an investment of USD $4.8 million in 2015 and the plant in Arauca that process about 11 million liter/year and its cost was USD $2.63 million in 2020. For warehouses, the investment is based on distribution centers owned by milk processing companies: 12000 square meters with an investment of about USD $ 11 million in 2016. Values are presented at the average Colombian COP exchange rate of USD in 2018.

Environmental data for calculating impact caused by both, milk transportation and milk processing were obtained through a specific excel-based tool for Colombian fuels constructed by the Colombian Mining and Energy Planning unit1 and the revision of sustainability reports of milk processing plants, respectively. Regarding the production process, both, scope one direct emissions for fuel combustion and fugitive emissions and scope two indirect emissions for purchasing electricity, heat, and steam are included. Finally, Colombian national statistics were considered to get data in the social dimension, unemployment rate and the percentage share of each municipality in the national GDP served as factors for the classification of the of regions regarding economic development.

In usual operation of the supply, processing plants receive raw milk coming directly from farms or from milk collection centers. The latter serves as a hub for the consolidation of milk coming from small dairy farms. It is worthy to note that since the model focuses on the strategic and tactical decision in the supply chain, routing plans to collect milk from different farms to collection centers are out of the boundaries of the study. Once at processing facilities, raw milk is pasteurized and homogenized to extend shelf life of milk and to ensure product quality. There, several dairy products are packaged, and some quality tests are applied before shipment approval. Although processed milk and other several dairy products such as yogurt, cream, cheese, and whey are produced and transported through the network, to simplify the mathematical formulation, we consider a single aggregated unit for the product going for farms to retailers (i.e., equivalent tons of milk), so different dairy products might be represented by their contain of milk. After processing, different types of milk and dairy products are shipped from the processing plants to the different distribution centers (DC's). Finally, the products are sent to retailers to meet demand in the market.

Results

As mentioned above the definition of target values for every objective constitute the first step in performing Chebyshev goal programming. To this regard, three separated linear programming models were executed without regard to the remaining two objectives. Experiments are run using GAMS (General Algebraic Modeling Systems) with the MIP solver ILOG CPLEX 12.2. The experiments were conducted on a PC with processor Intel Core i5 4200U, 1.60 GHz and 8.00 GB of RAM. The computational time for the problem is negligible, and therefore, no analysis will be done in this regard. Results from these experiments are shown in Figure 4.1. The first column of the table shows the three different objectives to be evaluated that correspond to equations (1), (2), and (3), respectively. In front of each one of them, columns 2, 3, and 4 present the respective associated value for the remaining sustainability dimensions. The second column shows the total cost of the configuration in thousands of millions COP. The total emissions in CO2 eq. tons are presented in column 3. The fourth column of the table presents the results for the social dimension, the objective function value (at the top) (i.e., social impact factor) as well as the number of created jobs and the number of contracted suppliers in each configuration (above). 4.1, it is worthy to note the trade-offs between the different objectives. Slightly variations are presented in each one of the single objective scenarios analyzed. The network configuration aiming to minimize the total amount of CO2 emissions is about 7% more expensive than the best option and presents a reduction of only 3% in the CO2e emissions level that it. The difference in these costs is mainly caused by the number of distribution centers in each network structure. Although only one milk processing plant is open in each one of the different models, the model focuses on cost minimization accounts with two distribution centers of large capacity in zone 1 and zone 6, meanwhile the model with the environmental objective consists of four facilities at this level, two small capacity distribution centers in zones 4 and 6, one medium capacity distribution center in zone 1 and one distribution center of large capacity in zone 3. Figure 4.2 presents a distribution of the drivers of cost for each one of the independent single-objective optimization problems. Production cost remains the same in every configuration. Small differences are observed in the procurement cost and transportation cost, while the cost of locations of facilities presents the most notable difference, particularly, to the reduction of GHG emissions. It is also noted that the cost for the configuration guided by the social objective is very similar to the optimal one, in fact, it is just above 0.3% greater, but the level of CO2e emissions is the highest among the evaluated possibilities. In fact, even when transportation costs in the scenario guided by the social objective increase just about 8% in comparison with the scenario guided by the environmental function, the level of emissions grows about 84%. Figure 4.3 presents a comparison in the level of CO2 emissions generated by transportation activities between suppliers and plants, plants and DC's and DC's and retailers for the three different single objective problems. The first scenario favors the location of a smaller number of processing plants, which increases the total number of kilometers traveled from farms to processing facilities, which is reflected in the notable contribution to the CO2 emissions in this link. Conversely, the opening of more processing plants favors the reduction of emissions from transportation in the second scenario. Farmers-Plants Plants-DC's DC's-Retailers

In the third scenario guided by the social objective, the number of tons of CO2 derived from transportation activities increases considerably, mainly due to the transport of products between the production plant and the distribution centers. The reason is that in this scenario the decision regarding the location of processing plants and the selection of suppliers privileges the areas with the least development and the highest unemployment rate, which usually corresponds to those areas remote from large consumption centers and challenging access routes. On the other hand, as also shown in Table 4.1, for all network configurations, the number of created jobs is the same: a processing plant of small capacity that requires 130 new employees.

Interestingly, although the optimization of the social dimension has negative impacts on the environmental performance measure as described before regarding the number of emissions, this does not occur in the other way around. In fact, the scenario guided by the environmental objective has a higher number of suppliers and reaches a social impact measure about 20% under the optimal. The main difference affecting the result on the social value indicator is the region in which the milk processing plant is installed and the region of the selected suppliers. While in the first case (i.e., environmental objective model) they are selected according to the minimum travel distance and the availability of use greener transportation means to cause the least number of emissions, in the second case (i.e., social performance objective) they are selected prioritizing the areas with the lowest economic development. So, although the number of suppliers is higher in the scenario optimizing the environmental impact, the distribution of selected suppliers in the social scenario presents better performance. 4.2 presents the objective function evaluated in the model. Columns two, three and four, present the number of suppliers at each category, Then, in column five to eight the potential location for processing facilities. We use the letter S from small, M from medium and L from large to present the capacity of the processing plant at the selected location. The same convention is used to describe the capacity of installed distribution centers in the six potential locations.

Chebyshev goal programming approach

Due to slight variations in different configurations of the SC, a non-weighted Chebyshev goal programming is used to balance the economic, environmental, and social objective in the problem under study. After defining, the target 𝑍 1 * , 𝑍 2 * , and 𝑍 3 * from the optimization of individual objectives in section 3. The Chebyshev goal programming is performed as described in section 4. From the execution is possible to note that there does not exist a configuration in which all objective targets are met without deviation. So, different trade-offs are presented in the new structure of the supply chain. Results of the execution are shown in Table 4.3. The first and second column present the objective and its related target, in the third column is presented the deviation respect to the target value with a plus sign (+) if it corresponds to a positive deviation or minus sign (-) if it corresponds to a negative deviation. Finally, the last column presents the percentage of variation for each objective and the value of lambda in bold. Variations are presented for all objectivesthe largest of these regarding the environmental issue. The new structure of the supply network has an increase of 4% in the level of CO2e emissions above the desired value for this objective. Is worthy to note how this value is higher than the emission caused in the scenario guided by the economic function and allows us to see the complexity of the relationship between environmental and social objectives. In fact, this solution prioritizes the social performance of the supply chain. Regarding the structure, 16 suppliers from the least developed regions are selected, and the processing plant is also installed in the region with the highest unemployment rate. Three distribution centers are open: one small capacity distribution center in zone 4, one medium capacity distribution center in zone 2 and on a large capacity distribution center in zone 6. Summary of the structure of the network given by goal programming is presented in Table 4.4 It is possible to observe how a reduction of emissions of CO2e requires an economic effort. Moreover, we highlight the relation between environmental and social performances; the pursuit of better results in social performance ends up affecting the environmental performance of the distribution network. One of the significant factors is the unavailability of efficient roads to transport products from isolated regions. Herein lies the relevance of defining objectives to the sustainable key indicators. The definition of preferences by the decision maker can lead to good solutions, however, even when these solutions mean an improvement over the current company situation, in a broader view, might remain unsustainable in reference to the social and environmental objectives of the sector or the country.

Conclusions

This chapter presented a multi-objective optimization model incorporating the three dimensions of sustainability for supply chain network design. The model addressed explicitly with strategic and tactical decisions while considering the minimization of the total costs (economic dimension), the minimization of CO2e emissions at both processing facilities and transport (environmental dimension), and two factors in the categories of work conditions and societal development (social dimension). Aiming to balance the solution without the inherence of bias or decision-maker preferences, this chapter presents a Chebyshev Goal Programming method, intended to balance the undesirable deviations of ideal points for every single objective.

A case-study research in the dairy sector of the central region of Colombia was taken as an exemplary application. The results evidence trade-off among economic, environmental and social objectives. The defined targets are ambitious in itself. The unweighted balance results give more priority to the social dimension, which obtains the least deviation, thus affecting the environmental performance of the chain. In regard to the proposed approach for supply chain design under sustainability metrics, decision-makers will have at hand a set of possible configurations to be chosen in order to comply with environmental and social regulations without neglecting economic performance. Indeed, the agro-industrial sector is prone to high impacts of supply chain and logistics decisions in terms of social and environmental performance, and so the dairy sector of emerging economies, in particular.

Results show how location and allocation decision might have an impact on sustainable development. However, it pops up different inquiries, for instance, although new supply chain structure could entail GHG emissions savings, question might be how much improvement is needed to consider the new structure as sustainable? Moreover, since most of the works address the evaluation of already constituted supply chain, how long it takes to go from the actual structure to the desirable structure? These questions are related with the definition of sustainable development and highlight the importance of the definition of objectives at assessing sustainability in any system. Following chapters address these previous questions at considering multi-period models to exemplify the execution of activities in the long-term leading to a stable state in the sustainability indicators of the chain. National and continental plans to the reduction of GHG emissions and the improvement of social health and living conditions are consider to the definition of goal for every sustainability dimension. Besides, a wider view of sustainability is analyzed at considering supply chains as part of community development.

Case Study Description

The current chapter presents a description of Colombia's dairy sector, considering its implications to the economy, environment, and society. We present a general description of the agricultural sector at national level. It highlights the relevance of the livestock sector for the society and the environment. Particularly, we present logistics, environmental and social conditions in the dairy industry. We highlight the most significant sectorial challenges nowadays, to lead a sustainable transformation. Addittionaly, we present a summary of the long-term sustainable objectives in the supply chain network design model in line with the sectorial development plans. Finally, we list plausible external scenario drivers, according to the existent long-term development policies in the sector.

Colombian Agricultural sector

Colombia is located in northwestern South America (see Figure 5.1 ). It borders Ecuador, Peru, Brazil, Venezuela, the Caribbean Sea, Panama, and the Pacific Ocean. Colombia is the 26 th largest country in the world, with an area of about 1,138,914 km 2 and 50.34 million inhabitants by 2019. It comprises 32 departments and the Capital District of Bogota. The climate of Colombia is mainly tropical, presenting variations within six natural regions, characterized by differences in altitude, temperature, humidity, winds, and rainfall, because of a three-branched subdivision of the Andes mountain range. Its territory encompasses Amazon rainforest, highlands, grasslands, and deserts. The rainy season is bimodal, being from April to June and from August to November. However, precipitation levels also vary widely within the country: The eastern Caribbean coast is impoverished in rainfall with less than 400 mm of rainfall per year, while in the west of the Andes, there are up to 16,000 mm of precipitation per year in some areas. This diversity of factors determines the potential of soils for a wide variety of agricultural activities. Agriculture has historically been one of the main engines of economic development in Colombia. Given its vast natural resources, diverse climate, and varied topography, agricultural business opportunities are abundant in the country as the potential role of Colombia as a global supplier continues to grow. The sector is supervised by the Ministry of Agriculture and Rural Development (MADR). Its central objective is to formulate, coordinate, and evaluate policies that promote competitive, equitable, and sustainable development of agricultural, forestry, fisheries, livestock, and rural development processes. Agriculture represents about 6.7% of the national GDP and accounts for over 20% of the national employment by 2019. Over the past five years, the sector has shown a slight and steady increase, to some extent due to the peace agreement that ended an internal armed conflict that lasted more than half a century. This peace has brought agricultural, and other economic interests to previously undeveloped rural areas and has raised concerns about the need to protect environmental biodiversity.

In 2018, after almost five years of cooperative work between MADR, the Colombian Ministry of Environment and Sustainable Development (MADS), and The Agriculture planning unit (UPRA), the national agriculture frontier was defined for the first time (UPRA & MADR, 2017). The document defines rural land boundary separating areas where agricultural activities are carried out from protected areas and other strategic ecosystems where agricultural activities are excluded by law. It aims to develop land formalization programs in areas with the aptitude to advance long term sustainable productive projects. It is a tool for coordinating competitive agricultural enterprises with the protection of biodiversity.

According to UPRA & MADR (2017), the Colombian national agriculture frontier includes about 36 million hectares, representing nearly 32% of its continental territory. There the development of agricultural, livestock, forestry, aquaculture, and fishing activities are allowed. Nowadays, about 50 million hectares are occupied with some sort of agricultural activity. About 5 million hectares are croplands, while about 39 million hectares correspond to grasses and fodder, mostly occupied for livestock husbandry. The remaining area is occupied with forest and other uses of land. One of the main challenges is to reduce land use conflict of agricultural activities in environmental protection territories, namely, forest reserve areas, moors, and national parks.

As reported by IDEAM (2018), historically, Agriculture, Forestry, and other land use (AFOLU) have been the most significant GHG emissions source in Colombia. From 1990 to 2014, the AFOLU sector has represented about 65% of the total national GHG emissions. However, the marginal contribution of AFOLU has been progressively decreasing over time, going from 77% in 1990 (158.02 Gg CO2 eq.) to near 55% in 2014 (129.51 Gg CO2 eq.), while total national emission has increased by only about 9.6%. As presented in the Colombian national GHG inventory in Figure 5.2, livestock activities account for around 40% of the GHG emissions within the AFOLU sector, mainly due to enteric fermentation, manure management, and forest land converted to pastures.

From the above description of the agricultural sector in Colombia, at least two notable facts emerge. On one hand, the potential of the country to become a global pantry without compromising environmental biodiversity, due to the wide availability of resources, but the imminent necessity of the reorganization of productive systems. On the other hand, the significant role of the livestock sector in the country and its influence on society and environmental development.

Colombian dairy sector

Colombia is currently the fourth-largest producer of milk in Latin America, excelled only by Brazil, Mexico, and Argentina. The dairy sector in Colombia gathers more than 400,000 productive units, generates about 900,000 direct jobs in milk production and more than 15,000 in the dairy processing industry. It also has an essential share in the country's economy, representing about 25% of the livestock sector's gross domestic product and near 12% of the total agricultural GDP. National production of milk has presented a constant rise during the last decade, mainly by increasing the livestock inventory and the expansion in the number of productive units of farms within the post-conflict context. Nowadays, Colombia produces around 7.19 billion liters of milk per year. However, only about 50% of this production goes to the industrial stage of the chain. The remaining milk production is sold in informal markets, usually in the surrounding regions of producing farms. Considering national milk production capacity and the recent free trade agreements signed by the United States, The European Union, and other Latin American countries, Colombia could become a significant exporter of dairy products. However, lack of processing capacity, low competitiveness in terms of animal productivity, and the sector's price regulation have been barriers to this objective [START_REF] Cadena | Precio Regulado de la Leche: Ineficiencias, Costos y Alternativas[END_REF].

For presenting what formal and informal markets mean in the case study context, it is prompt to mention some Colombian dairy sector regulations. One of the central policies applied to the sector address the definition of minimum sold price per liter of milk [START_REF] Cadena | Precio Regulado de la Leche: Ineficiencias, Costos y Alternativas[END_REF]. The price framework began with resolution 012 of 2007 and was modified years after by resolution 017 of 2012 of the Colombian Ministry of Agriculture and Rural Development. To strengthen the market supply with quality dairy products in a competitive process, the ministry defined a formula to calculate the price of a liter of raw milk considering its protein and fat content in grams per liter. Additionally, bonuses or discounts affect the final price of milk. For instance, the hygienic production of milk bonus, based on the estimated number of viable bacteria per ml of milk (colony-forming unit/ml), or cattle health quality bonus, considering the foot-and-mouth disease or brucellosis-free register. Finally, voluntary bonuses from the buying agent are considered. Discounts are also made explicit according to the type of transport. The resolution establishes the transportation cost according to the distance in kilometers to the round-trip from the processing plant to the farm or the collection point. Thus, the resolution specifies the amount of money per liter that must be discounted according to the distance and transport vehicle type.

Every buying agent, namely, intermediary or milk processing company, are compelled by the current regulations to execute every purchase according to the specification in the resolution and to report the purchase to the milk price monitoring unit (USP), including purchased volume, the price paid per liter, register of protein, fat and solids content in milk and bacterial levels by an authorized laboratory. Milk purchases meeting the regulatory requirements belong to the formal market. On the contrary, purchases executed out of the regulation criteria classify as transactions in the informal market.

Figure 5.3 shows the destination of the national production of milk in 2019, considering the formal and informal market and the agents involved in the transaction. According to USP, around 47% of the national production of milk was collected by the formal market, directly by milk processing industries, or through intermediaries, which correspond to associations of cooperatives of small and medium farmers that join seeking better negotiation conditions. About 7% is consumed on farms, and the rest of it goes to the market through non-formal agents. Although informality varies from one region to another, it is more prevalent in remote rural areas with smallholders' extended presence. According to [START_REF] Bridge | Mooooi Dairy Opportunities for a Colombian-Dutch win-win collaboration[END_REF], there are different conditions linked to producers in informal markets. Informality is related to low incomes since raw milk is paid at lower prices than the one defined by the Ministry of Agriculture and Rural Development on the formal market, which derives from low wages and informal labor. Informality is also related to low hygienic production practices because of a lack of cooling systems, deficient access to electricity distribution networks, and rudimentary collecting practices. Mainly factors promoting informality include difficult access to rural zones due to poor road infrastructure, high dairy products prices in the formal channel, lack of business vision and cooperation between smallholders, and the notable difference between production and processing capacity dairy sector. Succinctly, the high informality in the sector is one of the conditions that threaten the sustainable development of the industry. Farmers are paid less than they deserve, less to cover at least their own production costs. Processors compete against products with unfair prices, and consumers are exposed to products that, in some cases, do not meet safe and healthy regulations.

Figure 5.4 presents the general structure of the Colombian dairy supply chain, including its primary stages, expressly, production, collection or transportation, processing, and distribution. Noteworthy, the model considers activities exclusively on the formal channel. It involves the whole national production of milk and the total consumption through the apparent milk consumption, calculated by adding the national production and the imports, minus the exports. Since there is a direct link between formal collection and the processing industry, meaning that all milk collected in the formal channel end up in the formal processing industry, we consider a four-echelon supply chain including production, processing, distribution, and consumption.

Production

The production stage is mostly composed of small farmers, characterized by low production rates and low incomes [START_REF] Fedegan | Costos modales en ganadería de leche -trópico alto de Colombia: Ventana a la competitividad ganadera[END_REF]. As presented in Figure 5.5 from the property structure study results carried out by the Colombian Agriculture Institute ICA (FEDEGAN, 2018), about 40% of the productive units have less than ten animals. Almost 67% of the farms have less than 25 animals. This population often lives in remote rural areas, get limited access to health care systems, education, and technology. Cash flow provided by the sale of milk, low barriers to access to markets, and the high nutritional value of milk result attractive for a large group of smallholders who get their familiar livelihood from there. Within this range, the smallholder milk production can be considered as a subsistence activity or emerging farming.

Additionally, around 31.5% of the farms have between 26 and 500 animals per farm, including emerging and profitable businesses. Only 1% of the farms can be considered high-scale production with more than 500 animals per productive unit. As presented by (MADR & UPRA, 2018), the smallholders with up to 25 animals per farm produce about a quarter of the national milk production. The most prominent farmers contribute only around 9% of it. In the country, out of the six natural regions, five have the potential for meat and milk production. Not surprisingly, there is a register of milk farms in 1104 out of the 1122 municipalities conforming to the country (MADR & UPRA, 2018). Although, as mentioned before, the regions differ in temperature, rainfall and so on, they are often classified into two different categories: tropical highlands and tropical lowlands, according to some climate variables as presented in Table 5.1. These variables significantly impact the availability and quality of pastures, animal productivity, land cost, and other essential production variables. Hence, milk production comes from two different production systems: the specialized dairy system and the dual-purpose system. The former is exclusively dedicated to milk production, whereas meat and milk are produced in the latter. Specialized dairy farms are mainly located in highlands regions and usually close to urban centers. About 80% of dairy farms in highlands are exclusively oriented to milk production. In these regions, specialized dairy cattle husbandry, quality, and pasture availability, besides concentrate feed, allow reaching production rates between 12 and 15 liters per animal per day. In comparison, these values barely reach between 4 and 6 liters per animal per day in lowlands. Specialized dairy systems present higher levels of productivity (i.e., liters of milk/animal), higher animal load (i.e., animals/hectare), higher production cost ($/liter of milk), and better milk properties (i.e., fat and protein content) as well, in comparison with dualpurpose systems.

On the other hand, dual-purpose systems prevail in tropical lowlands. In this system, farmers use tropical cattle breeds crossed with dairy breeds, having the opportunity of producing meat, milk, or both depending on market conditions. When the price of milk is high, milk is commercialized; otherwise, milk is used to feed calves for meat production. From an economic and social perspective, dual-purpose systems are desirable to small and medium scale with reduced resources and low milk productivity, as the income for selling milk is used as a financial resource to support the long payback times on meat farms [START_REF] Fedegan | Hoja de Ruta[END_REF].

As shown in Figure 5.6, out of the nearly 27 million heads of bovine cattle, about 12 million contribute to milk's national production, which represents about 41% of the total livestock inventory by 2019. Despite the lower productivity rate per animal in dual-purpose systems, these farms contribute about 55% of the total national production of milk because of the number of animals they concentrate on. The remaining percentage of production comes from high productive animals in the specialized dairy system.

Collection and transportation

Broadly speaking, the formal collection of milk involves two different agents, as illustrated above in Figure 5.3, namely, milk processing companies and intermediaries. Usually, intermediaries are a set of small or medium farmers who form a cooperative association to collect fresh milk, cool it, and then sell it to the processing industry. The association let producers access credit lines to afford a cooling system and get a collection center to avoid food loss and get higher incomes due to better milk quality. Hence, processing companies collect milk from medium or large producers directly at farms or in the collection centers using cooled tank trucks.

