Sobhan Razm
email: sobhanrazm@gmail.com

Alexandre Dolgui
email: alexandre.dolgui@imt-atlantique.fr

Ramzi Hamammi
email: ramzi.hammami@rennes-sb.com

Associate Professor, Nadjib Brahimi
email: nadjib.brahimi@rennes-sb.com

Professor, Germany Stefan Nickel Full

Hadi Sahebi
email: hadi_sahebi@iust.ac.ir

A Two-Phase Sequential Approach to Design of Bioenergy Supply Chains under Uncertainty and Social Concerns

Keywords: Sustainable development, Bioenergy supply chains, Biomass, Uncertainty, Geographical information, Social sustainability

The use of renewable energies has become very attractive, because it protects the environment and boosts regional development. In this paper, a sustainable two-phase sequential approach is proposed for the design of bioenergy SCs under uncertainties. The first phase, integrating geographical information, social aspects, and multi-criteria decision-making techniques, helps find appropriate locations for the bio-refineries. High rates of unemployment, and high vulnerability to the variation in the markets in an economic crisis are considered as social concerns. Integrating these factors filters the areas for the second phase. The first phase reduces complexity in the computation of the problem, and helps set up sustainable development in the supply chain. In the second phase, to cope with the uncertainties in the bioenergy supply network, a robust model is introduced. It reduces the sensitivity to inaccurate input data, and the obtained solutions stay optimal when the parameters change slightly. In order to validate this two-phase sequential approach, a case study is investigated. The results of tests show that integrating the concepts of uncertainties and sustainability with geographical information of the area in a two-phase sequential approach outperforms the traditional models, and leads to the creation of 262 jobs. The jobs have a high impact on the surrounding area.

Introduction

The increase in greenhouse gas (GHG) emissions has led to an abnormal increase of the earth's temperature, to climate changes, and, subsequently, to an increase in natural disasters. The photographs sent by emission measurement satellites have shown increasing greenhouse gas emissions and have provoked considerable concern. It caused the representatives of more than 100 countries participating in the 2015 United Nations Climate Change Conference in Paris to sign the Paris Agreement with the aim of reducing these emissions. The concerns were related to energy demand, and the environmental, economic, and social problems generated by using fossil fuels. These issues have led researchers to develop sources of renewable energy, which can augment regional development and protect the environment while still meeting the energy demand. Sources of renewable energy, bioenergy (heat and electricity) and biofuel (bioethanol, bio-oil, biodiesel, pellets) can be obtained from biomass in various ways. These renewable sources of energy can be used as substitutes for fossil fuels. Bioenergy and biofuel can decrease greenhouse gas (GHG) emissions [START_REF] Gilani | A multi-objective robust optimization model to design sustainable sugarcane-to-biofuel supply network: the case of study[END_REF] and create new jobs and more vitality in the areas concerned [START_REF] D'amore | Strategic optimisation of biomass-based energy supply chains for sustainable mobility[END_REF][START_REF] Shavazipour | Sustainable Planning in Sugar-Bioethanol Supply Chain under Deep Uncertainty: A case study of South African sugarcane industry[END_REF]. One source of biomass is the feedstocks made from agricultural and forest residues. Forest residues contain: a) sawmill wastes: shavings, sawdust, hog fuel, chips; b) branches, leaves, tree tops, non-merchantable stems emanating from forest operations [START_REF] Razm | A global bioenergy supply network redesign through integrating transfer pricing under uncertain condition[END_REF]. The agricultural residues contain wheat straw, sugarcane bagasse, corn stover, etc., which are not used as food, and originate from the wastes made from agriculture [START_REF] Razm | A multi-objective mathematical model to redesign of global sustainable bioenergy supply network[END_REF][START_REF] Yue | Biomass-to-bioenergy and biofuel supply chain optimization: overview, key issues and challenges[END_REF]. Bioenergy, biofuel, and other bio-based products (chemicals, plastics, etc.) are the direct result of converting these residues through biochemical, chemical, and thermochemical basic processes [START_REF] Demirbas | Potential contribution of biomass to the sustainable energy development[END_REF][START_REF] Mckendry | Energy production from biomass (part 1): overview of biomass[END_REF][START_REF] Campbell | A feasibility study guide for an agricultural biomass pellet company[END_REF]. The methods used to convert the forest/agricultural biomass into bioenergy/biofuel are thermochemical (combustion, pyrolysis, and gasification) and biochemical (producing ethanol through hydrolysis and fermentation) [START_REF] Mckendry | Energy production from biomass (part 1): overview of biomass[END_REF][START_REF] Mckendry | Energy production from biomass (part 2): conversion technologies[END_REF].