The stage is characterized by a high level of concentration in the collection of fresh milk. The five biggest companies concentrate about 55% of the formal collection of milk, and the first 25 consolidate about 80% of it. This situation results in a high asymmetry of the chain, where a large number of producers offer their products to a small number of processors who end up concentrating the bargaining power. This situation might be attractive for the entry of new processing competitors in the market, who would ensure sufficient supply for their operations. It represents, arguably, one of the dairy industry's significant problems nowadays, since most of this surplus of milk is sold to under regulation prices at informal markets. To point out, the collection of milk has grown around 18% over the last ten years, going from near to 2.6 billion liters collected in 2010 to almost 3.2 billion liters collected in 2019. Nevertheless, the gap between production and collection is about 4 billion liters of milk, as shown in Figure 5.8. It means the industry's current capacity can process approximately only 47% of the total raw milk production.

Regarding the location of the collection centers, out of the 32 administrative divisions in which the country is divided, collection occurs in 26 of them. Antioquia, Cundinamarca, Boyacá, Cesar, Nariño, Caquetá, Santander, Caldas, Magdalena, and Valle del Cauca accounts for more than 90% total volume of milk, which also corresponds to the central locations of processing plants of the large companies of the dairy industry.

Processing

The milk processing stage consists of pasteurizers, dryers, and dairy product processing companies.

According to the National manufacturing survey (DANE, 2019), there are 155 companies in the line manufacture of dairy products. According to the new national regulation, those companies could be classified into micro, small, medium or large enterprises concerning their total incomes. About 6% of the companies belong to the category of large companies. These top ten companies account for almost 80% of the total market share as is shown in Figure 5.9. About 10% of the companies belong to the small and medium company category, and the remaining are micro-companies.

Distribution and consumption

The distribution of dairy products to national or international markets occurs through different channels.

First of all, the trade balance for dairy products in Colombia has been negative since 2009. The volume of dairy products exports from Colombia has been decreasing considerably over the last decade, representing, nowadays, less than 1% of the national production. In contrast, imports in the same category have considerably increased in the same period and are equivalent to about 4% of national production (MADR & UPRA, 2018). Therefore, most of the distribution occurs in the local market, here the traditional channel, meaning, neighborhood small food shops have the most significant participation, accounting for about 64% of the sales. Retailers represent about 26% of sales, hard discount 8%, and the remaining percentage of sales correspond to institutional purchases, army, hospitals, non-governmental organizations, etc.

According to the head of the office of planning and economic studies of the Colombian Cattle Ranchers Federation (FEDEGAN), Colombia's population has not a milk consumption culture. Although milk is a traditional product in the Colombian diet, the country's consumption per capita is around 158 liter per person per year. It is under the regular consumption of a milk producer country and below the minimum range recommended value by the World Health Organization [START_REF] Bridge | Mooooi Dairy Opportunities for a Colombian-Dutch win-win collaboration[END_REF]. For instance, it is below the consumption of other South American country producers like Argentina and Brazil. Hence, the promotion of dairy products' consumption is essential to bring the sector to a competitive position. Figure 5.10 displays the behavior on the apparent consumption of milk over the last ten years. The columns present the values for national production and total apparent milk consumption, while the line presents the average consumption per capita per year. Since 2016, MADR and other essential stakeholders in the sector have come developing campaigns to promote dairy products' consumption, aiming to raise the average consumption of milk to 170 liters per person per year. However, as MADR and UPRA (2018) pointed out, although consumption is growing, the share of national production is not, which exposes the chain's inefficiencies, mainly due to the price policy.

Environmental dimension

Several are the environmental impacts associate with farming livestock all around the world. For instance, it is a cause of land and water degradation, biodiversity loss, acid rain, coral reef degradation, and deforestation [START_REF] Gerber | Tackling climate change through livestock -A global assessment of emissions and mitigation opportunities[END_REF]. The production of ruminant meat and milk is associated with a relatively high greenhouse gas (GHG) production. Dairy cows and their manure produce GHG emissions, which contribute to climate change. Poor handling of manure and fertilizer can degrade local water resources.

Unsustainable dairy farming and feed production can lead to the loss of ecologically key areas, such as prairies, wetlands, and forests. Grazing causes soil compaction and eutrophication due to excessive accumulation of manure and trampling. It increases erosion, loss of macronutrients, and degradation of grasslands [START_REF] Rotz | Modeling greenhouse gas emissions from dairy farms[END_REF]. Particularly, milk cattle accounts for around 20% of the total global emissions from livestock, being the second type of livestock contributing the most, just exceeded by beef cattle [START_REF] Gerber | Tackling climate change through livestock -A global assessment of emissions and mitigation opportunities[END_REF]. According to FAO, at the global level, the two main sources of GHG emissions in dairy supply chains are enteric fermentation, which represents about 43% of the total emissions, and pasture management, contributing to about 36% of it [START_REF] Fao | Climate Change and The Global Dairy Cattle sector -The role of the dairy sector in a low-carbon future[END_REF]. Other sources include emissions from energy use in feed supply chains and emissions from energy consumption on farms that account for 10% and 8% percent, respectively.

Enteric fermentation is a natural part of the digestive process of domesticated and wild ruminants where anaerobic microbes, called methanogens, decompose and ferment food present in the digestive tract, such as celluloses, fiber, starches, and sugars, producing hydrogen (H2), carbon dioxide (CO2), and methane (CH4). Enteric methane, as a by-product of this process, is expelled by the host animal through burping. At the same time, other by-products such as acetate, butyrate, among others, are absorbed by the animal and used as energy precursors to produce milk, meat, and wool [START_REF] Knapp | Invited review: Enteric methane in dairy cattle production: Quantifying the opportunities and impact of reducing emissions[END_REF]. Methane emissions are a function of the ruminant population, directly related to an animal diet, quantity, quality of feed, amount of energy consumed, animal size, production level, and environmental temperature.

Gerber et al. ( 2013) stated that CH4 emissions are higher in low productivity systems, going up to the fifth fold compared to more industrialized production systems. Higher milk yields imply a shift in the animal's metabolism in favor of milk production and reproduction instead of body maintenance, contributing to lower emission intensities. Although CH4 has a shorter life span of a decade on average, while CO2 may stay for hundreds or thousands of years, methane traps more heat than carbon dioxide, reflected in the global warming potential (GWP). Methane's comparative warming effect is 28 times greater than carbon dioxide per ton in a one-hundred-year period in accordance with the fifth assessment report of the Intergovernmental Panel on Climate Change (IPCC) (IPCC, 2013).

Pasture management is the second leading source of GHG emissions related to livestock farming. Here the expansion of pastures into forested areas is the principal cause of carbon release. Forests are essential carbon reservoirs since trees and other plants absorb carbon dioxide (CO2) from the atmosphere as they grow, then this is converted into carbon and stored in its branches, leaves, trunks, roots, and in the soil. When forests are cleared or burnt, the stored carbon is released into the atmosphere, mainly as CO2. In Latin America and the Caribbean, one-third of the emissions from beef production are related to pasture expansion into forested areas [START_REF] Gerber | Tackling climate change through livestock -A global assessment of emissions and mitigation opportunities[END_REF].

In Colombia, livestock farming represents about 65% of the GHG emissions from the agricultural sector due to enteric fermentation and manure management. It contributes to nearly 40% of the forestry sector's emissions by converting natural forests to pastures [START_REF] Tapasco | The Livestock Sector in Colombia: Toward a Program to Facilitate Large-Scale Adoption of Mitigation and Adaptation Practices[END_REF]. The livestock sector contributes to approximately 20% of national GHG emissions. Figure 5.11 presents the distribution of GHG emissions for the agricultural and forestry sector. Precisely, CH4 is the most significant contributor in the sector, mainly by the ruminant digestion process. Indeed, livestock accounts for more than 50% of the total methane emissions at the national level. Nitrous oxide (NO2), whose primary sources are manure management or fertilizer application in the second place. To mention, NO2 has a GWP equal to 298 and remains in the atmosphere for 114 years, on average. On the other hand, as expected, forestry is dominated widely by CO2 emissions due to natural forest clearance. Not surprisingly, as stated in the National greenhouse gas inventory, at the regional level, GHG emissions are directly related to cattle population, and 7 out of 8 detected cores with the highest deforestation rates in the country are related to livestock husbandry. Additionally, milk production also puts tremendous pressure on hydric resources, making necessary its management and location. Water is used for animal consumption, milk cooling, cow cooling, cleaning, and sanitizing equipment, irrigating crops, moving manure, among other farm activities. A high-quality water supply is essential to dairy farms. Particularly in Colombia, pastures account for near 25% of water's total demand in the agriculture sector. Moreover, dairy farm expansion also affects some water regulators ecosystems, for example, 3.6% of pastures in dairy farms are located in wetlands, and 1.9 % are located in moors. The situation often leads to drying water sources, eutrophication due to inefficient or inexistent manure management, and water pollution.

One of the most common livestock activity stereotypes is the excessive use of land, often contrary to the soil's natural vocation. The expansion of the dairy sector threatens croplands and food safety. Increasing local and international consumers' commitment to sustainable and safety practices in agriculture demands the industry to turn into more sustainable practices. [START_REF] Chará | Intensive Silvopastoral Systems: Economics and Contribution to Climate Change Mitigation and Public Policies BT -Integrating Landscapes: Agroforestry for Biodiversity Conservation and Food Sovereignty[END_REF] stated that cattle ranching has traditionally relied on extensive systems with low stocking rates in Colombia and other Latin American countries. As mentioned before, more than 70% of the available land for agricultural activities in Colombia is used to develop some cattle husbandry, including beef and dairy cattle [START_REF] Leiva Barón | Programa Integral de Gestión Ambiental para el Subsector Lácteo[END_REF]. The conflict on land use is evident in the Colombian livestock sector, as is presented in Table 5.2. Currently, the total area used to develop livestock activities exceeds by more than 10 million hectares the potential area to withstand this activity. According to MADR, about 34% of the area occupied for milk production in Colombia is out of the agricultural frontier. It means they are located in areas with environmental constraints. Hence, it demands a reallocation of the dairy farms and a definition of growth boundaries to the sector aiming to ensure food security and make the most of the soil conditions and potential. To this end, UPRA has been working on the classification for the potential use of land. For instance, according to soil components, soil characteristics, rainfall, access road, access to markets, access to feed suppliers, labor cost, and other environmental and socioeconomic variables, Colombia has about 24 million hectares to develop dairy production activities. In detail, Colombia has 4.4 million hectares with high potential for developing the activity, about 6.5 million with medium potential, and 14 million in the low potential category.

Additional environmental impacts are caused downstream of the supply chain. Direct and indirect emissions for processing milk, wastewater disposal, and fuel combustion for transportation activities. According to [START_REF] Notarnicola | Environmental impacts of food consumption in Europe[END_REF], who evaluate the environmental impacts for a basket of representative food products in Europe, the agricultural link makes the most significant contribution due to agronomic and zootechnical activities. It is followed by food processing and logistic activities due to energy intensity and related emissions occurring during the heat, steam, and electricity production during industrial processing and fuel combustion during transportation. These results agree with previous studies mentioning [START_REF] Eberle | Environmental impacts of German food consumption and food losses[END_REF] and [START_REF] Muñoz | Life cycle assessment of the average Spanish diet including human excretion[END_REF]. These studies also pointed out the relevance of animal products, especially meat and dairy products, including cheese, butter, milk, yogurt, to GHG contribution. In particular, [START_REF] Notarnicola | Environmental impacts of food consumption in Europe[END_REF] highlight the impact of agriculture on relevant environmental impact categories such as climate change, acidification, human toxicity, cancer effect, eutrophication, and land use.

Social dimension

The livestock sector is one of the most significant contributors to poverty reduction. It constitutes livelihood for vulnerable communities all around the world. More than 500 million farmers rely on livestock herding for livelihood. Arguably, to a vast number of smallholders in precarious economic conditions, farm animals are a significant asset, representing capital, incomes, and a source of high-quality nutrients for their families.

Considering the trend in demand for livestock products, the livestock sector can contribute to poverty reduction and hunger eradication by promoting sustainable growth, inclusive social development, and efficient use of natural resources [START_REF] Fao | Climate Change and The Global Dairy Cattle sector -The role of the dairy sector in a low-carbon future[END_REF]. According to FEDEGAN (2018), Cattle raising is the most extensive economic activity in the Colombian countryside. It takes place in all regions, all topographical elevations, different scale productions, and different productive orientations. Livestock accounts for about 6% of the employees at the national level and about 20% of employment in the agricultural sector.

As mentioned before, a large percentage of the cattle farms in Colombia, near 44%, could be classified as subsistence farming. To describe it, it usually consists of informal business, where production control or records are rarely kept. Animals usually are inherited, and the genetic development of the breeds to milk production is scarce. The labor is most familiar, and the production is used for farm and family consumption, while the rest might be sold to local artisanal producers at low prices [START_REF] Bridge | Mooooi Dairy Opportunities for a Colombian-Dutch win-win collaboration[END_REF]. About 45% of the farms belong to the category of emerging farms. Farmers in this category have an entrepreneurial vision at managing their farms. Willing to meet regulations and obtain cattle health certifications if it represents profits in the future. Animals are provided with better feed quality than subsistence farming, and there is a transition to specialized breeds [START_REF] Fedegan | Hoja de Ruta[END_REF]. Milk production is usually sold in the formal market to medium-sized companies or large local ones, directly or through cooperatives, as explained in Subsection 5.2.2. Farms are usually managed for an employee, who can settle on the farm with family, have a contract, and receive legal benefits. Other employees might be contracted for specific tasks per day or week as required. Finally, the remaining 10% of the farms could be considered profitable businesses. Farms with more than 50 animals, professional management of breeds, obtaining high volumes, and high quality.

Companies managed under law regulations keeping production and accounts records, certified in good farming practices. Managers and technicians with a professional degree in zootechnical sciences, veterinary, agronomy, or business administration are in charge of developing a business plan, ensuring resources for animals' wellbeing, and ensuring productivity and quality standards compliance. Generally, milk is sold directly to large processing companies, solely, with whom a very close relationship is established.

According to (MADR & UPRA, 2018), with data from the National Department of Statistics (DANE), 63% of farm holders consider themselves as poor population. However, only 35.6% of rural households have incidence in the multidimensional poverty index (MPI). MPI complements traditional monetary poverty measures by capturing the acute deprivations in health and wellbeing, quality education, and living standards that an individual face, simultaneously. It includes nutrition, years of schooling, school attendance, drinking water availability, electricity, housing materials, among others [START_REF] Alkire | The Global Multidimensional Poverty Index (MPI) 2020[END_REF].

Considering Colombian rural households, some living standard conditions and quality education stand out. Low educational achievement is a factor affecting 85% of rural households. For instance, about 59% of producers have only reached the primary school level, 16% have not reached any formal education degree and only about 4% of producers are professional or technicians. Moreover, it is mentioned that 95% of the rural households do not have access to sewerage and 65% of them lack water services.

Regarding gender distribution, it is reported an even distribution in rural households, with 53% men and 47% women. Of the total, about 42% are between 27 to 59 years old, 25% are 18 to 26 years old, and 15% older than 60. Distribution in the labor market is not that even. According to (DANE, 2019), 76% of men develop some sort of labor, 6% home tasks, around 7% study, and 3% search for a job. While only 20% of women are reported as an employee, 69% are involved in in-home tasks, 7% study, and 1% searching for a job. However, the sector's informality labor rate goes up to 86%, which means that only 14% of the employees have a legally established contract receiving all the benefits, waves, and compensations assured by a regular permanent contract.

Regarding employment quality, the sector is characterized by generating more family employment than external employment, with a high non-monetary remuneration component. As shown in Figure 5.12, this type of employability is a distinctive feature of smallholder production, which are the vast majority, as mentioned before (see Figure 5.5). The greater the herd, the higher the demand for external labor. Similarly, as the number of animals per productive unit increases, so does the permanent labor. Nevertheless, occasional hiring or jornal retains high participation as a form of hiring regardless of herd's size. Nevertheless, national milk production, including dairy specialized farms and dual-purpose farms, generates about 700,000 permanent employees. According to Fedegan, specialized dairy farms and dual purposes also differ in the capacity of generating jobs. It is estimated that between 7 and 8 employees are required by every hundred animals in specialized dairy farms, while 5 to 6 for the same number of animals in dual-purposes farms [START_REF] Fedegan | Plan Estratégico de la Ganadería Colombiana[END_REF]. The most significant milk shed in the country, Antioquia and Cundinamarca, has the highest labor costs, partially because of qualified workers' demand for milking activities. In other regions, livestock activities compete for workforce with other, usually, more attractive industries, such as oil industry, which increases the average daily wage.

Other distinguishable social impacts in the industry are presented in the consumption stage. The high consumption of non-pasteurized milk represents a risk to consumers' health due to the high propensity of milk as a medium for bacterial growth. In this regard, there is a remarkable difference in the consumption of dairy products considering socioeconomic levels. As mentioned before, the country's average consumption of industrialized milk in 2019 was 158 liters per capita; however, in a more in-depth view of the consumption, notorious differences stand out. For instance, consumption in the lowest socioeconomic level is about 39 liters/person/year, while in the highest, it is 193 liters/person/year, as is presented in Figure 5.13. Socioeconomic stratification is parametrized mainly by housing conditions and living environment. It expresses a demonstrable socioeconomic way of life. In this sense it is directly related with the capacity acquisition of families. Therefore, the data displayed in Figure 5.13 is partially explained by the high cost of dairy products in the market, market penetration, and the notorious difference between economic conditions in rural and urban areas.

Challenges for sustainable development in the dairy industry

In a broad sense, producers, transporters, industrializers, and consumers will be sustainable when they are economically viable, ecologically safe, socially fair, culturally appropriate with a unified and holistic vision of the productive chain. From the supply chain's characterization in the previous sections, it is possible to enumerate some current dairy industry challenges to reach sustainability. However, since the aim of the work is to evaluate the application of public policies and their long-term impacts in the redesign of supply chains, it is necessary to give the dairy supply chain a context, considering external stakeholders. Specifically, this subsection is intended to establish a shared sustainability concept in the sector, diluting what sustainability means for stakeholders and how they display a sustainable dairy industry.

The dairy industry has been identified as an excellent ally of the country in reducing poverty, violence, closing the gaps between urban and rural livelihoods, and offering high nutritional value products. Moreover, as detailed in section 5.3, it plays a fundamental role in the country's intentions to reduce GHG emissions, stop deforestation, and give appropriate land use. Not surprisingly, during the last years, national institutions have come working in a supporting framework to the sustainable development of the livestock sector and particularly the dairy industry [START_REF] Tapasco | The Livestock Sector in Colombia: Toward a Program to Facilitate Large-Scale Adoption of Mitigation and Adaptation Practices[END_REF] [START_REF] Colombia | Colombia First NDC[END_REF] and the Program of productive sectorial transformation (DNP, 2010a).

These documents agree on highlighting the relevance of milk producers and processors in the supply chain's sustainable development. To the dairy industry's strategic business plan, the sector might be understood as a pyramid of value-focused on competitiveness and sustainability. The emphasis is placed on the joint and coordinated work of producers and industry to fulfill the development objectives of the sector. Simultaneously, other agents such as suppliers, distribution agents, agencies, and other institutions provide technical and legal support to meet domestic and foreign consumers' needs and consumer trends, as shown in Figure 5.14. Within this framework, most of the strategic development plan's burden falls on shoulders dairy sector at the national level, the productive transformation of the sector is undoubtedly a public policy objective aiming to:

 Promote milk consumption, and encourage milk processors to increment the milk collected, incrementing farmers' participation in the formal sector and benefiting the consumer by offering healthy tested products.  Increase farm productivity by having a more efficient use of natural resources, animal and livestock farming improvements to reach international competitive values of milk production per cow and hectare.  Ensure economic growth and fair incomes for milk producers to reduce poverty and enhance rural areas' living conditions.  Consider the potential use of soil as a base factor to the production's location and organization by removing livestock husbandry activities from areas under protection, natural parks, moors, and other restricted ecosystems and releasing overexploited land to more accurate land uses.

Sustainability in the dairy chain is understood as the need to respond to growing demand, in quantity and quality of milk, without compromising the quantity and quality of natural resources required in the whole process. It implies that resources are used at a rate that does not exceed the intensity at which these resources are being produced or assimilated by the system. At the same time, it deals with encouraging processors to increase industrial capacity and gain share at international markets, bringing benefits for themselves and also for farmers at the primary stage of the chain.

With this issue in mind, we decided, within our case study, not to focus at the scale of a single company, but to consider the entire production industry of Colombia within the scope of our study. Thus, in order to put in evidence, the differences between the various region of Colombia, we considered the scale of the region as a relevant subdivision for our model.

Sustainable objectives

The measurement and evaluation of sustainability require the definition of measurable objectives and accurate indicators. This section presents the indicators used to evaluate sustainability at the supply chain level, considering the dairy industry's main challenges in Colombia. To the best of our knowledge, there are no previous works defining sustainability criteria at the farm level in Colombia to be included in the modeling to design a supply chain network. At least two conditions are desirable to those criteria. First, to be linked with a measurable long-term objective in the industry, and second, to be represented by a quantitative expression.

The use of individual indicators allows taking a holistic view of sustainable development in each pillar, avoiding weighting sums of indicators that sometimes incur compensation between indicators. The major criticism of composite indicators is that the use of weights might disguise one indicator's poor performance with another indicator's good performance, causing misleading interpretations and leading to wrong decisions [START_REF] Goswami | Sustainability assessment of smallholder farms in developing countries[END_REF]. Moreover, since the long-term supply chain network design, considering policies development, involve the comparison of each indicator value with a reference value determined by either a global commitment trade, a national policy, or a sectorial objective, the use of individual indicators is useful to compare the current state of the indicator with the desired value.

The economic dimension is represented by one indicator. The total cost includes procurement costs, processing costs, investment costs for adding, removing, or replacing capacity, and the cost incurred by transporting materials from farms to retailers through every stage of the supply chain. This indicator is associated with goal 8 and specifically with target 8.1 that claims to sustain per capita growth under national circumstances. Run cost-efficient businesses is the essential compromises of firms to achieve sustainability. Regarding the environmental dimension, two indicators will be evaluated in our model. First, GHG emissions calculation covers production, processing, storage, and transportation linked to the amount of milk produced, transformed, and transported among facilities and till the retailer. Hereof, the indicator is associated with the target 12.a and 13 seeking to establish actions to combat climate change. As proposed by the IPCC methodology (IPCC, 2006) , we compute the total GHG emissions from one activity as the product of an emission factor associated with the activity and the activity level. For instance, the associated emissions at producing one liter of milk at one farm in one region considering the differences in production systems, specialized dairy system, or dual-purposes system. To this aim, we consider the farm system and the dairy industry as input-process-output boxes as presented in Figure 5.15(a) and (b), respectively. While the transportation among facilities is a product of the number of journeys, considering full truckload, multiplied by the emission factor, which includes distance between facilities and energy intensity according to the vehicle type.

Additionally, being the transformation of forest land one of the major cause of deforestation. We consider an indicator to calculate the number of hectares in each region dedicated to milk production. The factor considers differences in the animal stock rate to the different production systems and regions. This indicator is directly aligned with the sustainable development goal number 15, aiming to protect, restore, and promote sustainable use of territorial ecosystems, reverse land degradation, and detain biodiversity loss.

Finally, the social dimension considers two objectives. In response to target 9.3, which aims to increase the integration of small-scale businesses into value chains and markets, the increasing participation of farmers in formal and regulated economic activities is considered through the percentage of milk collected by formal companies. Several factors, such as demand, difficult road access, and profitability, lead farmers to sell their production to non-formal constituted firms, which pay lower prices. These ad-lib bargains affect the farmers' economic performance and the whole industry, letting into the market products with no compliance with health standards and unbeatable prices. Finally, in line with SDG number 8, job creation because of production and processing distribution capacity rise by region is accounted as an indicator of the social impact of the redesign of the supply chain in the long-term. As a synthesis of what have been said regarding the understanding of sustainability in the dairy industry in Colombia, Table 5.4 presents the sustainability key indicators selected for the case study and the associated sustainable development goals (SDGs), related to them.

External scenario drivers

To define scenario characteristics in the dairy industry's development, a set of external drivers is analyzed. These parameters cover changes in the market as well as the adoption of more efficient livestock husbandry techniques. Following some essential assumptions are highlighted.

Increasing milk consumption: An essential element for the straightening of the dairy sector in Colombia is the dairy products' local consumption. As FAO stated and used in previous studies, milk consumption in the country is estimated considering the dynamic of population growth (OECD & FAO, 2020; [START_REF] Schmit | Forecasting Fluid Milk and Cheese Demands for the Next Decade[END_REF]. The promotion of consumption of milk aims to raise the average annual consumption per capita in 30 liters. By 2016 the average consumption per capita in Colombia was 140 liters of milk, which correspond to a medium level consumption according to the Pan American Dairy Federation (FEPALE) (MADR & UPRA, 2018). Promoting consumption campaigns in the country has reached a continuous increment from 145 in 2017 to 148 in 2018 and 158 liter/inhabitant in 2019. The goal is to reach at least 170 liters per capita per year by 2022.

In a trending scenario to estimate the demand for 20 years ahead, we consider a 2% per capita consumption rate increasing per year until it reaches 170 liters. A conservative yearly behavior between minus 1% to positive 1.5% will be considered from that point on. The annual growth is a conservative estimation based on previous years' growth rate.

Increasing productivity rate: The dairy sector is in continuous development because of different changes that involve advances in research, transfer, and appropriation of technologies in pastures and forages, genetic improvement, increases in livestock inventory among others. These variables are not directly considered in the mathematical model. However, they might affect total production and productivity per animal and per land area in the long-term. In this regard, a trending advancement of the sector is considered, based on the last decade's behavior. Based on the milk production register from 2010 to 2019, a milk production increment of about1.5% per year is included in the sector's behavior.

Silvopastoral system implementation: Global demand for milk is expected to grow over the next decades, requiring a significant amount of natural resources to satisfy it. In countries like Colombia, where livestock husbandry takes place in vast pasture fields, pressing overproduction threatens biodiversity by changing land use. Nevertheless, recent studies have demonstrated the possibility of silvopastoral systems implementation. This system introduces environmental-friendly cattle production, improves productivity per animal, enhances biodiversity, and works as a sequestration system for GHG emissions (J [START_REF] Chará | Silvopastoral Systems and their Contribution to Improved Resource Use and Sustainable Development Goals: Evidence from Latin America[END_REF].

Recent studies on NAMA's (National appropriate mitigation action) for the agricultural sector in Colombia have highlighted silvopastoral system implementation as one of the most critical agricultural sectors' activities to mitigate climate change. In accordance with (MinAmbiente, 2014) this mitigation action has the most significant reduction potential of MtCO2eq. in the agricultural sector. Additionally, it presents a negative cost in the marginal abatement cost curve, as presented in Figure 5.16. Specifically, the agricultural sector accounts for a potential reduction of 344 million tons of CO2 eq. from 2010 to 2040. Out of the total, 337 million are related to the livestock sector, and 208 million correspond to the silvopastoral system's action, showing the measure's relevance to meet the intended reductions of the sector and the country [START_REF] Behrentz | Productos Analíticos para Apoyar la Toma de Decisiones Sobre Acciones de Mitigación a Nivel Sectorial: Sector Agropecuario[END_REF]. Marginal abatement cost (MAC) curves present the relationship between the cost-effectiveness of different mitigation options and the total amount of CO2 eq. reduced. Mainly, it reflects the additional cost of reducing the last unit of carbon. MAC curves focus on the direct cost associated with investment cost, operation cost, and maintenance cost for abatement measures [START_REF] Kesicki | Marginal abatement cost (MAC) curves: confronting theory and practice[END_REF]. Figure 5.16 shows the cost and the mitigation potential of each measure in the agricultural sector in Colombia. Each bar represents a mitigation option. The bar's width shows the potential of GHG emissions reduction expressed in MtCO2 eq., while the height of the bar indicates the cost of reducing one tCO2 eq. by applying the measure. The total cost of the measure could be calculated by calculating the area of the bar. The total width of the graph represents the total mitigation potential of the sector, and the sum of the area of all the bars sum up the total cost of all mitigation measures. The cost of each action represents the cash flow over the useful life of the project. Investment costs, operating and maintenance expenses, salvage costs and revenue generated by the action are considered. Thus, a negative cost represents savings compared to the baseline scenario in which no action is taken [START_REF] Behrentz | Productos Analíticos para Apoyar la Toma de Decisiones Sobre Acciones de Mitigación a Nivel Sectorial: Sector Agropecuario[END_REF]. A more detailed explanation of MAC curves, their construction and classification and its usefulness to visualize reduction opportunities for climate change in the agricultural sector can be consulted in [START_REF] Kesicki | Marginal abatement cost (MAC) curves: confronting theory and practice[END_REF] and [START_REF] Eory | Marginal abatement cost curves for agricultural climate policy: State-of-the art, lessons learnt and future potential[END_REF], respectively.

Electrical fleet for distribution: Several industrial partners are concerned about the impact of transportation on environmental performance. Some of them have gone forward with regulations to make higher and more challenging compromises with green production. For instance, some of the most relevant processing industries have signed compromises to work to be neutral carbon within a decade. These actions demand work in from different perspectives, processing, packing, and distribution. Indeed, distribution through all the supply chain contributes to a high number of emissions since the routes to collect and distribute milk work every day. Some efforts have been made to minimize distribution's environmental impact, such as minimizing the routes' driven distance through optimization models. Recently, some companies have been working with what seems a promising alternative to going further on reducing GHG emissions from the collection and distribution process using electric vehicles. To promote the use of this type of vehicle, some national policies have been set. Reduction in taxes, import fees, and elimination of mobility restrictions are some of the advantages to stimulate the adoption of this technology.

Introduction to sustainability assessment in policies actions

Evaluation of sustainability at the corporate level has received increasing attention since the spreading out of the triple bottom line concept. From that point on, the evaluation of commitment with sustainability has been extended to every supply chain member due to the interactions of a company with both, down or upstream companies in the supply chain that end up by affecting the social, the environmental and finally the economic performance of the company. However, there is a constant inquiry to step out of the company approach to consider a wide industry focus, although, the latter is not easy since the access to information upstream further than supplier in Tier 1, results one of the big barriers [START_REF] Muñoz-Torres | An Assessment Tool to Integrate Sustainability Principles into the Global Supply Chain[END_REF][START_REF] Schöggl | Toward supply chain-wide sustainability assessment: a conceptual framework and an aggregation method to assess supply chain performance[END_REF]. However, considering policies in the development of the sector might avoid this difficulty since, at this macro-level, it is plausible to consider that the development of the industry is influenced by overall macroeconomic factors, such as demand, labor costs, land costs and availability, rather than individual competitive behavior of single companies (Kannegiesser & Günther, 2014).

Classical approaches evaluating sustainability assessment at supply chain level, focus on a single company, which ends up shifting the burden to lower levels of the chain, but without considering the actions or plans to be developed. Moreover, there is a constant lack of definition of sustainability objectives. Although generic models offer the possibility of deciding between a set of equally optimal solutions in the presence of conflicting objectives, the applications fail to provide acceptable or desirable limits for the objectives under evaluation. The concept of development is closely linked to the achievement of objectives and it is no different when talking about sustainable development. According to [START_REF] Sala | A systemic framework for sustainability assessment[END_REF] when talking about sustainability assessment tools, the definition of objectives becomes indispensable, otherwise the measurement does not fulfill its role within the development dynamics. For example, a decrease in the emissions intensity of a company through the redesign of its operations does not in itself imply a sustainable practice without the existence of an objective to evaluate or contrast it.

In this regard, along with the growing concerns about climate change, poverty, hunger, among other social and environmental issues, there has been a commitment to the definition of global objectives and agreements at the international level. For example, the definition of the Millennium Development Goals (SDGs) is accompanied by targets in every category to be met by the end of the next decade (United Nations, 2020). Another example is the commitments per country to the reduction of emissions that aim to avoid a two degree increase in global temperature in relation to the pre-industrial era. One of the ways of establishing objectives for the evaluation of supply chains involves the application and evaluation of public policies for the development of these types of production chains. Policies may be sectoral, regional, or national and may include the promotion of various activities to achieve the objectives. Types of policies and actions include regulations and standards; taxes and charges; subsidies and incentives; information instruments; voluntary agreements; and implementation of new technologies, processes, or practices [START_REF] Iwr | Policy and Action Standard[END_REF].

In sectors constituting focal points for the regional or national development, the evaluation of policies at the sectoral level is decisive for the evaluation of the country's development. In this sense, policies allow the coordinated development of the sector under the parameters that best suit the common development by promoting clusters and enhancing productive capacities according to regional strengths. Moreover, in addition of including economic, environmental, and social dimensions, the political dimension is also included as a factor in the sustainable development of companies when considering policies and actions.

Classification of the sustainability assessment tool

Since the mention of the sustainable development concept in the Brundtland report [START_REF] Wced | Our common future[END_REF], the proposition of trustable and useful methods, methodologies, and tools has become one of the major challenges faced by researchers and practitioners, to assess the performance of systems and companies in the three different pillars of sustainability, namely economy, environment and society. Research on sustainability assessment tools (SAT's) have evolved during the last two decades and still attract the attention of researchers nowadays. Several considerations are involved in the construction of accurate SAT's. For instance, SAT´s might be classified according to different categories, including, timing and valuation perspective [START_REF] Gasparatos | Choosing the most appropriate sustainability assessment tool[END_REF], level of analysis, target group and data aggregation [START_REF] Bélanger | DELTA: An Integrated Indicator-Based Self-Assessment Tool for the Evaluation of Dairy Farms Sustainability in Quebec, Canada[END_REF], and according to the methodological approach to evaluate the defined sustainability indicators [START_REF] Lebacq | Sustainability indicators for livestock farming. A review[END_REF] as presented in Figure 6.1. Considering the wide range of alternatives for the construction of SAT, it is pertinent to detail the characteristics of the one proposed here to the evaluation of sustainability at the design of supply chain networks. It is important to highlight how the characteristics of the measurement tool match the problem's features and decision.

According to the time of evaluation, SAT's might be categorized in ex-ante or ex-post assessment tools.

The former is a forward-looking activity, which considers the expected effects on the implementation of policies, actions, or projects, aiming to compare it with the trending case in which no changes are done (Business as usual). It is usually based on forecasts of emissions drivers such as population growth, economic activity, trends development supported by historic data and the estimated impacts introduced by the assessed action. On the other hand, ex-post SAT's evaluate the impacts based on data collected during the time or after an action for sustainable development was implemented.

SAT's could also be classified according to its valuation perspective. In this regard, there exist monetary tools, mostly relying on essential valuation tools to calculate compensation values for the access or deprivation to certain commodity or service, such as willingness to pay, (WTP) or willingness to accept (WTA) [START_REF] Gasparatos | Choosing the most appropriate sustainability assessment tool[END_REF]. It generally includes values judgment regarding the commensurability of sustainability issues. Biophysical tools quantify the natural resources that have been invested during the production of a good or a service. Biophysical tools look at a set of environmental components including soil, vegetation wildlife, hydrology, and biodiversity to link the measured value with an environmental impact. Biophysical assessment tools are intended to prevent the deterioration of ecosystems and to maintain biodiversity, ensuring the consideration of physical, biological, and human components of the analyzed environment. In this respect, biophysical tools employ a rather eco-centric valuation perspective with the role of human preferences becoming obsolete when assessing the policy or action alternatives [START_REF] Gasparatos | Choosing the most appropriate sustainability assessment tool[END_REF].

Figure 6.1. SAT's classification categories Source : [START_REF] Bélanger | DELTA: An Integrated Indicator-Based Self-Assessment Tool for the Evaluation of Dairy Farms Sustainability in Quebec, Canada[END_REF][START_REF] Gasparatos | Choosing the most appropriate sustainability assessment tool[END_REF][START_REF] Lebacq | Sustainability indicators for livestock farming. A review[END_REF] In the same valuation perspective category, we find indicator-based sustainability assessment tools. They generally entail a ladder methodology during indicator selection. Generally, it presents a three or four hierarchical level approach. The most general concept, dimension, is at the top of the hierarchy. In the middle level, sustainability goals are translated to themes or subthemes according to the level of detail required. Finally, at the bottom of the pyramid indicators are measurable variables to evaluate the sustainable performance for the theme or subtheme as applicable [START_REF] De Olde | Assessing sustainability at farm-level: Lessons learned from a comparison of tools in practice[END_REF]. Here, the concepts of integration and aggregation emerge. Those are closely related with the data condensation characteristic. Aggregation is the result of combining different components or indicators into one single unit also called a composite indicator. Integration, on the other hand, refers to the use of multiple individual indicators to provide a holistic view of a theme or dimension [START_REF] Bélanger | DELTA: An Integrated Indicator-Based Self-Assessment Tool for the Evaluation of Dairy Farms Sustainability in Quebec, Canada[END_REF]. However, one of the major criticisms on composite indicators is that the use of weights might disguise the poor performance of one indicator with the good performance of another indicator, causing misleading interpretations and leading to wrong decisions [START_REF] Goswami | Sustainability assessment of smallholder farms in developing countries[END_REF].

According to [START_REF] Bélanger | DELTA: An Integrated Indicator-Based Self-Assessment Tool for the Evaluation of Dairy Farms Sustainability in Quebec, Canada[END_REF], there is a relation between data condensation and target group characteristics. For instance, scientists and technicians are keen on raw data to be able to do statistical analysis and identify every single relation. Contrarily, policymakers and the public that work at regional or upper levels need aggregated data to classify and rank alternatives to make decisions. In fact, decisions are more difficult to make when a great number of indicators are available. Nevertheless, it is important to do not fall into under-representation of what is intended to consider as expected impacts on the policy or action implementation. At the supply chain level, these impacts shall represent the more compelling challenges of the sector at economic, environmental and social dimensions (Chardine-Baumann & Botta-Genoulaz, 2014).

The main purpose of the current model is to determine the structure of a supply chain at the national or regional level, under a wide-industry perspective. It means rather than evaluating the decision of a focal company; the model aims to define in aggregated terms regulatory actions for sustainable development of the sector. An indicator-based model is proposed to this aim. The model evaluates an ex-ante baseline scenario of the supply chain, based on the current state of it and the trending development in the future. Then an evaluation on the implementation of a policy is made, considering the changes in the structure of the supply chain and the implications for the agents belonging to it. Analysis of desired conditions in the sector permits to define norms, standards or thresholds for what an organization's impacts must be; at the economy, environmental and social level, in order to aim towards sustainability. Thus, actual impacts can be contrasted against a reference value. As is stated by (de Olde et al., 2016) that sort of references values could be classified in two, absolute values and relative values. The formers usually represent desirable conditions through targets or threshold, while the latter is derived by comparison of the current value with its initial value or a regional or sample average. Figure 6.2 presents a graphical framework of the model, including the main components of it.

Mathematical model

Revisiting the work of (Kannegiesser & Günther, 2014), we present a framework for the assessment of sustainability in supply chains in the long-term. In this particular work, we consider economic, environmental and social impacts for the completely dairy supply chain. The sustainability criteria comprise production, processing and distribution activities. Unlike previous works focusing just on manufacturing activities, the current approach extends its reach to include sustainability criteria at the farm level. The indicators of sustainability are matched with the 17 sustainability goals and 169 targets announced by the United Nations (UN). Thus, it is establishing a context to declare desirable values for those indicators in the future according to the 2030 Agenda for sustainable development (UN General Assembly & United Nations, 2015).

The model considers four echelons of operations named: Production, processors, distributors, and retailers, as shown in Figure 6.3. From the supply chain network design perspective, the model addresses strategical and tactical decisions, defining the zones to milk production, where establishing processing and distribution facilities, which market serves from which locations, as well as the mode of transport required to meet a final aggregate demand in the market. These kinds of decisions affect the sustainable performance of a company and thus of the whole industry. For instance, allocation of new production capacity or expanding the existent capacity in one region, might increase the carbon footprint through a greater number of emissions coming from production and transportation. However, it could reduce the total operational costs of serving a new growing market and also improves local economy development and labor conditions in the zone.

Unlike most of the previous works in sustainable supply chain design, adopting a focal company point of view, the current approach involves the modeling of the industry-wide supply chain. Thus, a MILP formulation by [START_REF] Kannegiesser | The time-to-sustainability optimization strategy for sustainable supply network design[END_REF] for a sustainable supply chain network design is reconsidered. The main objective in this optimization framework is to minimize the time in which industry supply chain structures get within acceptable values the total set of sustainability indicators. The framework model is flexible to incorporate multiple sustainability indicators and to evaluate different industry-specific factors affecting the whole supply chain sustainability in the long term.

Since the intention of the model is to propose potential action lines for the sustainable development of the sector in the long-term, a high level of aggregation is considered. For instance, production and processing capacities are modelled on a regional level, as well as demand consumption. The assumption declares that at that level the development of the industry is primarily influenced by some macro-economic factors such a demand, availability of raw materials, rate of employment, technology parameters, global productivity; aiming to reach an economic stability in the future, rather than the individual competitive behavior of every single company in the market. The elements of the model are defined as follows:

Sets

𝑅𝑒𝑔𝑖𝑜𝑛𝑠 𝑟 ∈ 𝑅

Nodes in the network representing production, processing and distribution locations.

𝑃𝑟𝑜𝑐𝑒𝑠𝑠 𝑝 ∈ 𝑃 stand for production, processing and storage at different regions.

𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑠 Moreover, as a condition of agricultural sectors there are some products that do not go through the formal processing, channel, some quantity of product is used for auto-consumption on producing farms, processed in farm, or sold to local informal processors. Equation 10 calculates this value as the difference between the demand in the formal market and the apparent consumption of the product.

Cumulative equations

As a part of the optimization approach, we consider cumulative cost and cumulative emissions up to period t. Unlike other studies limiting GHG emissions period by period, this approach considers the cumulative nature of GHG emissions. As stated by [START_REF] Rhys | Cumulative Carbon Emissions and Climate Change: Has the Economics of Climate Policies Lost Contact with the Physics?[END_REF] At the time of the baseline scenario (𝑡 = 0), at least one indicator is considered as unsustainable. Hence the value of the variable 𝜏 0 = 1.

𝜏 0 = 1 (21)
𝜏 𝑡 is equal to one if at least one of the key performance indicators has not reached the target value, otherwise it will be equal to zero. During the following periods, the differences between the current value of the indicators and their target are accounted by 𝜋 𝑘𝑡 in equation 22. Here 𝐾𝑃𝐼 𝑘𝑡 corresponds to the value of key indicator k in period t. This value is computed using equations ( 16), ( 18), ( 19) and ( 20) for use of land, layoffs, cumulative cost and cumulative emissions, respectively.

𝜋 𝑘𝑡 ≥ 𝐾𝑃𝐼 𝑘𝑡 -𝜓 𝑘 + ∀ 𝑘 ∈ 𝐾, 𝑡 ∈ 𝑇 (22)
Constraint 23 ensures that once all indicators have achieved the targets, it must be preserved over incoming periods within the planning horizon.

𝜏 𝑡 ≤ 𝜏 𝑡-1 ∀ 𝑡 ∈ 𝑇: 𝑡 > 0 (23)

A key performance indicator is considered sustainable during a period if the actual value of the indicator 𝑘 is under the defined sustainability target value. Hence, 𝜏 𝑡 still being equal to one until the differences between the current value and the target are less or equal than zero.

𝐺 * 𝜏 𝑡 ≥ 𝜋 𝑘𝑡 ∀ 𝑘 ∈ 𝐾, 𝑡 ∈ 𝑇 (24)

The objective function is to minimize the number of periods until all indicators fall below the target value.

min 𝑍 = ∑ 𝜏 𝑡 𝑡 (25)

Optimization Strategy

The current section describes the optimization strategy to the definition of the ex-ante assessment model. The evaluation requires the definition of a baseline scenario in the long-term. Then results yielded in the first execution are inputs to the definition of objectives in the second scenario where policies and goals are set, considering key performance indicators in the three dimensions of sustainability. Figure 6.4 shows a graphical representation of the optimization strategy. Input data contains production, processing, storage and transportation capacities per region at the beginning of the evaluation period, among the required parameters presented in the previous section required to initialize the model. This data is used to solve a minimizing cost optimization model, and the results are input to the second optimization strategy.

Optimization strategy 1 and 2 are described below. The model considers processing activities as black boxes. Thus, the capacity of a facility can be expressed as a single value limiting the output flow for each product at this facility. The facility location decisions at plants and warehouses are guided by two types of costs. Fixed costs and processing costs, the formers are fixed while the latter depend on the production level of the corresponding facility. Transportation activities assume full truck load and its cost's function is assumed to be linear.

From the results of the first optimization strategy, we get the evolution of the installed capacity per process in each region, as well as the total operational cost during the time horizon. Moreover, the results show the value of the different sustainability key indicators in the business-as-usual scenario, such as, CO2 emissions stock, direct jobs, informality, among the others mention in Chapter 5 (see Table 5.4. Sustainability indicators and SDG's considered in the ex-ante sustainability assessmentTable 5.4). These values are important to compute the target values used in optimization strategy 2.