In recent years, the importance of the design, implementation, and management of bioenergy SC has increased. One of the significant obstacles to development of a bioenergy supply chain is the cost of the bioenergy supply network. For instance, high costs could be incurred by supplying biomass to the biorefinery due to the economic and environmental implications of gathering and transporting biomass feedstock from the biomass supply site. The location of the biorefinery is fundamental in terms of reducing costs and GHG emissions (e.g. due to transportation). The location of the biorefinery is also important, because it can generate new jobs and sustainable development in the surrounding area [START_REF] You | Optimal design of sustainable cellulosic biofuel supply chains: multiobjective optimization coupled with life cycle assessment and input-output analysis[END_REF].

When a wide geographic area is considered for planning, identifying the candidate locations of biorefineries is a complex process requiring accurate assessments on the ground, so geographic information of the area is important. These locations should suit the possible environmental, economic and social interactions of the area. They should also have access to the biomass, resources and power required for the conversion technologies throughout the year [START_REF] Demirbaş | Biomass resource facilities and biomass conversion processing for fuels and chemicals[END_REF]15]. There is also a need to consider the uncertainties related to biomass availability, demand, transportation, operation, and costs in the design of the bioenergy SC. Uncertainties could make the design of the SC unfeasible, or render its performance suboptimal [START_REF] Awudu | Stochastic production planning for a biofuel supply chain under demand and price uncertainties[END_REF][START_REF] De Meyer | Methods to optimise the design and management of biomass-forbioenergy supply chains: A review[END_REF]. Accordingly, it is important to integrate the concepts of sustainability and uncertainties as well as geographical information about the area into the planning and design of the bioenergy SC. Thus, the specific questions this study is seeking to answer are as follows:

 Which location strategy could be applied in order to design a bioenergy supply chain network in a large geographic area?

 What procedure could be adopted in order to achieve sustainable development in the supply network?

 Which approach could be followed in order to improve the stability of the bioenergy supply network under uncertain conditions?

In this paper, a sustainable two-phase sequential approach is proposed in order to design bioenergy SCs under uncertainties. The first phase tries to find the appropriate locations for the bio-refineries by integrating the geographic information system, the social aspects, and the multi-criteria decisionmaking techniques. In this phase, high rates of unemployment, and the high vulnerability of the areas to variations in the markets in an economic crisis, are considered as social concerns. Integrating these factors (the geographic information system, and the social sustainability) by using the multi-criteria decision-making techniques filters the areas to obtain appropriate locations as input for the second phase. The first phase augments the practicality of the supply network design, reduces complexity in the computation of the problem, and helps set up sustainable development. In the second phase, in order to cope with the uncertainties in the bioenergy supply network, a robust model is introduced to reduce the sensitivity to inaccurate input data. It means that the obtained optimal solutions are still optimal when the parameters change slightly.

In the remainder of this paper, a review of bioenergy supply chain network design is given in Section 2. The integrated two-phase approach is explained in Section 3. Section 4 formulates the deterministic and robust models of this approach. A case study is described in Section 5. Evaluation of the performance of the proposed method is presented in Section 6. Section 7 concludes and makes suggestions for future research.

Literature review

Modeling and optimization of bioenergy supply chains (SCs) have been attracting a great deal of attention from researchers recently. In bioenergy SC literature, from one point of view, many models only considered the economic aspect of the SC when designing the network. For instance, in the studies based on a bioenergy SC with agricultural and forest (AF) biomass, some researchers focused on geographical dispersion to find the sources and supply capacities [START_REF] Nguyen | Supplier selection and operation planning in biomass supply chains with supply uncertainty[END_REF][START_REF] Arabani | Facility location dynamics: An overview of classifications and applications[END_REF][START_REF] Soren | Resilient design of biomass to energy system considering uncertainty in biomass supply[END_REF]. Others worked on decisions related to the locations of bio-refinery and production capacity [START_REF] Schmidt | Potential of biomass-fired combined heat and power plants considering the spatial distribution of biomass supply and heat demand[END_REF], and another group concentrated on the design of the supply chain (network) that generates biofuel from various types of AF biomass [START_REF] Razm | A global bioenergy supply network redesign through integrating transfer pricing under uncertain condition[END_REF][START_REF] Marvin | Economic optimization of a lignocellulosic biomass-to-ethanol supply chain[END_REF][START_REF] Vikash | Conceptual design of a lignocellulosic biorefinery and its supply chain for ethanol production in India[END_REF].