Optimization Strategy 2 -Alternative scenario: Time to sustainability approach

The time to sustainability approach is a recent approach, that appears to be relevant for the evaluation of policies in the long-term industry context and the supply chain network structure. This optimization strategy seeks to minimize the number of periods until all key indicators reach a sustainable value or target (a value between its corresponding upper and lower limits). As is stated in (Kannegiesser & Günther, 2014), defining targets for every indicator requires to define a baseline values. In the current approach, targets are established considering the results yielded by the business-as-usual scenario in the first optimization strategy and national objectives for the sector. In this stage, the implementation of policies affects the development of the supply chain, adding new criteria for sustainable development. The model comprises equation ( 1) to ( 25), where equation ( 25) is the objective function.

As introduced by (WRI & WBCSD, 2014), the principles of relevance, transparency, completeness, consistency, accuracy, conservativeness are applied to the projection of the expected results. Besides, it is important to consider uncertainty as a relevant factor at developing ex-ante assessment model [START_REF] Iwr | Policy and Action Standard[END_REF].

Since the results might be associated with different variables, it is necessary to evaluate uncertain conditions on the results, to provide more trustable results. For instance, policies might be evaluated in environments with different initial conditions, having effect on the overall result of the application, in this case results derived by the application of the policy might be over or underestimated.

Data collection

First, worth mentioning that to model industry-wide supply chains, process capacities have been aggregated by region. Although arguably it brings an inevitable degree of limitation to the model, a very fine detail description it is neither desired nor practical on developing model evaluation in a long-term study. Moreover, since the purpose of the model is to work as a sustainability assessment tool for the evaluation of policies, the level of detail at regional level is appropriate to this goal. In this regard, capacities have been aggregated by region in each stage of the chain. Figure 7.1 presents a wide view of the location and capacities of production, processing, distribution and consumption all over the Colombian territory.

Production locations:

The primary production process refers to the milk production system in farm or dairy herd units, i.e. in dairy or dual-purpose farming. Highlands in the central region of the country, including Cundinamarca, Boyacá, Nariño and the northern region of Antioquia are characterized by specialized dairy systems. Dualpurpose farms are mainly located in the Magdalena and Cauca river valleys, the Atlantic Coast and the Eastern lowlands. Although production of milk take place all over the country the model considers eight departments (political administrative divisions) which add near the 80% of the total national production, according to the Colombian national agricultural survey (ENA, by its acronym in Spanish) (DANE, 2017). This selection includes four specialized dairy regions (Antioquia, Cundinamarca, Boyacá and Nariño) and four regions managing dual-purpose cattle (Magdalena, Caquetá, Cesar and Córdoba). The two systems differ both in their productivity and in their production costs. Table 7.1 presents some relevant data for each region including the average productivity rate by animal and area as well. The cost of producing milk in each region is shown in the fifth column. It is worthy to note how dual-purpose systems have lower productivity rates per animal, higher use of land and lower production cost as well. An additional point to considered is the cost of land at different regions. Since upland soils regions often have improved conditions for the development of several sowing activities, they also have advantages to access to large markets, it cost is higher than the cost for low tropical lands. Thus, the price paid per area for livestock development in the central region of the country is usually higher than that paid in coastal areas. Table 7.3 presents the cost per thousands of hectares in each region in thousands of dollars. The value is computed using the distribution of land and its real estate appraisal. The cost of increasing capacity at any region includes the material and manpower necessary to adapt a hectare or a thousand of them for the cattle activity. It includes installation of the fence, adequacy of the grass, labor, and materials. Meanwhile the cost of decreasing capacity only counts for the labor required to retire fences. Finally, in the third column, the table presents the number of employees by hundreds of animals in the two different farming production systems (i.e., specialized dairy and dual-purpose). These values come from [START_REF] Rivera | Life Cycle Assessment For The Production Of Cattle Milk In An Intensive Silvopastoral Systemn And A Conventional System In Colombia[END_REF] they are in the range of other studies like (Chará et al., 2017b;[START_REF] Rivera | Estimación de la huella de carbono en sistemas silvopastoriles intensivos y convencionales para la producción de leche bovina en Colombia[END_REF].

Processing locations and distribution centers:

According to MADR the formal collection of milk during 2019 did took place in 24 departments in Colombia. Twelve of them sum up to the 95% of the total collection which is about 3 billion liters per year. Table 7.5 shows the total collection capacity by department. Regarding the contribution of this stage to GHG emissions, we consider direct and indirect emissions. To this aim some sustainability reports from different processing companies were consulted [START_REF] Alpina | Informe de Sostenibilidad Alpina[END_REF][START_REF] Alquería | Informe de Sostenibilidad Alquería[END_REF]. Table 7. [START_REF] Ansari | A state-of-art literature review reflecting 15 years of focus on sustainable supply chain management[END_REF] shows the marginal values of GHG emissions by tons of final product. The factor considered to transform energy into CO2 eq. units is 164.38 g CO2 eq./kWh. This factor corresponds to the updated factor of the Colombian energy matrix which allows companies in the country to calculate the carbon footprint associated with electricity consumption, it was determined by studies carried out by the Colombian Ministry of Mines and Energy, the Mining and Energy Planning Unit (UPME, 2019)

Experimental context

The current section shows the conditions for the construction of the ex-ante baseline scenario and the alternative scenario. Table 7.7 presents the value and considerations of the different parameters involved. The Baseline scenario represents the Business As Usual (BAU) decision, in which the economic factor takes the lead. In this scenario, all sustainability indicators are non-restricted, and the minimum total cost guides the final decision. On the other hand, the Alternative scenario is driven by the minimum needed time to obtain acceptable values for every sustainability key indicator. To this purpose and considering national and sectorial plans for developing the agri-food sector, the livestock sector, and the dairy industry, an acceptable cap is imposed over each key indicator. For example, since the Intended National Determined Contributions presented by Colombia to the Conference Of the Parties (COP) establishes an unilateral and unconditional commitment for the reduction of at least 20% of GHG emissions [START_REF] Mads | Política Nacional de Cambio Climático[END_REF] in comparison to a BAU scenario, we define, for the alternative scenario, a cap of 80% on the cumulative GHG emissions in reference to the Baseline Scenario. The same approach leads to the definition of boundaries to the rest of the key indicators. The international agreements, national or sectorial plan considered to the definition of caps are listed in column four of Table 7.7. A 20-year horizon is considered, this period exceeds the term for compliance with the CMNUCC agreements and is in line with the strategical development plan for the Colombian livestock sector.

Noticeable the baseline scenario and the alternative scenario differ from the capabilities of the development of the sector. On the one hand, the baseline scenario depicts the current state of the sector with a low yearly transformation rate of silvopastoral systems and no use of an electric fleet. On the other hand, the Alternative scenario represents the large-scale adoption of mitigation and adaptation practices in the industry led by the scaling up on the appropriation of silvopastoral systems [START_REF] Tapasco | The Livestock Sector in Colombia: Toward a Program to Facilitate Large-Scale Adoption of Mitigation and Adaptation Practices[END_REF] at the agricultural level and the use of electrical fleet for distribution activities. Other scenario drivers, such as consumption patterns and farm productivity, remain interchangeable between the scenarios, but not static.

In this respect, the collection of milk is included in the model as a fixed pattern for both scenarios.

Results

Baseline scenario cost drivers

The model describes the behavior of the supply chain during a twenty years horizon when the decisions are guided by the total operational cost, with the conditions listed to the baseline scenario in Table 7.7. The first optimization run provides a better understanding of the cost structure of the supply chain, the sources of GHG emissions, the use of land, and the category of employment in the sector as presented in Figure 7.3. Realistic cost structures may be a relevant factor in considering the validity of the results. Moreover, the relative contribution of each factor to the achievement of the objectives is crucial and will affect the evaluation in the alternative scenario.

Results show the characteristics of the supply chain, where capacity cost and raw material represent about 30% and 40% of the supply chain's total costs, respectively. High costs of land in tropical highlands, where specialized dairy production occurs, are the main contributor to the capacity category. Further, the raw material cost is well known to be one of the highest contributors to the total production cost; previous studies have shown that it accounts for about 80% of the production stage costs [START_REF] Akin | Analysis of factors affecting production costs and profitability of milk and dairy products in Turkey[END_REF].

Regarding contributions to GHG emissions in the sector, transportation activities represent less than 5% of the sector's total emissions. In comparison, farming activities account for nearly 80% of the total and transformation activities at the industrial represent about 15%. These results are aligned with what was found by [START_REF] Notarnicola | Environmental impacts of food consumption in Europe[END_REF], regarding the contribution of food producers to overall environmental performance in food supply chains. Additionally, it also stresses that non-aligned mitigation activities coming from the industrial partner may undoubtedly achieve an important effect on the overall performance of the supply chain but be insufficient to achieve sustainable values for the whole sector. That condition should be a trigger for the definition of collaborative mitigation activities in the agri-food sector, where the impact of agricultural activities has the most considerable contribution.

The second key indicator related to the environmental performance of the supply chain is the use of land. Figure 7.3c shows that almost all of the milk production is based on extensive pastures, the conventional system for milk production in the country in the initial state. Although some projects have encouraged the adoption of silvopastoral systems in the livestock sector, their development is at a primary stage, and nowadays, it represents only near to the 1% of the total land used for the production of milk, including both specialized dairy and double purpose farms [START_REF] Tapasco | The Livestock Sector in Colombia: Toward a Program to Facilitate Large-Scale Adoption of Mitigation and Adaptation Practices[END_REF].

Additionally, regarding employment, milk production adds up to about 85% of the total employees of the supply chain, while the remaining percentage is at the industrial tier in processing and storage activities. This distribution reflects what was mentioned before regarding the imbalance in the sector, in which there are many producers but a small number of buyers. This is a common scenario in developing countries, where many farm smallholders contribute to the supply of food for regions. Moreover, it highlights the importance of the sector at the social level as a trigger of economy development in rural areas and the need for all-inclusive policies to transform the agricultural sector.

Worthy of note that from the initial stage of the supply chain and its current conditions, it is possible to infer that alternative scenarios considering only mitigation options at the industrial level might not be practical, neither enough to meet sustainable values. For instance, an alternative scenario considering only electric vehicle fleet usage is not practical since even the total reduction of transportations emissions is not enough to reach the sector's sustainable goal. Besides, it would not modify land use, which is one of the key sustainability indicators. For that reason, the proposed alternative scenario must consider all mitigation strategies at once.

Baseline scenario capacities

Table 7.8 presents a summary of the changes in milk production capacity in the baseline scenario for each one of the eight regions in the study case. The total number of hectares dedicated to conventional livestock for milk production reduces by about 5%. It goes from 3,758,685 hectares in year 1 to 3,646,930 hectares in year 20. Conventional livestock system reduces its capacity in all specialized dairy regions. While it presents expansions in three out of four low tropical land regions, where dual purposes farms are located.

At the same time, the number of hectares transformed to silvopastoral systems goes up in all the regions, reaching a total of 97,780 hectares. There are not extreme differences between specialized dairy and dualpurpose regions on the appropriation of silvopastoral systems. At the end, the total number of hectares transformed represents around 3% of the total area utilized. Considering the gains and losses in the total land area, the model achieves a reduction of slightly over 3% of the total occupied area, mostly led by considerable reductions of fields in the high tropical lands, associated with specialized dairy farms.

This effect is mostly explained by the high cost of the tropical highlands, which maintains an advantage for developing dual-purpose activities in the tropical lowlands. Besides, it is worth pointing out that the reduction in the number of farms is a well-known consequence of the productivity transformation of agricultural sectors [START_REF] Cadena | Precio Regulado de la Leche: Ineficiencias, Costos y Alternativas[END_REF].

Baseline scenario Employment

Figure 7.5 presents the distribution of employees in the initial and the final situation. As a result of the decline of capacity in the conventional production of milk, there is a reduction in the number of employees at the agricultural level, partially compensated with the transformed silvopastoral areas' jobs. However, over the twenty years, about 19% of the initial jobs in agriculture are lost. It means about forty thousand employees at the agricultural tier must be generated in other agricultural activities to compensate for the loss in the dairy sector. This situation requires the promotion of alternatives agro-business, which a political level must include financial programs aimed at training and reorganization of farmers and their productive units.

Regarding the industrial tiers, including processing and storage activities, around fifteen thousand new employees are created, representing a growth of about 2.6% by year in the sector. This outstanding growth is related to the systematic rise in the formal collection of milk at all production regions, supposing a more significant amount of milk for processing and distributing. The following section presents further analysis of cost, emissions, and employment results in the baseline scenario. Next section presents a comparison between baseline and alternative scenarios and analyze the capabilities of the industry to achieve the imposed sustainable goals.

Alternative scenario

The current section presents the results of the alternative scenario. In this scenario, each key indicator is given a target related to national or sectoral objectives. The model aims to calculate the minimum number of years in which all key indicators reach this sustainable value. To this purpose, the model considers a list of scenario drivers, as presented above in Table 7.7.

Implementation of nationally appropriate mitigation actions (NAMA's), and the productive transformation to the sector aiming to meet sustainable measures, demands cooperation between stakeholders in the promotion of policies that assist in the transition, and investments from actors of the supply chain. Therefore, considering the sector's competitiveness over the time horizon, the total cost in a specific year in the alternative scenario cannot exceed by more than 10% the cost of the same year in the baseline scenario. Additionally, the total cumulative cost at the end of the year 20 cannot exceed by 5% the base scenario's total cumulative cost. That condition brings attention to the need of investing money to the development of green initiatives. However, boundaries must be established in this regard, otherwise, a friendly-environment development could lead to a loss of competitiveness, which is not sustainable (Kannegiesser & Günther, 2014).

Cumulative GHG emissions versus costs

The alternative scenario considers scaling up silvopastoral systems and using an electric vehicle fleet for distribution activities. Although these actions might have positive economic benefits, in the long run, initial investments are a barrier to its adoption. Figure 7.6 shows how GHG emissions could significantly reduce in the alternative scenario, slightly increasing the total costs. Here, a higher development rate of silvopastoral systems led quickly to considerable reductions. For instance, after three years, a 10% reduction in accumulated emissions is achieved; additional improvements take longer, and the proposed 20% reduction in total cumulative emissions is achieved 15 years later, in period 19. Once the goal is reached, the model ensures compliance in the subsequent periods. Throughout the time horizon, it is necessary to expand the capacity to develop more sustainable activities.

It implies the use of resources, which is reflected in the difference in costs between the scenarios. In years 6 and 7, this difference reaches its highest point of 10%. However, this behavior is compensated with lower investments in other periods, which allows reaching a total accumulated cost at the end of the 20 years not higher than 5% of the base scenario's total accumulated cost as presented in Figure 7.7. The economic goal is achieved from period 18, same way as the rest of the objectives, the model ensures its fulfillment for future periods. Considering the sources of GHG emissions, the reduction is particularly concentrated at the production stage. The use of electric vehicles contributes to small reductions of GHG emissions, from transportation activities. During the first five years an accelerated reduction in emissions from the transport sector is shown. Then subsequent changes in the network structure, end up reducing the impact of the fleet electrification. As a result, the total number of emissions from transport activities in the chain decreases by around 4% over the emissions of the baseline scenario as is shown in Figure 7.8, despite the consistent growth in the number of electric vehicles. In this regard, most reductions in GHG emissions at the sector level comes from the re-allocation of production zones and the development of silvopastoral systems at regions with highest production potentials. In this sense it promotes the development of productionprocessing clusters across the country as shown in Figure 7.9

Notably, the central region of the country supports the largest production, mainly by high level productivity in regions such as Antioquia (1), Cundinamarca (2) and Boyacá (4). Moreover, the figure shows the high processing capacity at Cundinamarca and Antioquia, followed by Boyacá and Nariño. The results is explained by the highest centralization of the country. For instance, around 20% of the total population of the country is concentrated in Cundinamarca. For other regions located in the north or in the south the results show the favorability of inner productionprocessing like in Cesar [START_REF] Ansari | A state-of-art literature review reflecting 15 years of focus on sustainable supply chain management[END_REF], Magdalena (7) y Nariño (3).This reflects the importance of network structure and policy development in the fulfillment of environmental and social compromises. The following section shown the evolution of conventional and silvopastoral systems at different regions over the time horizon.

Year

Baseline scenario Alternative scenario Figure 7.9. Production -Processing regional clusters

Re-allocation of capacities

Table 7.9 summarizes the changes in production capacity that occurs in the alternative scenario for every region. In this case, the total area occupied for extensive pastures goes near to 64% of the initial capacity, from 3,745,600 to 2,385,190 ha. Simultaneously, silvopastoral systems present a substantial expansion over the time horizon, mainly in the regions specializing in milk production. The total number of hectares transformed to silvopastoral systems adds up to 245,890 ha, representing 9% of the total area used by the year 20.

It is worth pointing out how the total area occupied remains practically unchanged in the tropical highlands. Indeed, Cundinamarca, central region of the country, increases its capacity around 50%. In contrast, the occupied land reduces considerably in the low tropical lands, until the disappearance of milk production activity in Córdoba. This situation shows how the productive transformation of the sector leaves farmers with low levels of productivity behind. Hence, the production is mainly centered on the highlands, here soil conditions, road infrastructure and closeness to the greatest consumption points constitute a trigger for the development of the industry. Additionally, at the end of the time horizon, the total occupied area sums up 2,631,080 ha, representing the release of more than 30% of the initial use of land. During near the first decade, as an effect of the higher animal load per area and the increase in productivity per animal, the alternative scenario presents a constant and smoothly release of land, this behavior gets more intense from year 13 and onwards, finally the land use objective is achieved after 19 periods. Figure 7.10 presents the yearly use of land for both baseline and alternative scenarios. The re-organization of the supply chain bring within it some labor market dynamics. On the one hand, the expansion of the sector and the reduction of informality in the industry, promote the creation of new job opportunities in manufacturing and distribution process. On the other hand, reduction of occupied land and promotion of silvopastoral systems cause the loss of certain number of employees at rural areas, mainly in dual-purpose farms. However, it is not fair neither desirable to compensate agricultural and industrial job opportunities since the skills required to go execute one or the other are not equiparable. Hence, to avoid adopting a compensate mentality by bypassing the differences between agricultural and industrial job offers a separated analysis of employment in the supply chain is presenting in the next section.

Employment in the alternative scenario

In the alternative scenario, the generation of employment at processing and storage tiers remains unchangeable regarding the baseline scenario. At these stages, employment generation results from the industry's efforts to expand the coverage of demand by including new smallholders in the formal sector. On the other hand, there are differences in the number of layoffs at the production tier, between baseline and alternative scenarios, because of the capacity to transform lands. Figure 7.12 presents the number of lost jobs in farming activities over the time horizon for baseline and alternative scenarios.

Because of a higher capacity for land conversion to silvopastoral systems and enhance productivity, the alternative scenario presents a larger layoff rate in the agricultural sector during the first years of the planning horizon. In period 7, for both scenarios, the number of new employees created in silvopastoral activities matches the number of employees lost in conventional farming, which means the number of employees at this point is equal to the initial number of employees in period 0. From this point on, there is an increasing loss of jobs in the sector due to reduced land for milk production. Finally, in period 19, the employment goal is reached.

As stated before, the model ensures that the alternative scenario does not incur greater layoffs than the baseline scenario during the planning horizon. Nevertheless, this output forces the relocation of nearly forty thousand agricultural jobs. It implies the training of workers in new agricultural activities and the specialization of activity in the farms. For instance, dual-purpose farms with low milk production rates, might concentrate efforts in increasing meat production. The result is related with release of land explained in the previous section. The reduction of productive units is a common output of productive transformation process in the dairy industry as is noted in [START_REF] Cadena | Precio Regulado de la Leche: Ineficiencias, Costos y Alternativas[END_REF].

The model estimates the number of lost jobs per region, which is a valuable source of information for the development of economic land use policies, and it is useful as well to the construction of regional development plans. For instance, it might be useful for establishing growth boundaries for the development of the milk production activity or production quotas per region. Correspondingly, it reveals that to construct a competitive agricultural sector, the agricultural development plan must be aligned with land productive capacities by regions.

Figure 7.12. Employment in farming activities

Transportation activities in the alternative scenario

Currently the use of electric vehicles in the network is in a primary phase, although is in the plans of the main actors in the industry, and there are tax benefits to their acquisition, the capacity is still reduced and their growth does not seem to have an acceleration in the short term. Figure 7.13 shows the increase in the quantity of dairy products transported using electric vehicles from distribution centers to demand points. Although there is a constant growth in the capacity, the current number of vehicles that can be incorporated into the sector is still too low to make a significant impact on the entire sector, as presented in Figure 7.8. Indeed, these about seventy millions of liters of milk transported by electric fleet per year does not represent more than near to 1.3% of the total amount of products sent to consumption regions.

Analysis of the results

The current section provides an overview of the results of the optimization approach. Figure 7.14 is a graphic representation of the behavior of the optimization approach in the alternative scenario, here, red slots represent periods in which the goal is not met, and on the contrary whether the goal is reached it is represented with a green slot. The graph shows how all the key sustainability indicators manage to achieve the proposed objective at the beginning of year nineteen, and the model ensures compliance in onwards periods.

Figure Criteria for cost and land occupation get within acceptable values in year 18, while target for GHG emissions and employees are achieved in year 19. The results show the advantages of policy implementation in the promotion of silvopastoral systems. Advantages on its promotion are appreciated in the long term, however, it is important to develop financial mechanisms for supporting involved farmers.

In the final configuration of the sector about a million of hectares are released for other agricultural uses. However, this situation also causes the destruction of about forty thousand employees in the agricultural sector. Hence, the promotion of friendly environmental policies must work along with the implementation of social policies, aiming to create regional capabilities for reallocating workforce in croplands or forestry activities.

One of the most interesting results is the displacement of productive capacities to highlands regions. These regions are characterized by higher population density and high cost of land. However, according to the results the creation of production and processing clusters is a relevant issue for the integral development of the sector. The central region of the country which host near 40% of the total population also hosts 75% of the milk processing activity and 37% of milk production lands. Possible conflict land uses are ahead since high quality soils are utilized in the region to the construction of residential units to accommodate the growing population in the center of the country. These results evidence the need for promotion of decentralized activities and the encouragement industry development in distant regions. Moreover, it reflects the importance on the development of road infrastructure to access markets in reaching sustainability goals.

At the company level, results at useful to define promising regions for the installation or expansion of processing activities, according to the development of the sector.

Sensitivity analysis

On the evaluation of policy implementation one of the most relevant issues, is the consideration of uncertainty in the development of the policy as well as in the outcomes of the implementation. The data used to evaluate the application of policy might be subject to certain inaccuracies, either by the source of the data or the extrapolation to different context situations. Although, every assumption has been made following the principles of relevance, transparency, completeness, consistency, accuracy and conservativeness, the standard action protocol to the evaluation of policies suggests an uncertainty analysis in these cases (WRI & WBCSD, 2014). The current section presents a sensitivity analysis of some of the main factors affecting the outcomes of the implementation of silvopastoral systems in the dairy industry in Colombia. Sensitivity analysis assesses the contributions of the inputs to the total uncertainty in analysis outcomes.

Level of adoption

Implementation of silvopastoral systems in dairy and dual-purpose farms is associated with enhanced productivity, increasing in animal load, and growth in farmer´s incomes. As reported by [START_REF] Tapasco | The Livestock Sector in Colombia: Toward a Program to Facilitate Large-Scale Adoption of Mitigation and Adaptation Practices[END_REF], silvopastoral systems promotion is one of the initiatives meeting the conditions to go for a scaling up to help the sector facing mitigation and adaptation to climate change. Moreover, it is recognized as an institutional initiative and component of the policy of the agricultural sector transformation. However, as mentioned by [START_REF] Tapasco | The Livestock Sector in Colombia: Toward a Program to Facilitate Large-Scale Adoption of Mitigation and Adaptation Practices[END_REF], there is no plan designed to its large-scale promotion. Indeed, scalingup potential of silvopastoral systems has been topic of interest since its early implementation [START_REF] Calle | A Strategy for Scaling-Up Intensive Silvopastoral Systems in Colombia[END_REF]. In this regard, national and regional capabilities to the development of silvopastoral systems remaining uncertain. Largely due to the high initial investment and knowledge required for the implementation of these grazing systems [START_REF] Montagnini | Systèmes silvopastoraux et atténuation du changement climatique en Amérique latine[END_REF]. Therefore, and analysis on different values to transformation capabilities might be useful to understand the impact of this parameter in the outcomes of the policy.

The current short scale projects in the country have reached on average a transformation rate over five thousand hectares per year as evaluated in baseline scenario. As parameter uncertainty cannot be determined, it is not possible to represent it through a probability distribution, instead of that the current approach considers different adoption level rates during the horizon planning. It considers, for instance, large-scale appropriation values in ranges fivefold, sevenfold, tenfold and fifteenfold respect to the baseline scenario. Table 7.10 presents the impact on the timeframe until meeting of sustainability goals considering different yearly transformation rates to silvopastoral systems. From the results it is possible to observe that larger transformation capabilities are associated with quicker return investment since the timeframe costs reduce as the transformation capability increase. For instance, considering a transformation rate of 28,000 ha/year the economic objective gets under control in year 18, at incrementing the transformation rate to 40,000 the period goes down to 15.

Likely, the larger the adoption level, the shorter the period to meet environmental goals. As expected, because of enhanced productivity rate at implementing silvopastoral systems, releasing of land to other agricultural activities occurs within a shorter period. GHG emissions objectives are met sooner.However, the reduction finds a boundary since the model includes also a maximum level to the reduction of lands in conventional production systems.

Finally, at scaling-up silvopastoral systems, the social dimension is less affected, becoming the limiting factor in achieving sustainability over the time horizon. Large scale appropriation influences the time to reach sustainable goals in the sector. However, the path to reach sustainability goals in the sector goes beyond fifteen years in any case. Then is important to evaluate how to manage financial resources to its promotion. Higher appropriation rates could lead to higher investments during the first periods, however, considering a joint action in the three dimensions, it does not represent and considerable speed up for environmental and social conditions. In this regard, the transformation rate should consider the inner conditions of the sector along with the development of the industry carried out by processing companies, trough the promotion of clusters and the assurance of supply for existent and new competitors. In other words, there is no need to rush pushing unnecessary pression on the sector but to consider the harmonious reach of goals, which necessarily included in a holistic view of the sector and region.

Policy effectiveness

A second condition worthy to consider is related with the performance of the policy implementation. From an economic point of view, silvopastoral systems are associated with higher farm revenues due to improve cattle productivity [START_REF] Montagnini | Systèmes silvopastoraux et atténuation du changement climatique en Amérique latine[END_REF]. From an environmental point of view, silvopastoral systems offer improve erosion control, watershed protection, biodiversity enhancement, and larger carbon sequestration when compared with conventional grazing lands [START_REF] Braun | Upscaling Silvopastoral Systems in South America[END_REF]. At analyzing social impacts in terms of employees, combination of forestry and cattle activities might provide larger jobs opportunities. Previous studies analyzing the role of silvopastoral systems at reaching sustainable goals, have revealed differences in the outcomes regarding cattle productivity. For instance [START_REF] Solorio | The Potential of Silvopastoral Systems for Milk and Meat Organic Production in the Tropics[END_REF] state milk production might go up twofold per hectare when compared with conventional production systems. [START_REF] Chará | Intensive Silvopastoral Systems: Economics and Contribution to Climate Change Mitigation and Public Policies BT -Integrating Landscapes: Agroforestry for Biodiversity Conservation and Food Sovereignty[END_REF], found a wide range of improvement going from 70% up to 300% after a 9year evaluation of substitution of conventional milk production to silvopastoral systems. As mention by [START_REF] Reyes | Measuring Sustainability on Cattle Ranches -Silvopastoral Systems[END_REF], not all the farms have the same baseline situation in terms of forage and animal production. Some farms, especially dairy specialized farms, might have starting point with high productivity mainly due to intensive use of chemical fertilizers while other farms have a very low production due to an extensive use of grasslands.

Considering the conditions of the case study, where the sector is mainly composed by smallholders, with low business investment and low technological development, improvements through silvopastoral systems implementation could cause a higher improvement that the one which was conservatively considered in the alternative scenario. Figure 7.2b. shows the estimated production improvement during the horizon planning when silvopastoral systems are implemented in relation with the trending improvement of conventional husbandry. In this regard, the assumed production enhancement is expected to be a high source of uncertainty in the assessment. As a result, scenario uncertainty is included to evaluate the impacts derived from different outcomes level of the policy. Although, some limits are known data is scarce to construct a probability distribution. The analysis made assumptions about the production efficiency improvements derive from the implementation of silvopastoral systems based on yielded results in previous studies. Table 7.11 presents the assumed values for productivity improvement over the assessment period. Table 7.12 shows the sensitivity of the overall results to the variation in each key indicator representing sustainability dimensions. The results indicates that the model is not highly sensitive to assumption about efficiency improvements. Considering higher productivity rates in alternative scenario 2 and 3 derives in only minor reductions on total cumulative cost and GHG emissions. Because of the condition of the model, the goal of total release land is met, and the difference in the minimum required time to reach all of the sustainable goals, is reduced only in one year in alternative scenario 3. On the other hand, the number of agricultural jobs reduce as the productivity rate increases. Alternative scenarios 2 and 3 have increased in the number of jobs lost associated with milk production, 4% and 11%, respectively in comparison with Alternative scenario 1. These results reveal the importance of the chain structure on meeting sustainability objectives. The reallocation of production zones and the construction of production-processing regional clusters result vital to sustainability objectives compliance. In addition, the results stress the importance of land use according to its productive potential. The development of production capacity at specialized dairy regions is a consistent outcome.

Conclusions

This chapter presents the performance of the ex-ante sustainability assessment model to the design of a supply chain network in the dairy industry. A specific case of the Colombian dairy industry has been evaluated. The model uses real data coming from national agencies, sector unions, milk industry's stakeholders to stablish a baseline scenario and to stablish trending conditions to the evaluation of the future development of the sector. The model contrasts, in a multi-period approach, the evolution of the sector when the decisions are guided solely by economic interests and its evolution under environmental policies and national commitments for sustainable development. Based on the sustainable development objectives and national sustainable development commitments, the model establishes desirable target values for the multiple key indicators addressing sustainability identified in Chapter 5.

In the first step the model evaluates the performance of the sector regarding economic criteria. Results for cost structure are in the range of previous analyses considering cost drivers in the dairy industry. It let us in partial extent to validate the results and trust the outcomes of the model. The model yields values for GHG emissions, land use, employment generation and cost for a twenty-year time horizon, while consider trending evolution on milk productivity and ensure informality reduction in the market.

In the second step, the model considers the implementation of an action policy, and calculates the required time to reach the targets in the three dimensions of sustainability as the structure of the supply chain network is modified. The results show the relevance of considering production tier in agri-food supply chains in social and environmental factors. It reaffirms the need for a holistic view of the supply chain when assessing sustainability. Moreover, it shows the relevance of policy application at encompassing efforts to reach sustainable development. Particularly, it shows how the impact on GHG emissions of electric fleet usage for distribution activities might be limited and insufficient to reach accountable results. Meanwhile, support to production activities and the creation of production-processing clusters might represent advantages for the sector.

A sensitivity analysis has been developed to evaluate how different factors related with action and policies application, could have impact in the results. Specifically, we consider, first, policy adoption level that refers to the investment scale for action development, and second, policy effectiveness that allude to the expected improvement of policy application. The results show that sustainable development for the dairy industry in Colombia is a long-term effort, which requires the implementation of joint actions at the national and regional level.

123

Conclusions and future research

This thesis addresses the problem of designing a supply chain network when considering social, environmental, and economic factors. To deal with the problem different modeling approaches are proposed during the development of the project. Indeed, this thesis explores single-objective and multi-objectives modelling approaches, using, individual and composite indicators to represent sustainability criteria at the supply chain level and discuss their applications, opportunities, and shortcomings. Unlike other studies on the matter, which focus mainly on developing computational efficient algorithms, this work is additionally centered on the discussion of sustainability and the link between supply chain management and sustainability assessment. In particular this work is specially interested in the evaluation of sustainability in strategical decisions in the supply chain under policy application.

Recognizing the link between sustainable development and sustainability assessment, this thesis starts by presenting a review on the supply chain network design problem, with an intentional interest in compiling the metrics included in the problem to address with economic, environmental, and social criteria. The work was mainly focused on the evaluation of the indicators used in real application of the network design problem. The review presents the most common criteria used to represent different categories in the three dimensions of sustainability. Briefly, it identifies financial performance being the most predominant category in supply chain management at assessing sustainability at economic level, air pollution in the environmental dimension, and in social dimension, the most influential categories are working conditions and social development.

Besides, the studies were classified according to sector of application and country of origin of the case study. It shows how manufacturing sector has received great attention mainly in Europe and Asian countries. Other sectors, particularly the agricultural sector have been neglected, despite of the relevant interactions of social, environmental and economy factors that converge there. In this regard, the review discusses opportunities to the evaluation of sustainability in other sectors, to explore cases in Latin American countries and to adopt and to define sustainability criteria in relation to the specific greatest challenges faced by every industry. In this sense the proposition is instead of developing generic models to assess sustainability, turn towards the proposition of custom model that address with the real sustainability factor in the industry.

This work considers the assessment of sustainability at supply chain level from two different perspectives.

In the one hand, it considers a corporate sustainability view at supply planning optimization. In Chapter 3, we present a dimension-driven approach, a MILP for the design of a generic supply chain network. The model is solved considering three different objectives, one for each dimension of sustainability. The results show the effect of the decision criteria on the supply chain structure. It is useful to recognize the capacity of improvement in the supply chain by computing ideal values to every dimension considered. Moreover, it exposes the impossibility of reach them all at once due to the conflicting nature of the objectives. Chapter 4 presents, a multi-objective approach to deal with the synchronic inclusion of sustainability criteria. We discuss the different multi-objective approaches in the related academic literature and their ways to deal with decision-maker preferences. Besides, it discusses some shortcomings related to the disregard of setting goals for every dimension at assessing sustainability. The model is solved using a Chebyshev goal programming approach. The non-preference solution's approach led to a feasible solution without establishing biased preferences on the objectives. But, more important, it opens the discussion about targets and time horizon considering sustainable development in supply chains.

On the other hand, this work addresses sustainability in a wide-industry perspective. This work discusses the need of holistic view at addressing sustainability in long-term decisions at supply chain level, since the separated and individual efforts from companies might not cause the reduction of emissions that is required to achieve national and global commitments to climate change and sustainable development. Therefore, this work contributes to the definition of an ex-ante sustainability assessment model to the design of the supply network in the dairy sector in Colombia presented in Chapter 6. The multi-period model deals with the mega-location of production, processing, and distribution facilities to meet a set of sustainability objectives under the application of policies and actions. Unlike previous works adopting a trade-off mentality on economic, environmental, and social performance, the model aims to meet defined target for the defined key indicators in each dimension of sustainability, as modifying the structure of the supply chain over a time horizon. As a novel modeling aspect, the evaluation includes the use of land for agricultural activities and their transformation into sustainable practices.

The model examines different scenarios, considering variability for relevant parameters on the policy execution, and their outcomes were compared. The results in Chapter 7 shown the relevance of creating production-processing clusters taking advantage of the potential land use. Besides, the results shown the loss of productive units and jobs in the sector because of the productive transformation. These results are consistent with productive transformations of agricultural sector in other countries [START_REF] Cadena | Precio Regulado de la Leche: Ineficiencias, Costos y Alternativas[END_REF]. The model may give insights for policymakers as it shows the need for supportive economic, social, and environmental policies to the fulfillment of sustainability objectives. Public administration plays a fundamental role in promoting innovation and sustainability among enterprises. It is also in charge of facilitating capital access, regional capabilities construction and the definition of lever and incentives as encouraging voluntary behavior change [START_REF] Paletta | A Step-by-Step Process towards an Evolutionary Policy Encouraging the Adoption of Sustainable Business Models[END_REF]. It also results useful for companies to support strategic decisions since it may identify promising supplier regions, define the organization of productionprocessing clusters, and point out the main drivers for sustainability in the sector.

Considering the relevance of understanding the industry at assessing sustainability, this work dedicates a separated section to present an overview of the dairy industry in Colombia. It discusses the relevance of the sector considering national greenhouse gas inventory and social conditions. It discusses the importance of considering stakeholder's sustainability definition to identify key indicators criteria in the three dimensions of sustainability. Hence, although there exists common factor to assess sustainability at supply chain level, it is important to verify, the relevance of these factors in the context of the industry. At least two reasons might be mentioned in this regard. First, the availability of data, to measure and control the proposed key indicator. Second, the relation between the factor and the current challenges of the sector to move towards sustainable development.

As a part of the description of the case study, we present a brief of the planned mitigation and adaptation policies and actions in the agricultural sector and the relation with environmental and social factors. By considering the most related and promising action to be implemented in the sector, we evaluate future scenarios to the productive transformation of the sector. The results show the inherence of policy in sector development and its major role in the promotion of sustainable development paths. It shows as well that sustainable development for the dairy industry in Colombia is a long-term effort, which requires the implementation of joint actions at the national and regional level.

This work contributes to the discussion on sustainability assessment and the need of establishing sustainability goals at addressing supply chain management decisions, here particularly, in supply chain design. As stated by [START_REF] Pope | Conceptualising sustainability assessment[END_REF] assessing sustainability requires a well-defined concept of sustainability. Efforts might fall short at presenting alternative solutions when targets are not defined. In this regard, this work highlights the relevance of assessing improvements within a context in which desired targets or goals are discussed. Moreover, it examines the definition of sustainability key performance indicators consequently with what sustainability means for the stakeholders in the specific case of study here presented.

It also presents a set of key indicator performance to assess sustainability in the agrifood sector, specifically in the dairy industry in the long-term. Decisions at the strategical level of supply chain, might define tracks for improvements and actions at tactical and operational level. In this sense, decisions in the long-term play a significant role at limiting improvement potential of decisions in a shorter action period. The performance of the ex-assessment sustainability assessment model is tested on a case study in Colombia, a developing economy, with realistic data coming from trade unions and public entities in the country. Few works have considered a wide-industry perspective to the evaluation of sustainability in the design of supply chains and in the best of our knowledge, no work have presented an ex-ante sustainability model to the evaluation of policies in the long-term and its impacts on industry structure.

Additionally, on the basis of the work developed in this thesis, some ways for further research are suggested below. First, it focuses in the definition of key performance indicators for assessing sustainability in the context of the case under study. In this regard, more attention should be given to the accurate definition of sustainability criteria at evaluating strategical decisions in the supply chain context. Definition of metrics and measurement methods must foster an interdisciplinary approach which includes future views or prospective analysis from local authorities, trade unions, public administration, scientific counselors and managers, closing the gap between ecology and supply chain management field at addressing sustainability [START_REF] Blass | Same Supply Chain, Different Models: Integrating Perspectives from Life Cycle Assessment and Supply Chain Management[END_REF]. A proper definition of sustainability will allow for an appropriate selection of sustainability measurement criteria. This provides guidance to bring supply chain participants and outsider institutions together towards a common goal and minimizes the risk of greenwashing.

There is a void to fill regarding the development of social aspects at addressing long-term decisions in supply chain management. Although quantifying social aspects is a complex and challenging task. The definition of indicators based on social indexes and the association of them to SDG's offer the opportunity of establishing a framework and a goal for those criteria. However, it is important to stablish clear and measurable implications between supply chain management decisions and social aspects. Although, this effect uses to be clearer in operational and tactical decisions, such as, labor gender equity, fair payment rates or health conditions, among others. This relation often vanishes or blurs at evaluating long-term decisions. For instance, economy development by industrialization is not straightforward a solution for poverty reduction. Economy growth may or may not come together with growth on inequality during the development process depending on national characteristics, including how growth is achieved and mainly the policies to achieve it [START_REF] Kniivila | Industrial development and economic growth Implications for poverty reduction and income inequality[END_REF].

Regarding the modelling features, other realistic assumptions like imports and exports can be included into consideration. Globalization and free trade agreements represent a big challenge to meet environmental and social objectives. For instance, specialization and automation offer higher productivity rates in developing countries. Countries tend to produce commodities for which they have a comparative advantage offering low prices products in the existence of trade agreements. It might increase food footprint, and become a threat for local producers. In this regard, the model might deal with maximum quotas or taxes to analyze the behavior of the industry and serve as a support for policymakers.

Finally, uncertainty might be considered, regarding two elements. First, uncertainty as a characteristic of long-term decisions. It comprises parameters on the market, such as, supply, demand and costs. Despite accuracy on forecasting methods, decisions in the long-term are always subject to variability. Moreover, uncertainty could be associated to environmental assessment methodologies as it may or may not include some sources of GHG emissions [START_REF] Sonnemann | Uncertainty assessment by a Monte Carlo simulation in a life cycle inventory of electricity produced by a waste incinerator[END_REF]. In this sense, instead of establishing a unique value, it could be useful to consider an interval that with a certain level of confidence contains the actual contribution by unit of aggregation. Consideration of uncertainty may lead to more robust solutions. In this regard, solution approaches combining simulation and optimization techniques might be useful to deal with uncertainty at multiple parameters. To this aim input parameters are considered random but restricted by a known probability distribution for each parameter. Repeated executions permit the evaluation of multiple baseline scenarios and produce a distribution of output values, reflecting the combined uncertainty of multiple parameters.

Second, uncertainty on policy implementation and on policy efficiency. While the first case deals with parameter uncertainty, the second case deals with scenario uncertainty. In this case multiple methodological choices are available to implement. For instance, previous to the definition of action and policies, some pilots tests are carried out on a small scale, or expected results are calculated from the application of the same policy in an environment with similar conditions. However, results on implementation might variate for several factors including social and ecological conditions, and the construction of capacities to fund and construct the required capacities to support the development of the policy. Therefore, expected results coming from policy or action application might be different from the initially expected. Understanding uncertainty might provide useful insights to apply conservative assumptions.

The purpose of this work is to propose an efficient assessment procedure for the joint assessment of economic, environmental, and social performance for the design or redesign of supply chain network. A mathematical formulation considering the evolution of the supply chain and the construction of capacities in the long term is presented. To this regard, we define sustainability objectives according to the current conditions of the sector and the country. We compare the supply chain structure changes over a time horizon following an ex-ante sustainability assessment approach. Moreover, sustainability key performance indicators are chosen considering current sustainability challenges of the sector. The performance of the model is tested with an application in the dairy industry in a developing-economy country. It illustrates the utility of the model to evaluate national mitigation and adaptation activities in the design of supply chain networks. The need of setting targets when measuring sustainability in the supply chain field is highlighted.

Results offer meaningful decision support to policymakers in evaluating implementation of policies and actions, and in the definition of strategical paths towards sustainability.

  Figure 0.1. Structure du document ............................................................................................................. xiv

  Figure 0.1. Structure du document ............................................................................................................. xiv Figure 1.1. Document structure ....................................................................................................................

Figure 2

 2 Figure 2.1. Overview of the chapter ...........................................................................................................

Figure 2

 2 Figure 2.2. Supply chain network design activities by decision level ........................................................

Figure 2

 2 Figure 2.3. Classification scheme for sustainability indicators ...................................................................

Figure 2

 2 Figure 2.4. Relative frequency of use of cost drivers .................................................................................

Figure 2

 2 Figure 2.5. GHG emissions scopes .............................................................................................................

Figure 2 . 6 .

 26 Figure 2.6. Driver factor for GHG emissions environmental impact assessment .......................................

Figure 2

 2 Figure 2.7. Number of studies per continent ...............................................................................................

Figure 3

 3 Figure 3.1. Network structures ....................................................................................................................

Figure 4

 4 Figure 4.1. Structute of the forward supply chain .......................................................................................

Figure 4

 4 Figure 4.2. Cost drivers for the individual objectives .................................................................................

Figure 4 . 3 .

 43 Figure 4.3. CO2eq emissions for transportation activities at different tiers ................................................

Figure 5

 5 Figure 5.1. Case study location ...................................................................................................................

Figure 5

 5 Figure 5.2. Colombian greenhouse gas inventory by 2014 .........................................................................

Figure 5

 5 Figure 5.3. Destination national production of milk per year in 2019 ........................................................

Figure 5

 5 Figure 5.4. Structure of the Colombian dairy supply chain ........................................................................

Figure 5

 5 Figure 5.5. Livestock farms size in Colombia ............................................................................................

Figure 5 . 6 .

 56 Figure 5.6. National livestock productive orientation and milk production in 2019 ..................................

Figure 5 . 7 .

 57 Figure 5.7. National production of milk from 2010 to 2019 .......................................................................

Figure 5 . 8 .

 58 Figure 5.8. Production and formal collection of milk per year ...................................................................

Figure 5 . 9 .

 59 Figure 5.9. Market share distribution in the dairy industry .........................................................................

Figure 5 .

 5 Figure 5.10. Total apparent consumption of milk and apparent consumption per capita ...........................

Figure 5 .

 5 Figure 5.11. GHG inventory emissions of agricultural and forestry sector ................................................

Figure 5 .

 5 Figure 5.12. Labor type participation per farm size. ...................................................................................

Figure 5 .