Bairamzadeh et al. [START_REF] Bairamzadeh | Modelling different types of uncertainty in biofuel supply network design and planning: A robust optimization approach[END_REF] investigated the strategic and tactical decision levels of the biofuel supply chain based on AF biomass. The authors considered agricultural residues such as corn stover, wheat straw, barley straw and rice straw as feedstock biomass and proposed an MILP model to minimize the total cost of the SC by selecting the capacity, location, and technology of the biorefineries, as well as the amounts of production, inventory, allocation, and transportation. A hybrid robust optimization approach was suggested to cope with the uncertainties. Santibañez-Aguilar et al. [START_REF] Santibañez-Aguilar | Sequential Use of Geographic Information System and Mathematical Programming for Optimal Planning for Energy Production Systems from Residual Biomass[END_REF] proposed an approach for optimal planning of the biomass residues obtained from crops such as sugar cane, corn, agave, palay rice in a processing system. The authors suggested a mathematical programming model involving mass balances to achieve the interconnections among different nodes of the supply chain. They considered constraints for the technologies in terms of capital investment and cost of production. The objective was to maximize the annual profit obtained from the revenue of selling products, minus the transportation cost, manufacturing cost, and raw material cost. They did not consider the related uncertainties in the model that may lead to a design for the SC network which is not feasible. Mohseni et al. [START_REF] Mohseni | Robust design and planning of microalgae biomass-to-biodiesel supply chain: A case study in Iran[END_REF] developed a mixed-integer linear programming model (MILP) model to minimize the total cost of the biodiesel supply chain. The study focused on third-generation biofuel, so the proposed mathematical model and approach are specific to a microalgae biomass supply chain. These studies only considered economic aspects of the supply chain, and social concerns or the concepts of sustainability related to the microalgae-based biodiesel SC were not investigated.

In terms of sustainable development, in [START_REF] Rabbani | Developing a sustainable supply chain optimization model for switchgrass-based bioenergy production: A case study[END_REF] the authors proposed an MILP model to design a sustainable bioenergy supply chain network for switchgrass-based biomass. The model included economic, environmental and social objectives and aimed to find the maximum capacity in the biomass centers, the location and capacity of the power plants, and the amount of the collected and stored switchgrass. The authors used a hybrid method involving augmented ε-constraint and TOPSIS approach to consider preferences of decision-makers. The study did not consider any uncertainty.

According to [START_REF] Bairamzadeh | Multiobjective robust possibilistic programming approach to sustainable bioethanol supply chain design under multiple uncertainties[END_REF], designing a new biofuel supply chain can create jobs for local people in the area and protect the environment [START_REF] D'amore | Strategic optimisation of biomass-based energy supply chains for sustainable mobility[END_REF]. However, in the bioenergy supply chain literature, most of the studies just considered economic aspects of the supply chain, and less attention was given to the sustainability of the bioenergy SC, especially social aspects. Nevertheless, it is crucial to consider sustainability when designing bioenergy supply chains. Thus, there is a gap in the literature and a need to take into account, at the design stage, sustainability aspects, alongside economic effects [START_REF] Ghaderi | Biomass supply chain network design: an optimization-oriented review and analysis[END_REF]. Considering social criteria, in the article [START_REF] Bairamzadeh | Multiobjective robust possibilistic programming approach to sustainable bioethanol supply chain design under multiple uncertainties[END_REF], the authors designed a bioethanol supply chain network using corn stover and wheat straw (lignocellusic biomass). They considered job opportunities as a social objective in a multi-objective MILP model to determine the location and capacity level of the facilities used in the biorefineries, inventory levels, and material flows. There are other studies in the literature which considered social aspects [START_REF] Carter | A framework of sustainable supply chain management: moving toward new theory[END_REF][START_REF] Bijarchiyan | A sustainable biomass network design model for bioenergy production by anaerobic digestion technology: using agricultural residues and livestock manure[END_REF]. Bijarchiyan and Sahebi [START_REF] Bijarchiyan | A sustainable biomass network design model for bioenergy production by anaerobic digestion technology: using agricultural residues and livestock manure[END_REF] used the Guidelines for the Social Life Cycle Assessment of a Product (GSLCAP) method to find the social impact of a bioenergy supply chain network, and Carter and Rogers [START_REF] Carter | A framework of sustainable supply chain management: moving toward new theory[END_REF] introduced job creation as a social objective.