 5 Figure 5.13. Average milk consumption per capita by socioeconomic status ............................................

Figure 5 .

 5 Figure 5.14. Value pyramid of the dairy sector ..........................................................................................

Figure 5 .

 5 Figure 5.15. Simplified Input-Process-Output milk production and dairy processing processes ...............

Figure 6 .

 6 Figure 6.1. SAT's classification categories ................................................................................................

Figure 6 .

 6 Figure 6.2. Framework of the model...........................................................................................................

Figure 6 .

 6 Figure 6.3. Dairy supply chain under study ................................................................................................

Figure 6 .

 6 Figure 6.4. Optimization strategy ...............................................................................................................

Figure 7

 7 Figure 7.1. Supply chain locations and capacities ....................................................................................

Figure 7

 7 Figure 7.2. (a) Collection of milk, and (b) farm productivity over the time horizon ................................

Figure 7

 7 Figure 7.3. Costs structure, GHG emissions sources, use of land, and employment distribution conditions in the baseline scenario .............................................................................................................................

Figure 7

 7 Figure 7.4. Evolution of processing and storage capacities from (a) Year 1 to (b) Year 20 .....................

Figure 7

 7 Figure 7.5. Employment creation in the baseline scenario .......................................................................

Figure 7 . 6 .

 76 Figure 7.6. GHG emissions comparison under policy implementation ....................................................

Figure 7

 7 Figure 7.7. Cumulative cost comparison between scenarios ....................................................................

Figure 7

 7 Figure 7.8. GHG Comparison in emissions from transport activities between baseline and alternative scenarios ....................................................................................................................................................

Figure 7

 7 Figure 7.9. Production -Processing regional clusters ...............................................................................

Figure 7 .

 7 Figure 7.10. Use of land according to baseline and alternative scenarios ................................................

Figure 7 .

 7 Figure 7.11. Production and storage capacity in the alternative scenario .................................................

Figure 7 .

 7 Figure 7.12. Employment in farming activities ........................................................................................

Figure 7 .

 7 Figure 7.13. Electric fleet capacity in the alternative scenario .................................................................

Figure 7 .

 7 Figure 7.14. Time to sustainability graphic summary...............................................................................

Figure

  Figure 0.1. Structure du document

Figure 1

 1 Figure 1.1. Document structureTo this purpose a systematic literature review was carried out with a specific scope in metrics and measurement methods for sustainability assessment in SCND. In the academic literature, reviews in the field of sustainability and supply chain management might be classified according to its scope in five categories (a) Summary of progress and trends in SSCM, (b) Tracking sustainability concept and its evolution in the SC field, (c) Solution methodologies for SSCM, (d) Review on specific supply chain activities with sustainability purpose, and (e) Sustainability performance measurement and identification of metrics. The literature review on this project belongs to category (e) and it is presented in Chapter 2. For presenting a complete state of the art in the matter, other relevant articles have been added to the literature review chapter in this document, since they might be excluded from the intended scope of the initial review.

  Chapter 5. It presents a wide context of the case study, at defining what sustainability means for stakeholders and participants in the dairy supply chain in Colombia. It also presents the key performance indicators for the evaluation of sustainability considering supply chain network design. Till that point on, the scope of the research goes from corporate perspective to a sectorial perspective. During the development of this project, relevant political actions, related with sustainable development and climate change, have taken place. Particularly, in the context of the United Nations Framework Convention on Climate Change, and specifically COP21 in Paris. The Intended National determined contributions reports have been in construction and the initial version of National determined contribution (NDC) have been submitted by December 2020, following the Paris Agreement. NDC's present the auto-imposed compromises of the parties to transform their development trajectories to set the world on a course towards sustainable development. It displays each country's strategy, plans, and actions to reduce national emissions and adapt to the impacts of climate change providing numerical mitigation targets for 2025 and/or 2030

  Figure 2.1 presents an overview of the content of the chapter.

Figure 2 . 1 .

 21 Figure 2.1. Overview of the chapter

Figure

  Figure 2.3. Classification scheme for sustainability indicators (Chardine-Baumann & Botta-Genoulaz, 2014) 3.1. Economic indicators

Figure 2 .

 2 Figure 2.4 presents a summary of the relative frequency of use of the set of cost drivers identified during the review.

Figure 2 . 4 .

 24 Figure 2.4. Relative frequency of use of cost drivers (Moreno-Camacho et al., 2019)

Figure 2 . 6 .

 26 Figure 2.6. Driver factor for GHG emissions environmental impact assessment (Moreno-Camacho et al., 2019)

  Figure 2.7. Number of studies per continent .

Figure 2

 2 Figure 2.7. Number of studies per continent (Moreno-Camacho et al., 2019)

Figure 3

 3 Figure 3.1. Network structures

Figure 4

 4 Figure 4.1. Structute of the forward supply chain A description of the assumptions considered to the construction of the model is presented here below. Decisions on the location of plants and distribution centers in the regions are guided by two types of costs.Fixed costs, related to the capacity of the facility, are paid only if the corresponded facility is selected. Variable costs are related to the total volume of production at the corresponding facility. In our study only road transportation is available. However, given the plurality of road conditions to access farms, distribution centers in small villages, or retailers in downtown, etc., different types of trucks are considered. It is assumed that a restricted set of suitable transportation modes has been identified a priori for each supplier and retailer, considering the road characteristics. For instance, due to road conditions, such as road width, freight weight restrictions and so on, some suppliers, collection centers or retailers might present restrictions to the use of certain types of trucks. The model considers three types of trucks, namely, light truck, medium truck, and heavy truck, all conditioned for the transport of refrigerated freight and differentiated by different load capacities and consumption of fuel. The transportation cost is assumed linear in function to the quantity carried and the covered distance to each type of truck. GHG emissions are calculated by multiplying the consumption of fuel by its correspondent emission factor.

  𝑥 𝑠𝑝𝑚 : quantity of litters of raw milk shipped from supplier 𝑠 ∈ 𝑆 to processing plant 𝑝 ∈ 𝑃 delivered in vehicle type 𝑚 ∈ 𝑀 𝑥 𝑝𝑑𝑡 : quantity of aggregated units of processing milk delivered from processing plant 𝑝 ∈ 𝑃 to distribution center 𝑑 ∈ 𝐷 by vehicle type 𝑡 ∈ 𝑇 𝑥 𝑑𝑟𝑡 : quantity of aggregated units of processing milk sent from distribution center 𝑑 ∈ 𝐷 to retailer 𝑟 ∈ 𝑅 by vehicle type 𝑡 ∈ 𝑇 𝑦 𝑠 : equal to 1 if supplier 𝑠 ∈ 𝑆 supplies any quantity of raw milk to processing plants or collecting centers, 0 otherwise.𝑦 𝑝𝑐𝑝 : equal to 1 if a processing plant is in potential zone 𝑝 ∈ 𝑃 with capacity 𝑐𝑝 ∈ 𝐶𝑃 𝑦 𝑑𝑐𝑑 : equal to 1 if a distribution center is open in potential zone 𝑑 ∈ 𝐷 with capacity 𝑐𝑑 ∈ 𝐶𝐷 Parameters We distinguish parameters in three different aspects: location, production, and transportation costs in the economic dimension. 𝐿𝐶 𝑐𝑝 : fixed cost of opening a processing plant with capacity 𝑐𝑝 ∈ 𝐶𝑃 𝐿𝐶 𝑐𝑑 : fixed cost of opening a distribution center with capacity 𝑐𝑑 ∈ 𝐶𝐷 𝑃𝑟 𝑠 : Price of raw milk per ton at supplier s∈ 𝑆 𝑃𝐶: processing cost per aggregated unit at processing plants 𝐷𝑖𝑠𝑡1 𝑠𝑝 : Distance in km between the supplier 𝑠 ∈ 𝑆 and the processing plant 𝑝 ∈ 𝑃 𝐷𝑖𝑠𝑡2 𝑝𝑑 : Distance in km between the processing plant 𝑝 ∈ 𝑃 and the distribution center 𝑑 ∈ 𝐷 𝐷𝑖𝑠𝑡3 𝑑𝑟 : Distance in km between the supplier 𝑑 ∈ 𝐷 and the retailer 𝑟 ∈ 𝑅 𝑇𝐶 𝑡 : transportation cost per ton of milk in transport 𝑡 ∈ 𝑇 𝐶𝑆 𝑠 : maximum supply capacity of supplier 𝑠 ∈ 𝑆 𝐶𝑀 𝑐𝑝 : production capacity of a processing plant with capacity 𝑐𝑝 ∈ 𝐶𝑃 𝑀𝑜𝑝: maximum desired occupation rate of processing facilities 𝑀𝑢𝑝: minimum allowed operation rate for processing plants 𝐶𝐷𝐶 𝑐𝑑 : storage capacity at distribution center with capacity 𝑐𝑑 ∈ 𝐶𝐷 𝑀𝑢𝑑𝑐: minimum allowed operation rate for distribution centers 𝐷𝑒𝑚 𝑟 : Demand of retailer 𝑟 ∈ 𝑅 𝑇𝑟𝑣 𝑠𝑚 : equal to 1 if vehicle type 𝑚 ∈ 𝑀 have access to retailer 𝑠 ∈ 𝑆 𝑇𝑟𝑣 𝑟𝑡 : equal to 1 if transport type 𝑡 ∈ 𝑇 have access to retailer 𝑟 ∈ 𝑅 𝐹𝑐𝑜𝑛𝑠 𝑚 : Fuel efficiency of vehicle type 𝑚 ∈ 𝑀 kilometers per gallon 𝐹𝑐𝑜𝑛𝑠 𝑡 : Fuel efficiency of vehicle type 𝑡 ∈ 𝑇 kilometers per gallon 𝐶𝑎𝑝 𝑚 : Capacity in tons of milk of vehicle type 𝑚 ∈ 𝑀 𝐶𝑎𝑝 𝑡 : Capacity in tons of milk of vehicle type 𝑡 ∈ 𝑇 We use the following notation in referring to the environmental factors of the model 𝐸𝑚𝑓𝑐: CO2e emission produced per consumed gallon of fuel 𝐸𝑚𝑝𝑟: CO2e emissions produced per ton of milk processed at the plant Additionally, we use the following parameters evaluating the social performance in the social dimension 𝐽𝑜 𝑐𝑝 : jobs opportunities created by locating a processing facility with capacity 𝑐𝑝 ∈ 𝐶𝑃 𝑈𝑟 𝑝 : Unemployment rate at the potential location of processing plant 𝑝 ∈ 𝑃 𝜑 𝑠 : Added value factor of the region of supplier 𝑠 ∈ 𝑆

Figure 4

 4 Figure 4.2. Cost drivers for the individual objectives

Figure 4

 4 Figure 4.3. CO2eq emissions for transportation activities at different tiers

Figure 5

 5 Figure 5.1. Case study location Source: Modified from COL Orthographic. License: CC BY-SA 3.0

Figure 5

 5 Figure 5.2. Colombian greenhouse gas inventory by 2014 Data source: (IDEAM, 2016)

Figure 5 . 3 .

 53 Figure 5.3. Destination national production of milk per year in 2019 Data source: FEDEGAN 2020

Figure 5 . 4 .

 54 Figure 5.4. Structure of the Colombian dairy supply chain Source: National Dairy Council

Figure 5 . 5 .

 55 Figure 5.5. Livestock farms size in Colombia Data source: FEDEGAN 2018

Figure 5 . 6 .

 56 Figure 5.6. National livestock productive orientation and milk production in 2019 Data source: FEDEGAN, 2019, UPRA 2019 During the last decade, milk production has grown by 1.6% on average per year, as shown in Figure 5.7. It had a remarkable recovery over the last three years, after the devastating consequences of the El Nino phenomenon during 2015 and 2016, which caused 40 thousand animal casualties and more than 700 thousand displaced animals due to flooding of fields and pastures.

Figure 5 . 7 .

 57 Figure 5.7. National production of milk from 2010 to 2019 Data source: FEDEGAN, 2020

  Figure 5.8. Production and formal collection of milk per year Data source: FEDEGAN 2020, UPS 2020

Figure 5

 5 Figure 5.9. Market share distribution in the dairy industrySource:[START_REF] Asoleche | Ranking Lácteo[END_REF]

Figure 5 .

 5 Figure 5.10. Total apparent consumption of milk and apparent consumption per capita Data source: (FEDEGAN, 2020)

Figure 5 .

 5 Figure 5.11. GHG inventory emissions of agricultural and forestry sector Data source: (IDEAM, 2016)

Figure 5 .

 5 Figure 5.12. Labor type participation per farm size.Source:[START_REF] Fedegan | Plan Estratégico de la Ganadería Colombiana[END_REF]

  Figure 5.13. Average milk consumption per capita by socioeconomic status Data source: FEDEGAN, 2018

  Figure 5.15. Simplified Input-Process-Output milk production and dairy processing processesSource: (a)[START_REF] Garg | Greenhouse gas emission intensity based on lifetime milk production of dairy animals, as affected by ration-balancing program[END_REF], (b)[START_REF] Nutter | Greenhouse gas emission analysis for USA fluid milk processing plants: Processing, packaging, and distribution[END_REF]

Figure 5 .

 5 Figure 5.16. Marginal abatement cost curve of the agricultural sectorSource:[START_REF] Behrentz | Productos Analíticos para Apoyar la Toma de Decisiones Sobre Acciones de Mitigación a Nivel Sectorial: Sector Agropecuario[END_REF]

Figure 6 .

 6 Figure 6.2. Framework of the model

Figure 6 .

 6 Figure 6.3. Dairy supply chain under study

Figure 6 .

 6 Figure 6.4. Optimization strategy Optimization Strategy 1 -Baseline Scenario: Cost-driven supply chain network decision-makingThe first optimization strategy, known as Business as Usual scenario (BAU), consists of defining the structure of the supply chain in the long term, based on the total operational costs. To this aim, the model includes equations (1) to (20), being equation (19) the objective function. The single objective function includes the total processing and the total transportation costs.

Figure 7 . 3 .

 73 Figure 7.3. Costs structure, GHG emissions sources, use of land, and employment distribution conditions in the baseline scenario

Figure 7 .

 7 Figure 7.4 presents a comparison between the initial state of the network and the final situation of it regarding the allocation of processing and storage capacities. The size of the circle is associated with the amount of installed capacity in each region. In broad sense, processing capacity increases by 29% over the time horizon. The most notable changes are Cordoba, Magdalena, and Nariño, where it is at least doubled (green squares in Figure 7.4b). Other regions like Caldas and Quindío suffer a total reduction in capacity until the disappearance of the processing industry (red square in Figure 7.4a). Concerning storage capacity at distribution centers, it increases around 27% during the 20 years window. The most significant variations are presented in Meta and Valle del Cauca, where the storage capacity grows up to four times with respect to the year 1(orange triangles in b).

  Figure 7.4. Evolution of processing and storage capacities from (a) Year 1 to (b) Year 20

Figure 7

 7 Figure 7.5. Employment creation in the baseline scenario

Figure 7 . 6 .

 76 Figure 7.6. GHG emissions comparison under policy implementation

Figure 7 . 7 .

 77 Figure 7.7. Cumulative cost comparison between scenarios

Figure 7 .Figure 7 .

 77 Figure 7.10. Use of land according to baseline and alternative scenarios

Figure 7 .

 7 Figure 7.13. Electric fleet capacity in the alternative scenario

  ...

	Acronyms
	AFOLU	Agriculture, Forestry and Other Land use
	CONPES	National Council for Economic and Social Policy -Colombia
	DANE	National Administrative Department of Statistics -Colombia
	DNP	National Planning Department -Colombia
	FAO	Food and Agriculture Organization of the United Nations
	FEDEGAN Colombian Federation of Ranchers
	FEPALE	Pan-American Dairy Federation
	GDP	Gross Domestic Product
	GHG	Greenhouse gas
	GWP	Global Warming Potential
	ICA	Colombian Agricultural Institute
		Institute of Hydrology, Meteorology and Environmental Studies -
	IDEAM	Colombia
	IGAC	Agustin Codazzi Geographical Institute -Colombia
	IPCC	Intergovernmental Panel for Climate Change
	M.A.S.L	Meters Above Sea Level
	MADR	Ministry of Agriculture and Rural Development -Colombia
	MADS	Ministry of Environment and Sustainable Development -Colombia
	MCIT	Ministry of Commerce, Industry and Tourism -Colombia
	MILP	Mixed Integer Linear Programming
	NAMA	National Appropriate Mitigation Action
	ODS	Ozone-Depleting Substances
	OECD	Organization for Economic Co-operation and Development
	PTP	Program for productive transformation -Colombia
	SCM	Supply Chain Management
	SCND	Supply Chain Network Design
	SDG	Sustainable Development Goals
	SSCND	Sustainable Supply Chain Network Design
	UPRA	Agriculture Planning Unit -Colombia
	USP	Milk Price Monitoring Unit -Colombia
		ix x

  la durabilité au niveau de la chaîne d'approvisionnement. Il est possible de travailler au développement de modèles non génériques qui évaluent la durabilité tout en considérant des objectifs réalisables dans chaque dimension observée.

La performance du modèle d'évaluation de la durabilité ex-ante est testée sur une étude de cas en Colombie, une économie en développement, avec des données réalistes provenant des syndicats et des entités publiques du pays. Peu de travaux ont pris en compte une perspective industrielle large pour l'évaluation de la durabilité dans la conception des chaînes d'approvisionnement et, à notre connaissance, aucun travail n'a présenté un modèle de durabilité ex ante pour l'évaluation des politiques à long terme et ses impacts sur la structure industrielle. Les résultats de ce travail mettent en évidence le lien entre la durabilité et les outils xvii de mesure de xviii This page intentionally left blank Introduction In 1987, the publication "Our common future," from the World Commission on Environment and Development of the United Nations opened, at the global level, the discussion about sustainable development and sustainability as a final goal (WCED

Table 1

 1

	.1. Publication outputs of this research
	Reference	Publication type	Indexed	Related chapter
	C.A. Moreno-Camacho, J.R. Montoya-Torres,
	A. Jaegler, N. Gondran, "Sustainability metrics
	for real case applications of the supply chain
	network design problem: A systematic
	literature review", Journal of Cleaner
	Production, Vol. 231, September 2019, pp.
	600-618.

Table 1 .

 1 1. Publication outputs of this research (continued)

	Reference	Publication type	Indexed	Related chapter
	C.A. Moreno-Camacho, J.R. Montoya-Torres,	On-line Workshop	n.a.	Ch. 6
	A. Jaegler, N. Gondran, "Sustainable Supply	Proceedings-Book
	Chain Network Design in the Dairy Industry",
	9 th International Workshop on Advances in
	Cleaner Production, (On line), Melbourne,
	Australia
	C.A. Moreno-Camacho, J.R. Montoya-Torres,	Poster at doctoral	n.a.	Ch. 3
	A. Jaegler, N. Gondran, "Evaluating economic,	school
	environmental and social criteria in supply
	chain network design", XXIII Ibero Latin
	America Summer School of Operational
	Research (ELAVIO'19), Lleida, Spain.

Partial content of this chapter is published in Moreno-Camacho, C. A., Montoya-Torres, J. R., Jaegler, A., & Gondran, N. (2019). Sustainability metrics for real case applications of the supply chain network design problem: A systematic literature review. Journal of Cleaner Production, 231, 600-618. https://doi.org/10.1016/j.jclepro.2019.05.278

Table 2 .

 2 1. Modeling approaches for SSCND

	Modeling approach	Reference
	Single objective
		Eco + Env
	Deterministic

Table 2

 2

	Sector	Total	Sector	Total
	Bioenergy	25	Commerce	4
	Technology	19	Agrobusiness	3
	Food & Beverage	12	Pharmaceutical	2
	Industrial goods	10	Timber	2
	Automotive	9	Mining	2
	Fashion	7	Construction	1
	Energy	6	Information & Communication	1
	Chemicals	5	Steel	1
	Home & Office products	4

.2. Number of studies by economic sector from 2015 to 2018

[START_REF] Moreno-Camacho | Sustainability metrics for real case applications of the supply chain network design problem: A systematic literature review[END_REF]

  𝑗 𝑚𝑡 : number of jobs created in the facility of manufacturer 𝑚 equipped with technology 𝑡 𝜑 𝑠 : social index associated with active supplier 𝑠

	𝑠 suppliers 𝑚 manufacturers 𝑑 warehouses 𝑟 retailers 𝑡 technologies 𝑓 fleet Parameters 𝐺: Big number Variables Integer decision variables with 𝑠 = 1, 2, … , 𝑆 with 𝑚 = 1, 2, … , 𝑀 with 𝑑 = 1, 2, … , 𝐷 with 𝑟 = 1, 2, … , 𝑅 with 𝑡 = 1, 2, … , 𝑇 with 𝑓 = 1, 2, … , 𝐹 𝑑𝑒𝑚 Auxiliar parameters 𝑥

𝑟 : demand of retailer 𝑟 𝑐𝑎 𝑚𝑡 : production capacity of manufacturer 𝑚 equipped with technology 𝑡 𝑚𝑜𝑓 𝑚 : minimum expected operational efficiency of manufacturer m 𝑐𝑎 𝑑 : inventory capacity in warehouse 𝑑 𝑚𝑠𝑢𝑝 𝑠 : minimum order quantity from active suppliers Cost parameters 𝑐𝑝 𝑚𝑡 : unitary production cost at manufacturer 𝑚 equipped with technology 𝑡 𝑐𝑡 𝑠𝑚 : unitary transportation cost from supplier 𝑠 to manufacturer 𝑚 𝑐𝑡 𝑚𝑑 : unitary transportations cost from supplier 𝑚 to warehouse 𝑑 𝑐𝑓𝑥 𝑚𝑡 : fix operational cost of manufacturer 𝑚 equipped with technology 𝑡 𝑐𝑓𝑥 𝑑 : fix operational cost of warehouse 𝑑 CO2 emissions parameters 𝑒 𝑠𝑚 : contribution of CO2 emissions per unit during transportation from supplier 𝑠 to manufacturer 𝑚 𝑒 𝑚𝑑 : contribution of CO2 emissions per unit during transportation from manufacturer 𝑚 to warehouse 𝑤 𝑒 𝑑𝑟 : contribution of CO2 emissions per unit during transportation from warehouse 𝑑 to retailer 𝑟 𝑒𝑝 𝑚𝑡 : contribution of CO2 emissions per unit during production process at manufacturer 𝑚 equipped with technology 𝑡 𝑒𝑝 𝑑 : contribution of CO2 emissions per unit during handling product at distribution center 𝑑 Social parameters 𝑠𝑚 : units of raw material transported from supplier 𝑠 to manufacturer 𝑚 𝑦 𝑚𝑡𝑑 : units of final product transported from manufacturer 𝑚 equipped with technology 𝑡 to warehouse 𝑑 𝑤 𝑑𝑓𝑟 : units of final product transported from warehouse 𝑑 to retailer 𝑟 using fleet type 𝑓 Binary decision variables 𝛿 𝑚𝑡 : 1 if manufacturer 𝑚 equipped with technology 𝑡 is open, 0 otherwise 𝛾 𝑑 : 1 if warehouse 𝑑 is open, 0 otherwise 𝜆 𝑠 : 1 if supplier 𝑠 is active, 0 otherwise

  1 = ∑ 𝑓𝑥 𝑚 * 𝛿 𝑚𝑡

		+ ∑ 𝑓𝑥 𝑑 * 𝛾 𝑑	+ ∑ 𝑐𝑡 𝑠𝑚 * 𝑥 𝑠𝑚	+ ∑(𝑐𝑡 𝑚𝑑 + 𝑐𝑝 𝑚𝑡 ) * 𝑦 𝑚𝑡𝑑
	𝑚,𝑡	𝑑	𝑠,𝑚	𝑠,𝑚
	+ ∑ 𝑐𝑡 𝑑𝑟 * 𝑤 𝑑𝑓𝑟
	𝑠,𝑚

Table 3

 3

	.1. Range of social performance metrics
	Metric	𝑀𝑖𝑛 𝑖	𝑀𝑎𝑥 𝑖
	𝐽 𝑚𝑡	272	461
	𝜑 𝑠	0.307	4.656

Table 3 .