In terms of uncertainty, stochastic programming (two-stage) has been used in a large number of models. For example, a stochastic MILP model to design a biofuel SC under uncertainties of product price and cost of the feedstocks was proposed in [START_REF] Dal-Mas | Strategic design and investment capacity planning of the ethanol supply chain under price uncertainty[END_REF]. The authors considered the net present value and the conditional value at risk as two objective functions in their model. A stochastic programming model under price and demand uncertainties which were solved by simulation and a Benders decomposition algorithm was proposed in [START_REF] Awudu | Stochastic production planning for a biofuel supply chain under demand and price uncertainties[END_REF] for the planning of a biofuel SC. A bioethanol SC considering demand as uncertainty was modeled by a stochastic MILP and solved with two-stage method in [START_REF] Kostin | Design and planning of infrastructures for bioethanol and sugar production under demand uncertainty[END_REF]. The sample average approximation method was used in that study in order to provide a set of configurations for facing uncertainty. Chen and Fan [START_REF] Chen | Bioethanol supply chain system planning under supply and demand uncertainties[END_REF] presented a stochastic programming (two stage) model for resource allocation and strategic planning of a biofuel SC under uncertainty related to demand and supply. The authors solved it by using a decomposition algorithm based on Lagrange relaxation. In order to maximize the profit and decrease the carbon emissions with price, demand and supply uncertainties in a bioethanol supply chain, a two-stage stochastic MILP was proposed in [START_REF] Osmani | Economic and environmental optimization of a large scale sustainable dual feedstock lignocellulosic-based bioethanol supply chain in a stochastic environment[END_REF].

When a large geographic area is considered for a bioenergy SC network, identifying the locations where the bio-refineries may be installed is very important, because the network structure, costs, social performance, and environment are affected by these decisions. The methods used in the existing publications are not always clearly out. For instance, some researchers considered sets of locations which were as large as possible, covering most of the desired territory, to obtain more opportunities. Some others considered a continuous territory in their facility location models by assuming that the facilities could be placed anywhere [START_REF] Arabani | Facility location dynamics: An overview of classifications and applications[END_REF]. These methods present some problems such as: 1) they cannot guarantee that optimal places are chosen in the whole of the desired territory, 2) those that considered continuous territory in their facility location models [START_REF] Arabani | Facility location dynamics: An overview of classifications and applications[END_REF] usually restricted their models to a limited number of levels and parts, 3) also when the planning space increases, not only the computational complexity is significantly increased, but functionality is also severely limited [START_REF] Melo | Facility location and supply chain management-A review[END_REF]. What is why, the conventional agricultural and forest (AF) biomass SC models [START_REF] Schmidt | Potential of biomass-fired combined heat and power plants considering the spatial distribution of biomass supply and heat demand[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] Ahmed | Impact of carbon emissions in a sustainable supply chain management for a second generation biofuel[END_REF] usually focused on limited and predetermined candidate locations. In this case, simultaneously considering geographical information and social sustainability of the wide geographical territory is very important to select such candidate locations. Nevertheless, the existing models usually did not take them into account. By embracing the Geographic Information System (GIS) and the sustainability, and by using the multi-criteria decision-making techniques it is possible to consider more map layers in order to determine more appropriate places for bio-refineries. Moreover, if the bioenergy SC decisions do not take uncertainties sufficiently into account, the design model will not be trustworthy nor feasible. These are the factors which motivate this paper versus the state of the art.

Table 1 shows the outcomes of the literature review concerning the bioenergy SC problem. It shows that there is an essential research gap to optimize bioenergy supply chains by considering a two-phase sequential approach containing the geographical information, sustainability, multi-criteria decisionmaking techniques and uncertainty conditions. This study makes an effort to fill this gap.

Consequently, this paper includes the following contributions: 1) it develops a model for designing and planning the agricultural/forest residues-to-bioenergy supply chains; 2) it proposes a two-phase approach to solve the introduced SC model; 3) it integrates geographical information, social sustainability, and the multi-criteria decision-making techniques to find appropriate locations for biorefineries; 4) it uses robust optimization to hedge against uncertainty; and 5) it validates the developed two-phase approach by applying it to a case study.