 3 2 presents the results of every key indicator when the decision is guided by the objective in the second row. Optimal values for each dimension one of the measures in the three dimensions of sustainability are in bold. The different structures of the supply chain network based on the decision criteria of each one of the dimensions of sustainability are presented in Figure3.1

		Table 3.2. Results for the separated evaluations
			Objective
	Dimension	Economic	Environmental	Social
	Economic	8.80931E+07	1.16083E+08	1.79956E+08
	Environmental	62.4810	30.6245	90.8294
	Social	1.6334	1.8515	0.1380
	Jobs	272	223	448
	Suppliers	1.901	2.080	4.3550

  ) limits the total amount of raw milk shipped from supplier s ∈ S to processing plants p ∈ P to the capacity of each supplier. Constraint (8) establishes bounds for the quantity of production at each opened processing plant. Constraint (9) ensures that the capacity of the distribution center is not exceeded.

			∑ 𝑥 𝑠𝑝𝑚	= ∑ 𝑥 𝑝𝑑𝑡	∀ 𝑝 ∈ 𝑃	(5)
		𝑠∈𝑆,𝑚∈𝑀		𝑑∈𝐷,𝑡∈𝑇
			∑ 𝑥 𝑑𝑟𝑡	= ∑ 𝑥 𝑝𝑑𝑡	∀ 𝑑 ∈ 𝐷	(6)
		𝑟∈𝑅,𝑡∈𝑇		𝑝∈𝑃,𝑡∈𝑇
	Facilities capacity constraints
			∑ 𝑥 𝑠𝑝𝑚	≤ 𝐶𝑆 𝑠 * 𝑦 𝑠	∀ 𝑠 ∈ 𝑆	(7)
			𝑝∈𝑃,𝑚∈𝑀
	∑ 𝑥 𝑝𝑑𝑡	≤ ∑ 𝐶𝑀 𝑐𝑝 * 𝑦 𝑝𝑐𝑝 * 𝑀𝑜𝑝	∀ 𝑝 ∈ 𝑃	(8)
	𝑑∈𝐷,𝑡∈𝑇		𝑐𝑝∈𝐶𝑃
			∑ 𝑥 𝑑𝑟𝑡	= ∑ 𝑥 𝑝𝑑𝑡	∀ 𝑑 ∈ 𝐷	(9)
		𝑟∈𝑅,𝑡∈𝑇		𝑝∈𝑃,𝑡∈𝑇
	Constraint (7Transportation availability
		∑ 𝑥 𝑠𝑝𝑚	≤ 𝐶𝑆 𝑠 * 𝑇𝑟𝑣 𝑠𝑚	∀ 𝑠 ∈ 𝑆, 𝑚 ∈ 𝑀	(10)
		𝑝∈𝑃
	∑ 𝑥 𝑑𝑟𝑡	≤	∑ 𝐶𝐷𝐶 𝑐𝑑 * 𝑦 𝑑𝑐𝑑 * 𝑇𝑟𝑣 𝑟𝑡	∀ 𝑟 ∈ 𝑅, 𝑡 ∈ 𝑇	(11)
	𝑑∈𝐷	𝑑∈𝐷,𝑐𝑑∈𝐶𝐷
					𝑑𝑟𝑡	= 𝐷𝑒𝑚 𝑟	∀ 𝑟 ∈ 𝑅	(4)
			𝑑∈𝐷,𝑡∈𝑇

Table 4

 4

	.1. Results for single objective linear programming models
		Sustainability performance indicators
	Optimizing objective	Total cost (COP '000M)	CO2 emissions (Ton)	Jobs quantity	Suppliers
	(1) Economic objective	278.7*	46,015	130	0.994	19
	(2) Environmental objective	297.1	44,513*	130	1.024	24
	(3) Social objective	279.8	47,633	130	1.28*	23
	*Ideal value for every objective
	From Table

Table 4 .

 4 2. Summary of the network structure for each independent model

			Suppliers		Processing plants		Distribution Centers
	Objective function	F1	F2	F3	P1	P2	P3	P4	C1 C2 C3 C4 C5 C6
	𝑍 1	14	2	3			S		L	L
	𝑍 2	13	6	5				S	M	L	S	S
	𝑍 3	17	4	2	S				L	L

Table 4 .

 4 2 presents a summary of the results specifying the number of suppliers by zone and selected location for opening processing plant and distribution centers. To avoid a more massive extension of the table suppliers are divided into three different categories according to its value-added parameter (𝜑 𝑖 ). Let F1 be the set of suppliers with the lowest values, 𝐹1 = {𝑠 𝑖 |0.1 ≤ 𝜑 𝑖 ≤ 0.8}, 𝐹2 = {𝑠 𝑖 |0.8 < 𝜑 𝑖 ≤ 1.5}, finally, suppliers located in regions with the highest value are grouped in set 3 𝐹3 = {𝑠 𝑖 |𝜑 𝑖 ≥ 1.5}. Moreover, potential facility locations for processing plants are listed from P1 to P4, being P1 the potential location with the highest unemployment rate, P2 the second and so on. The first column of Figure

Table 4

 4

		.3. Results of Chebyshev goal programming
	Objective	Target	Calculated deviation	𝜆 (%)
	𝑍 1	2.787E+11	(+) 1.017E+10	3.61
	𝑍 2	44,513	(+) 1,780.55	4.01
	𝑍 3	1.28	(-) 0.044	3.44

Table 4 .

 4 4. Structure of the supply chain Chebyshev goal programming

			Suppliers		Processing plants	Distribution Centers
	Objective function	F1	F2	F3	P1	P2	P3	P4	C1 C2 C3 C4 C5 C6
	𝐺𝑃	16	1	3	S				M	S	L

Table 5

 5

	Climate variable	Tropical Lowlands	Tropical Highlands
	Temperature	> 22°C (72°F)	< 14°C (57°F)
	Precipitation	< 800 mm (31in)	600 to 2600 mm (24 to 102in)
	Altitude	4 to 1250 m.a.s.l.	1750 to 4200 m.a.s.l.
	Soil type	Alkaline and sodic soils	Acid soils, volcanic slabs

.1. Classification of land in Colombia according weather and soil conditions Source:

(Reyes, N.D)

Table 5

 5

	.2. Use of land in Colombia
	Data source: FEDEGAN 2020, IGAC 2012

  . The framework includes, among others, the document CONPES 3675 National policy to improve the competitiveness of the Colombian dairy sector (DNP, 2010b), Dairy sector business plan (MCIT & PTP, 2016), Agricultural sector plan for the mitigation of GHG (MADR, 2017), National Appropriate Mitigation Action for the sustainable bovine livestock sector, Colombian livestock Roadmap 2018 -2022 (FEDEGAN, 2018), which are covered by national development plans including, National Climate change policy (MADS, 2014), Nationally Determined Contributions

Table 5 .

 5 4. Sustainability indicators and SDG's considered in the ex-ante sustainability assessment

	Sustainability Dimension	Impact category	SDG's	Indicator
	Economic	Total operational cost	8	Total annual processing and distribution cost
				Tonnes of CO2 eq. produced by
		GHG emissions	12, 13	production, processing, and
	Environmental			transportation emissions
		Use of Land	15	Number of hectares of land used for dairy cattle activities
		Formal businesses	9	Percentage of milk production collected in the formal channel
	Social
		Employment	8	Number of jobs in production and processing activities

  Quantity of product j shipped from r to s using mode m in period t Total capacity cost adds up to the cost associated with maintaining a level of capacity to perform processing activities and the cost associated with changing capacity over the time horizon. To include into the model increases in cost future periods, we define a constant growth in function of the time represented by 𝜋 𝑡 , where 𝜋 > 1 is a constant value and 𝑡 is the index of the time.Total processing cost includes adds up to the cost associated with maintaining a level of capacity to perform processing activities and the cost associated with changing capacity over the time horizon.Total transportation cost includes the cost of all transportation activities required to deliver products from producers to retailers through every tier and the incurred costs when adding or removing transportation capacity for all modes.The evolution of the industry considers adjustment on capacity, reduction, and expansion are considered. Migration from one region to another, as well as the construction of new capacity by actual or new competitors, is addressed. Constraint 5 computes the capacity of process p at region r in period t Output product quantity going from one process to another, coming either, same or different region, must respect the current capacity process installed. Yield factor (𝑌𝑓 𝑝𝑟 𝑡 ) is used to convert units of process into quantity of output products at each stage.

	Time to Sustainability Time to Sustainability	90 91
	𝑇𝑐 𝑟𝑠 𝑚 Constraints	Transportation cost per unit shipped from region r to region s using mode 𝑚
	𝐸𝑓 𝑚 Calculated variable equations. Emission factor for transportation mode m per kilometer
	𝜙 𝑚	Maximum capacity change rate for transportation mode m
	𝑃𝐶 𝑝𝑟 𝐶𝑎𝑝 𝑝𝑟 + , 𝐶𝑎𝑝 𝑝𝑟 𝑚∈𝑀 𝑠∈𝐿2(𝑗) -∑ ∑ 𝑄𝑝𝑟 𝑗𝑟𝑠 Processing cost per unit of process 𝑝 at region 𝑟 Increase/decrease capacity cost rate of process 𝑝 at region 𝑟 𝑠𝐿2(𝑗) 𝑚𝑡 + ∑ 𝑄𝑖𝑛𝑓 𝑠𝑟 𝑡 ≤ 𝑄𝑝𝑜 𝑝𝑟 𝑡 * 𝑌𝑓 𝑝𝑟 𝑡 ∀ {𝑗, 𝑟} ∈ 𝑃𝑅, 𝑗 ∈ 𝑃𝑂(𝑝, 𝑟), 𝑡 ∈ 𝑇	(7)
	𝑗 ∈ 𝐽 𝑃𝑒𝑟𝑖𝑜𝑑𝑠 𝑡 ∈ 𝑇 𝐸𝑖 𝑝𝑟 𝑚∈𝑀 Indirect CO2 eq. emission factor per unit of process 𝑝 at region 𝑟 include raw material, intermediate products and finished products consumed in performing a process 𝑟∈𝐿1(𝑗) define division within the time horizon. 𝐶𝑎𝑝 𝑝𝑟 Installed capacity cost rate for process 𝑝 at region 𝑟 𝜃 𝑝𝑟 Likewise, the quantity of input products delivered to each process in any region, must be enough to perform Maximum capacity change rate for process p at region r 𝜋 𝐶 𝑐𝑎 𝑡 = ∑ 𝐶𝑝𝑜 𝑝𝑟 𝑡 * (𝐶𝑎𝑝 𝑝 * 𝜋 𝑡 ) + 𝐶𝑝𝑜 𝑝𝑟𝑡 + * (𝐶𝑎𝑝 𝑝 + * 𝜋 𝑡 ) + 𝐶𝑝𝑜 𝑝𝑟𝑡 - * (𝐶𝑎𝑝 𝑝 - * 𝜋 𝑡 ) the intended quantity of process in this region. ∀𝑡 ∈ 𝑇 (1) Cost escalation rate 𝐸𝑑 𝑝𝑟 Direct CO2 eq. emission factor per unit of process 𝑝 at region 𝑟 {𝑝,𝑟}∈𝑃𝑅 ∑ ∑ 𝑄𝑝𝑟 𝑗𝑟𝑠 𝑚𝑡 ≥ 𝑄𝑝𝑜 𝑝𝑟 𝑡 * 𝑌𝑓 𝑝𝑟 𝑡 ∀ {𝑝, 𝑠} ∈ 𝑃𝑅, 𝑗 ∈ 𝑃𝐼(𝑝, 𝑠), 𝑡 ∈ 𝑇 (8)
	𝑀𝑜𝑑𝑒𝑠 𝑚 ∈ 𝑀 𝐽𝑏 𝑝𝑟 Constraint 9 ensures that external demand is met through supply from distribution locations. As a common represent the different options to the transport of goods through the supply Direct employees in process 𝑝 at region 𝑟 chain. 𝑀 Big number 𝐶 𝑝𝑜 𝑡 = ∑ ∑ ∑ ∑ 𝑄 𝑗𝑟𝑠 𝑚𝑡 * 𝑃𝐶 𝑝𝑟 (2) ∀𝑡 ∈ 𝑇 condition in long-term studies with yearly periods, no inventory is carried out between periods.
	Subsets 𝑝 ∈ AP 𝑗 ∈ 𝑃𝑂(𝑝, 𝑟) {𝑗, 𝑟} ∈ 𝑃𝐹 𝑄 𝑗𝑟𝑠 𝑚𝑡 𝐶𝑡𝑟 𝑚 𝑡 𝐶 𝑡𝑟 𝑡 = ∑ 𝑗∈𝐽,𝑚∈𝑀 process-region combination products used as input in process p at region r product-location combination for final product j Transportation capacity of mode m in period t, (t ≠ 0) 𝜋 𝑡 ∀𝑡 ∈ 𝑇 ∑ 𝐿𝑓 𝑚 * 𝐷𝑖𝑠 𝑟𝑠 * 𝑇𝑐 𝑟𝑠 𝑚 * 𝑄𝑝𝑟 𝑗𝑟𝑠 𝑚𝑡 {𝑟,𝑠}∈𝑇𝐿 + 𝐶𝑡𝑟 𝑚𝑡 + * 𝐶𝑎𝑝 𝑚 𝑡𝑟+ * 𝜋 𝑡 + 𝐶𝑡𝑟 𝑚𝑡 - * 𝐶𝑎𝑝 𝑚 𝑡𝑟- * (3) 𝑗 ∈ 𝑃𝐼(𝑝, 𝑟) 𝐶𝑝𝑜 𝑝𝑟𝑡 + , 𝐶𝑝𝑜 𝑝𝑟𝑡 -Increase/decrease capacity of process p at region r in period t products produced as output in process p at region r 𝑄𝑝𝑜 𝑝𝑟 𝑡 Quantity of process p executed at region r in period t Agricultural activities 𝐶𝑝𝑜 𝑝𝑟 𝑡 Capacity of process 𝑝 at region 𝑟 in period 𝑡, (t ≠ 0) {𝑝, 𝑟} ∈ 𝑃𝑅 𝑚∈𝑀 𝑟∈𝐿1(𝑗) Decision variables 𝑠∈𝐿2(𝑗) 𝑚∈𝑀 𝑗∈𝑃𝑂(𝑝,𝑟) (𝑝,𝑟)∈𝑃𝑅 ∑ ∑ 𝑄𝑝𝑟 𝑗𝑟𝑠 𝑚𝑡 ≥ 𝐷𝑒𝑚 𝑟 𝑡 ∀ {𝑗, 𝑠} ∈ 𝑃𝐹, 𝑡 ∈ 𝑇 (9)
	𝑟 ∈ 𝐿1(𝑗) 𝑟 ∈ 𝐿2(𝑗) 𝐶𝑡𝑟 𝑚𝑡 + , 𝐶𝑡𝑟 𝑚𝑡 -Capacity handling equation region where product j is produced region where product j is used as input Increase/decrease transport capacity of mode m in period t
	𝑟 ∈ 𝑅𝑃(𝑝) {𝑟, 𝑠} ∈ 𝑇𝐿(𝑗) Constraint (4) establishes upper and lower boundaries to the different processes performed in every region region where process p is performed Dependent variables in each period. A minimum capacity utilization factor is used to ensure economic feasibility in the process. transportation lane for product j from region r to s ∊ R 𝐶 𝑝𝑜 𝑡 Total processing cost in period t 𝐶 𝑐𝑎 Total capacity cost in period t 𝑡 𝐶𝑝𝑜 𝑝𝑟 𝑡 * 𝛼 𝑝 ≤ 𝑄𝑝𝑜 𝑝𝑟 𝑡 ≤ 𝐶𝑝𝑜 𝑝𝑟 𝑡 ∀ {𝑝, 𝑟} ∈ 𝑃𝑅, 𝑡 ∈ 𝑇 (4)
	Parameters 𝐶 𝑡𝑟 𝑡	Total transportation cost in period t
	𝐷𝑒𝑚 𝑟 𝑡 𝐸 𝑝𝑜 𝑡	Demand at consumption region r in period t Total emission caused by processing in period t
	𝐴𝑐𝑚 𝑟 𝑡 𝐶𝑎𝑝 𝑝𝑟 𝑜 𝑡 𝐸 𝑡𝑟 𝑈𝑙 𝑡	Apparent consumption region r in period t Initial capacity at process p at region r Total emissions caused by transportation in period t Total hectares of land use for production activities 𝐶𝑝𝑜 𝑝𝑟 𝑡 = 𝐶𝑝𝑜 𝑝𝑟 𝑡-1 + 𝐶𝑝𝑜 𝑝𝑟𝑡 + -𝐶𝑝𝑜 𝑝𝑟𝑡 -∀ {𝑝, 𝑟} ∈ 𝑃𝑅, 𝑡 ∈ 𝑇	(5)
	𝛼 𝑝 𝑌𝑓 𝑝𝑟 𝑡 𝐽 𝑡 𝐽 𝑝 𝑡 Since the expansion of capacity requires construction of new facilities, adequation of new soils or the Minimum capacity utilization factor for process p Yield factor per unit of process p at region r in period t Total jobs in period t Total jobs in process p during period t adaptation of the existing ones (facilities and soils), a maximum rate of change per period is used in
	𝐷𝑖𝑠 𝑟𝑠 𝐿𝑑 𝑡 constraint 6 to limit the growth from period to period. Distance between regions r and s ∊ R Total labor dismissals in production process during period t
	𝑇𝑟𝐶𝑎𝑝 𝑚 𝑜 𝐶𝑎𝑝 𝑚 𝑡𝑟+ , 𝐶𝑎𝑝 𝑚 𝐿𝑓 𝑚 𝐸 𝑐𝑢 𝑡 𝐶 𝑐𝑢 𝑡 𝑡𝑟-Increase/decrease transportation capacity cost rate of mode m Initial capacity for transportation mode m Cumulative emissions up to period t Loading factor for transportation mode m Cumulative cost up to period t 𝑄𝑖𝑛𝑓 𝑟𝑠 𝑡 Quantity of milk in the informal channel going from region producer 𝑟 to retailer 𝑗 in period 𝑡 𝐶𝑝𝑜 𝑝𝑟𝑡 + ≤ 𝜃 𝑝𝑟 and 𝐶𝑝𝑜 𝑝𝑟𝑡 -≤ 𝜃 𝑝𝑟 ∀ {𝑝, 𝑟} ∈ 𝑃𝑅, 𝑡 ∈ 𝑇 (6)

  Besides, to consider the possibility of alternatives transport modes, it is necessary to establish limits to the capacity of each mode. Although the availability of resources and the transportation capacity of goods by road is virtually unlimited, the adoption of alternative modes like rail or electrical vehicles are introduced gradually. Hence, equation 11 limits the total freight to the available capacity in each period allows for direct and indirect emissions sources. Direct emission comes from production and processing activities in each region, meanwhile indirect emissions are associated with the use of energy during the process. Constraint 14 computes the total emissions per period.Since pressure over the productive systems is a cause of biodiversity loss, deforestation, soil compaction and eroding. Constraint 16 adds up the total number of hectares used at the first stage of the chain.

	Emissions equations
	GHG emissions count 𝐸 𝑝𝑜 𝑡 = ∑ (𝐸𝑑 𝑝𝑟	+ 𝐸𝑖 𝑝𝑟 ) * 𝑄𝑝𝑜 𝑝𝑟 𝑡	∀𝑡 ∈ 𝑇	(14)
		{𝑝,𝑟}∈𝑃𝑅
	Another source of GHG emissions is transport activities between stages of the network. Equation 15
	determines the total emissions according to the volume of product sent among facilities and the
	transportation mode for each period.
	𝐸 𝑡 𝑡𝑟 = ∑ ∑	∑ 𝐸𝑓 𝑚	* 𝐷𝑖𝑠 𝑟𝑠 * 𝐿𝑓 𝑚 * 𝑄𝑝𝑟 𝑗𝑟𝑠 𝑚𝑡	∀𝑡 ∈ 𝑇	(15)
	𝑗∈𝐽	𝑚∈𝑀	{𝑟,𝑠}∈𝑇𝐿(𝑗)
	Use of land equation
		𝑈𝑙 𝑡 =	∑		𝐶𝑝𝑜 𝑝𝑟 𝑡	∀𝑡 ∈ 𝑇	(16)
			𝑟∈𝑅𝑃(𝑝 ∈𝐴𝑃)
	Employment equation
	∑ 𝑄𝑖𝑛𝑓 𝑠𝑟 𝑡 𝑠𝐿2(𝑗) Constraint 17 computes the total number of jobs in each period offered at various stages of the supply ≥ 𝐴𝑐𝑚 𝑟 𝑡 -𝐷𝑒𝑚 𝑟 𝑡 ∀ 𝑟 ∈ 𝑅, 𝑡 ∈ 𝑇 (10) chain.
		𝐽 𝑡 = ∑ 𝐽𝑏 𝑝𝑟 * 𝑄𝑝𝑜 𝑝𝑟 𝑡	∀𝑡 ∈ 𝑇	(17)
			{𝑝,𝑟}∈𝑃𝑅
	Equation 18 calculates the number of labor dismissals at agricultural level. Productive transformation of
	∑ ∑ 𝑄𝑝𝑟 𝑗𝑟𝑠 𝑚𝑡 agriculture industry is often accompanied by labor dismissals at agriculture productive units. * 𝐿𝑓 𝑚 ≤ 𝐶𝑡𝑟 𝑚 𝑡 ∀ 𝑚 ∈ 𝑀, 𝑡 ∈ 𝑇	(11)
	{𝑟,𝑠}∈𝑇𝐿(𝑗) 𝐿𝑑 𝑡 = 𝑗∈𝐽 ∑	𝐽𝑏 𝑝𝑟 * (𝑄𝑝𝑜 𝑝𝑟 0	-𝑄𝑝𝑜 𝑝𝑟 𝑡 ) ∀𝑡 ∈ 𝑇	(18)
		𝑝∈𝐴𝑃,{𝑝,𝑟}∈𝑃𝑅
	Finally, to define changes in transportation capacity from period-to-period equation 12 compute the total
	capacity per mode per year and equation 13 establish the maximum change from one year to another since
	the adoption of new technologies implies a step-by-step implementation. Initial transportation capacity (i.e.,
	𝐶𝑡𝑟 𝑚 0 is given as a parameter to the model.
	𝐶𝑡𝑟 𝑚 𝑡 = 𝐶𝑡𝑟 𝑚 𝑡-1 + 𝐶𝑡𝑟 𝑚𝑡 + -𝐶𝑡𝑟 𝑚𝑡 -	∀ 𝑚 ∈ 𝑀, 𝑡 ∈ 𝑇	(12)
		𝐶𝑡𝑟 𝑚𝑡 + ≤ 𝜙 𝑚 and 𝐶𝑡𝑟 𝑚𝑡 -≤ 𝜙 𝑚 ∀ 𝑚 ∈ 𝑀	(13)

  is the cumulative concentration of GHG that drives future climate disturbance, -the stock rather than the flow. Equation19and Equation 20 present total cumulative cost and total cumulative emission up to period t, respectively.To use time to sustainability optimization approach to construct the ex-assessment model to the application of policies, the following sets of elements are added to the model.

			𝐶 𝑐𝑢 𝑡 = ∑ 𝐶 𝑝𝑜 𝑡 + 𝐶 𝑐𝑎 𝑡=0 𝑡 + 𝐶 𝑡𝑟 𝑡∈𝑇 𝑡	(19)
			𝐸 𝑐𝑢 𝑡 = ∑ 𝐸 𝑝𝑜 𝑡=0 𝑡 + 𝐸 𝑡𝑟 𝑡∈𝑇 𝑡	(20)
	Sets
	𝐾𝑒𝑦 𝑖𝑛𝑑𝑖𝑐𝑎𝑡𝑜𝑟𝑠 𝑘 ∈ 𝐾	set of indicators selected to evaluate sustainable development {cumulative operational costs, CO2 emissions stock, use of land, total layoffs}
	Parameters
	𝜃 𝑝 𝐴𝐿𝑇	Maximum capacity change rate for process p in the alternative scenario
	𝜙 𝑚	Maximum capacity change rate for transportation mode m in the alternative scenario
	𝜓 𝑘 +	Upper limit of the sustainable value for indicator k
	𝜓 𝑘 -	Lower limit of the sustainable value for indicator k
	𝐺	Big number
	Variables
	𝜏 𝑡	1, 𝑖𝑓 𝑎𝑡 𝑙𝑒𝑎𝑠𝑡 𝑜𝑛𝑒 𝑘𝑒𝑦 𝑖𝑛𝑑𝑖𝑐𝑎𝑡𝑜𝑟 𝑖𝑠 𝑜𝑢𝑡 𝑜𝑓 𝑠𝑢𝑠𝑡𝑎𝑖𝑛𝑎𝑏𝑙𝑒 𝑟𝑎𝑛𝑔𝑒 { 0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
	𝐾𝑃𝐼 𝑘𝑡	Actual value of KPI k in period t
	𝜋 𝑘𝑡	Total deviation respect to acceptable value of KPI k in period t
	Time to sustainability constraints

Table 7 .

 7 1. Production systems characterization Table 7.2. Animal load and production capacity per region

Table 7 .

 7 3. Cost of land and employment capacityRegarding GHG farm emissions, we use data from studies in Colombia comparing different conventional production systems in tropical highlands as in tropical lowlands with silvopastoral systems strategies. Most of the studies are developed by the Center for Research on Sustainable Agricultural Production Systems (CIPAV by its acronym in Spanish). A cradle to farm gate approach is used to quantify the emissions in these farm systems. Table7.4 presents a comparison of the values of GHG emissions for silvopastoral Systems (SPS) and Conventional System (CS) by functional unit in high lands, dry tropic and acidic soils.

	Location	Classification	Productivity rate* (l/head/day)	Area yield † (l/ha/year)	Milk producing cost⸙ (USD/l)
	Antioquia		11.4		3065.5	0.22
	Boyacá	Specialized	7.6		3107.0	0.21
	Cundinamarca	dairy system	11.3		3538.0	0.21
	Nariño		9.8		1878.0	0.22
	Caquetá		4.0		751.0	0.22
	Cesar	Dual-purpose	3.1		1099.0	0.18
	Córdoba	system	2.9		687.0	0.15
	Magdalena		4.0		1123.0	0.18
	* Encuesta Nacional Agropecuaria. DANE, 2017
	† Unidad de Planeación agropecuaria, UPRA, 2019
	⸙ Costos de producción. Fedegan 2019. 1
	Location	Stocking rate* (head/ha)	Milking cows † (head)	Yearly production capacity † (in liters)
	Antioquia	0.9			605,844	2,526'479,296.6
	Boyacá	1.2			251,401	693'936,009.8
	Cundinamarca	1.2			322,787	1,336'979,540.3
	Nariño	1.6			83,037	295'628,401.9
	Caquetá	0.5			158,245	232'429,298.8
	Cesar	0.5			250,957	287'640,792.1
	Córdoba	0.5			270,787	290'197,266.9
	Magdalena	0.5			293,294	437'964,722.0
	* Data from (Fedegan, 2014)
	† Data from DANE, 2017

Table 7

 7

		.4. GHG emissions factors at farming level
			Source: (Rivera et al., 2016)
				Dairy systems -Colombia
		High fields (<2k mamsl)	Dry tropic	Acidic soils
		ISPS	CS	ISPS	CS	ISPS	CS
	Kg CO2 eq./ Kg of milk	1.47	1.56	2.16	4.15	1.54	1.68
	Kg CO2 eq./ Kg of milk (FPCM)	1.87	2.05	2.06	4.08	1.60	1.78
	Kg CO2 eq./ Kg of milk (ECM)	1.52	1.69	2.06	4.08	1.60	1.78
	mamsl : meters above mean sea level

Table 7

 7 Consumption departments were defined considering the presence of the principal retailer company in Colombia. Grupo Éxito has presence in 22 out of the 32 departments in Colombia. The list includes Antioquia, Atlántico, Bolívar, Boyacá, Caldas, Caquetá, Casanare, Cauca, Cesar, Córdoba, Cundinamarca, Huila, Magdalena, Meta, Nariño, Norte de Santander, Quindío, Risaralda, Santander, Sucre, Tolima, and Valle del Cauca. As is stated in previous studies, two of the main variables describing the behavior of milk consumption are population and apparent consumption, which is lastly related with population incomes(FAO, 2014). Thus, in this work, we use the very same variables to estimate the demand for the upcoming years. Data include apparent consumption estimation for the whole set of dairy products including, pasteurized milks, sour milks products, sweetened milks, butter and cream, and milk powder. The annual Unidad de seguimiento de precios de leche. MADR 2019 growth is based on previous years' growth rate and is a conservative estimate. A list of the data sources to the validation of the model is presented in Appendix 1.

	.6. GHG emission factors for processing process
		Direct emissions	Indirect emissions
	Ton CO2 eq./ Ton final product	0.17	0.138
	Consumption locations:

Table 7

 7

		.7. Experimental context parameters
		Baseline scenario	Alternative scenario
	Decision driver	Total cost	Time to sustainability
	Time horizon	20 years	20 years
	Key indicators			Guidelines
	Total cost	Objective	≤ 1.05 Baseline Total cost
	Cumulative GHG emissions	Non-restricted	≤ 0.8 Baseline GHG emissions	NDC Colombia (MADS, 2015)
	Use of land	Non-restricted	≤ 0.7 Baseline Total hectares	PAS GEI SA (MADR, 2017)
	Layoffs	Non-restricted	≤ Baseline Layoffs	PAS GEI SA (MADR, 2017)
	Formal collection of	0.48 to 0.6 collection	0.48 to 0.6 collection	PIGA SL
	milk	of milk	of milk	(Leiva B., et al., 2016)
	Scenario drivers
	Silvopastoral systems	+ 5600 ha/year	+ 28000 ha/year
	Electric fleet usage	-	+ 200 trucks/year
	Consumption pattern	Forecast	Forecast
	Farm Productivity	Trend	Trend

  It defines a minimum acceptable level for the formal collection of milk. Simultaneously, it makes the baseline and alternative scenarios comparable between them, concerning the economic, social, and environmental indicators for sustainable development in the dairy industry. Hence, a conservative per year growth takes the national collection level of milk from 48% in year 1 to about 60% in year 20. These values are within the range presented by other ongoing prospective studies of the dairy sector (MADR & UPRA, 2018). Moreover, there are external variables influencing the development of the dairy sector, such as, livestock enhancing, genetic development, crossbreeding activities, and a construction of know how through experience, which are not included into the model. To consider the changes caused by these variables a productivity trending factor has been stablished, according to a conservative historical behavior. These factors are usually established to consider optimistic, pessimistic and trending scenarios for the sector (MADR & UPRA, 2018). The parametrized behavior for these conditions is presented in Figure7.2.Figure7.2b presents the percentual productivity increase by area for the two different production systems, namely, silvopastoral systems and conventional livestock. In this respect, productivity per hectare might increase by about 30% for conventional systems and more than 60% for silvopastoral systems over 20 years. These values are in the range of previous studies representing the sector's trending behavior and the expected improvements at implementing silvopastoral systems[START_REF] Chará | Silvopastoral Systems and their Contribution to Improved Resource Use and Sustainable Development Goals: Evidence from Latin America[END_REF][START_REF] Madr | Análisis Prospectivo de la Cadena Láctea Bovina Colombiana[END_REF].

		65%
	(%)	60%		60%
	of milk	55%
	Collection	45% 50%	48%
		40%
			1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
			Year
			(a)
	80%
	70%	Silvopastoral systems	Conventional livestock
	60%
	50%
	40%
	30%
	20%
	10%
	0%
		1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Year
			(b)
	Figure 7.2. (a) Collection of milk, and (b) farm productivity over the time horizon

Table 7 .

 7 8. Production capacity in the baseline scenario (ha)

	Region	Conventional		Silvopastoral systems	Farm type
	Antioquia				Dairy
	Boyacá				Dairy
	Caquetá				Dual purpose
	Cesar				Dual purpose
	Córdoba				Dual purpose
	Cundinamarca				Dairy
	Magdalena				Dual purpose
	Nariño				Dairy
	Y1	Y20	Y1	Y20

Table 7 .

 7 9. Production capacity changes in the alternative scenario

	Region	Conventional	Silvopastoral systems	Farm type
	Antioquia			Dairy
	Boyacá			Dairy
	Caquetá			Dual purpose
	Cesar			Dual purpose
	Córdoba			Dual purpose
	Cundinamarca			Dairy
	Magdalena			Dual purpose
	Nariño			Dairy
	Y1	Y20	Y1	Y20

Table 7 .

 7 10. Timeframe in years to meet sustainability objectives

	Sustainability goals

Table 7 .

 7 11. Estimated values for productivity improvement in a 20-year horizon time between silvopastoral systems and conventional systems

		Alternative scenario 1	Alternative scenario 2	Alternative scenario 3
	Productivity improvement	+70%	+100%	+150%

Table 7 .

 7 12. Sensitivity analysis for ex ante scenarios

	KPI	Alternative scenario 1	Alternative scenario 2	Alternative scenario 3
	Total cumulative cost (USD Billions)	72.43	72.18	72.26
	Total cumulative
	GHG emissions	129.55	129.33	128.94
	(Mton CO2 eq.)
	Total release land (thousand hectares)	2631.07	2615.08	2631.07
	Layoffs	29.4	30.6	32.6
	(thousand employees)
	Time to sustainability (Years)	19	19	18

  Sciences et Génie de l'EnvironnementMots clefs : conception de réseaux de supply chains, politique de développement durable, supply chain durable, optimisation, évaluation de la durabilité, industrie laitière.Cette thèse s'inscrit dans les recherches sur l'aide quantitative à la prise de décision dans la conception de réseaux de chaînes d'approvisionnement durables (SSCND). Dans un premier temp, nous identifions les indicateurs clés communs utilisés dans des publications scientifiques pour évaluer la durabilité dans les applications de conception de chaînes d'approvisionnement. Nous proposons ensuite (i) une approche de modélisation à objectif unique et (ii) une approche de modélisation multi-objectifs pour inclure les critères environnementaux et sociaux dans la conception d'un réseau de chaîne d'approvisionnement du point de vue de l'entreprise. En considérant la perspective plus large de la durabilité dans les chaînes d'approvisionnement, l'unité d'analyse est étendue d'une perspective d'entreprise pour considérer l'ensemble d'une filière au sein des différentes régions d'un pays donné. En particulier, nous étudions les effets de la mise en oeuvre des politiques de développement durable sur la structure du réseau d'approvisionnement pour l'industrie laitière en Colombie.L'objectif de ce travail est de proposer une procédure efficace d'évaluation conjointe des performances économiques, environnementales et sociales pour la conception ou la reconception d'un réseau de chaînes d'approvisionnement. Une formulation mathématique est présentée, qui tient compte de l'évolution de la chaîne d'approvisionnement et du renforcement des capacités à long terme. Nous proposons une approche d'évaluation ex ante de la durabilité pour comparer les changements dans la structure du réseau de la chaîne d'approvisionnement en vue d'atteindre les objectifs de durabilité. En outre, les indicateurs clés de performance en matière de durabilité sont choisis en tenant compte des défis actuels du secteur en matière de durabilité. La performance du modèle est testée avec une application dans l'industrie laitière d'un pays à économie en développement. Elle illustre l'utilité du modèle pour évaluer les activités nationales d'atténuation et d'adaptation dans la conception des réseaux de chaînes d'approvisionnement. La nécessité de fixer des objectifs pour mesurer la durabilité dans le domaine de la chaîne d'approvisionnement est soulignée. Les résultats offrent une aide à la décision significative aux décideurs politiques dans l'évaluation de la mise en oeuvre des actions et la définition des voies stratégiques vers la durabilité.

	École Nationale Supérieure des Mines
	de Saint-Étienne
	NNT: 2021LYSEM023
	Carlos Alberto MORENO-CAMACHO
	CONCEPTION DE RESEAUX DE CHAINES LOGISTIQUE AGROALIMENTAIRES DANS
	LE CADRE DE POLITIQUES DE DEVELOPPEMENT DURABLE
	Spécialité :

Résumé :

L'objectif de ce travail est de proposer une procédure efficace d'évaluation conjointe des performances économiques, environnementales et sociales pour la conception ou la reconception d'un réseau de chaînes d'approvisionnement. Une formulation mathématique est présentée, qui tient compte de l'évolution de la chaîne d'approvisionnement et du renforcement des capacités à long terme. Nous proposons une approche d'évaluation ex ante de la durabilité pour comparer les changements dans la structure du réseau de la chaîne d'approvisionnement en vue d'atteindre les objectifs de durabilité. En outre, les indicateurs clés de performance en matière de durabilité sont choisis en tenant compte des défis actuels du secteur en matière de durabilité. La performance du modèle est testée avec une application dans l'industrie laitière d'un pays à économie en développement. Elle illustre l'utilité du modèle pour évaluer les activités nationales d'atténuation et d'adaptation dans la conception des réseaux de chaînes d'approvisionnement. La nécessité de fixer des objectifs pour mesurer la durabilité dans le domaine de la chaîne d'approvisionnement est soulignée. Les résultats offrent une aide à la décision significative aux décideurs politiques dans l'évaluation de la mise en oeuvre des actions et la définition des voies stratégiques vers la durabilité.Mots clés : conception de réseaux de supply chains, politique de développement durable, supply chain durable, optimisation, évaluation de la durabilité, industrie laitière. xii

À ce stade, trois aspects ressortent du champ de recherche sur la conception des réseaux de chaînes d'approvisionnement. Premièrement, bien que l'évaluation de la durabilité revendique une vision holistique de la chaîne d'approvisionnement, elle se concentre parfois sur les opérations en aval et les impacts provenant des fournisseurs en amont sont souvent omis, y compris lorsque des activités agricoles ont lieu à ce niveau. Ce phénomène peut conduire à des solutions superficielles ayant un faible impact sur la durabilité de la chaîne d'approvisionnement. Deuxièmement, la plupart des travaux considèrent une perspective de durabilité centrée sur l'entreprise ; les approches du développement durable à l'échelle de la filière sont rares. Des études récentes ont suggéré que les améliorations environnementales progressives apportées par les entreprises individuelles peuvent être inadéquates pour faire face aux problèmes environnementaux mondiaux. À cet égard, les organismes publics sont appelés à être les points de connexion entre les objectifs de développement durable et les stratégies de gestion de la chaîne d'approvisionnement des entreprises, afin de transposer les aspirations mondiales dans les contextes régionaux et locaux[START_REF] Paletta | A Step-by-Step Process towards an Evolutionary Policy Encouraging the Adoption of Sustainable Business Models[END_REF].

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[START_REF] Galvez | Reverse logistics network design for a biogas plant: An approach based on MILP optimization and Analytical Hierarchical Process (AHP)[END_REF] address the location of a biogas plant to valorize organic residual waste. The authors propose a hybrid method combining MILP and Analytical Hierarchical process. At first a location problem is solved considering three different scenarios, and then the optimal solution of these scenarios is compared considering different criteria including total CO2 emissions by waste transportation activities.[START_REF] Izadikhah | A new preference voting method for sustainable location planning using geographic information system and data envelopment analysis[END_REF] present a new ranking method combining Data Envelopment Analysis (DEA) and discriminant analysis to solve location planning problem. Productive, supportive, logistics and environmental factors are evaluated using geographic information, to define the best location to the construction of facility among a set of candidates locations.[START_REF] Neumüller | Integrating three-dimensional sustainability in distribution centre selection: The process analysis method-based analytic network process[END_REF] present an Analysis Network Process for the selection of distribution, including economic, environmental, and social sustainability aspects. In the examples above, consideration of sustainability criteria occurs outside of optimization models. Sometimes multi attribute decision making methodology (MADM) feeds the model with a set of promising alternatives considering environmental and social key indicators and sometimes MADM are used after optimization to compare a set of solutions regarding sustainability aspects.On the contrary, other approaches consider environmental and social key indicators within optimization model. When the case, environmental and social criteria are involved into the optimization problem, the

Therefore, on the one hand, there is room for developing models considering key indicators simultaneously, while consider targets for sustainable development in the context of supply chain design, to evaluate the impact of long-term decisions. In this sense, compromise between objectives is ruled by sustainability definition rather than decision-maker preferences. On the other hand, being time an important variable towards sustainable development, still interesting add dynamism within supply chain structure transformation.

The database is available at http://www.upme.gov.co/Calculadora_Emisiones/aplicacion/calculadora.html

Processing capacityStorage capacity

of producers and processors that constitute, in the supply chain, the core and the engine of the strategic plan to reach sustainable conditions (MCIT & PTP, 2016). Review of previously mentioned documents presenting the current challenges and the sector's future vision serve as input for identifying the most relevant factors to reach sustainability in the sector at the economic, social, and environmental dimension. Some of the major problems affecting the processing stage include lack of innovation, scarcity of strategy activities for accessing new markets, and minimal emphasis on international markets. Moreover, it is mentioned that, for some regions, processing facilities are located away from production areas, which causes transportation problems on collecting milk. Being milk a perishable good, these difficulties cause cost overrun, impacting the incomes of farmers expenditures of processors. Table 5.3 presents a list of the leading sustainability challenges in the supply chain. Since the analysis unit goes beyond a focal company, public policies encompass the direction of development of the sector to the whole industry. Aside from the individual effort of producers or processors at seeking their own competitiveness and profitability to contribute to the global competitiveness of the

Time to Sustainability

The content of this chapter is part of the paper submitted for publication as: Moreno-Camacho, C. A., Montoya-Torres, J. R., Jaegler, A., Gondran, N. "Agrifood Supply Chain Network Design Under Sustainable Development Policies". European Journal of Operational Research

Considering a wide-industry approach and the changes caused because of action and policies aiming to meet climate change and sustainable development objectives, this chapter presents a mathematical model to the design or re-design of supply chain networks under policies implementation. The chapter revisits a model presented previously in [START_REF] Kannegiesser | The time-to-sustainability optimization strategy for sustainable supply network design[END_REF] and go further by considering uncertainty in the expected results of policies and the construction of reference scenarios in line with the IPCC guidelines [START_REF] Ipcc | IPCC Guidelines for national greenhouse gas inventories[END_REF]. The model is intended to work as an ex-post assessment tool for the implementation of policies at sectorial level. It estimates the effects of action and policies in the three dimensions of sustainability, while considering the strategical decisions associated with the location, capacity, and distribution in supply chain networks.

TTS Results and Analysis

The content of this chapter is part of the paper submitted for publication as: Moreno-Camacho, C. A., Montoya-Torres, J. R., Jaegler, A., Gondran, N. This chapter presents the results from the execution of the model described in Chapter 6 and applied to the case study introduced in Chapter 5. First, the chapter presents a summary of the data collected to the case study and the experimental context. Using an ex-ante baseline scenario approach, the model considers the impacts at economic, environmental and social levels on the structure of the dairy supply chain when a national policy aiming to meet international commitments facing climate change is implemented. Since, the expected results of the policy may be influenced by implementation parameters, a sensitivity analysis is carried out, considering uncertainty in the efficiency of the implementation.

Production locations Processing locations

Distribution locations Market locations Lactation cycle is an important factor within the milk producing systems. Considering this issue, a percentage of current milk producing cows is calculated for each milk-production system (i.e., specialized dairy system or dual-purpose system). According to the ENA 2017, the average of milking cows in specialized dairy systems is around 55% of the total cows in production age, while in dual-purpose this percentage is around 40%. It is an important factor not only for the account of direct emissions from cattle but also for the computation of use of land. The total number of milking cows per region, the yearly production capacity by region and its corresponding stocking rate are shown in