Problem definition

The bioenergy SC of AF residues is a complex multi-phase supply network that starts with the supply of raw materials (biomass) for bio-refineries and finishes with the market end-products. In such a network, the bio raw materials contain non-merchantable AF residues usually collected from piles left at the roadsides of the harvesting blocks and from plants that produce AF products. Next, these raw materials are sent to bio-refineries installed as independent units or set up near plants that produce AF products. Proximity reduces biomass transport/management costs [START_REF] Demirbaş | Biomass resource facilities and biomass conversion processing for fuels and chemicals[END_REF]. In this paper, it is considered that bio-refineries can also act as suppliers of renewable energy for AF plants. Different biochemical, chemical, and thermochemical processes can change the biomass into biofuel, pellets, heat, electricity, etc. The biomass type and the features of the desired products determine type of technology [START_REF] Mckendry | Energy production from biomass (part 1): overview of biomass[END_REF]. The bioenergy produced (electricity/heat) is either used in the bio-refinery or sold to local heat grids/system. The biofuel products are sent to various markets.

Figure 1 shows the studied structure of the SC that obtains bioenergy from agricultural and forest residues. In this figure, S is the biomass supply site, R represents the various types of AF biomass, and B are the candidate locations for bio-refineries.

The proposed two-phase approach

The design process for the SC network that converts AF biomass to bioenergy involves two phases. In the first phase, as shown in Figure 2, the appropriate locations that could be candidates for biorefineries are selected based on geographical information and social concerns by using multi-criteria decision-making techniques. These locations are then used as inputs in the model for the second phase to yield the final locations of the bio-refineries and the entire supply network minimizing costs.

The first phase of the proposed two-phase approach

Identifying the candidate locations to set up bio-refineries is a complex process requiring accurate assessments over a wide geographic area. These locations should conform to the regions' possible environmental, economic and social interactions, and should have access to biomass/resources, and the power required for conversion technologies all through the year [START_REF] Demirbaş | Biomass resource facilities and biomass conversion processing for fuels and chemicals[END_REF]15]. Accordingly, a set of criteria grouped into those related to resources, environment, society, and economy is determined to find the location of bio-refineries according to the information existing in literature [START_REF] Perpiña | Multicriteria assessment in GIS environments for siting biomass plants[END_REF][START_REF] Teixeira | Forest biomass power plant installation scenarios[END_REF][START_REF] Vukašinović | Optimization and GIS-based combined approach for the determination of the most cost-effective investments in biomass sector[END_REF][START_REF] Zhang | Integrating GIS with optimization method for a biofuel feedstock supply chain[END_REF] and also quantitative/ qualitative information which can be obtained from consulting the experts of the national mapping agency of each country.

In the first phase, with experts of the national mapping agency of each country as decision-makers, the AHP method as a well-known Multi-Criteria Decision Making (MCDM) technique [START_REF] Wheeler | Combining multi-attribute decision-making methods with multiobjective optimization in the design of biomass supply chains[END_REF] can be used to weight every map layer and the specific criteria to select candidate locations. The layers are then overlaid on the base map using GIS overlay analysis. Each layer's allocated importance weight is multiplied by the value of each digital cell considered on the base map. Then, all of them come together using a summation in order to generate the digital cells' total suitability scores on the base map [START_REF] Malczewski | GIS-based land-use suitability analysis: a critical overview[END_REF]. Next, a suitability index is calculated that divides the area studied into a range between high suitability and low suitability. Finally, the first phase achieves its goal by proposing high-suitability, favorable locations in the considered geographical area.

Figure 2: Different aspects of geographical information in the bioenergy supply chain.

The social dimension of the bioenergy supply network (BE-SN)

For example, given the research done by Isfahan University of Technology's college of agricultural engineering, Iran's Ministry of Economic Affairs and Finance prepared a vulnerability index 𝛯 for agriculture and forest, that withstands the variations in the markets of AF products. The economic variety in the territory is introduced by the 𝑣𝑎𝑟𝑖𝑒𝑡𝑦 𝑖𝑛𝑑𝑒𝑥 𝛱, which varies between 0 and 100. Value 0 means the territory relies totally on one section, whereas 100 means the territory relies identically on each section. A portion of the recruitment income that is earned from forest and agricultural sections in the territory is shown by the 𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑐𝑦 𝑖𝑛𝑑𝑒𝑥 𝛥 which is in between 0 and 1. Thus, the index 𝛯 is introduced as the 𝑖𝑛𝑑𝑒𝑥 𝑜𝑓 𝑓𝑜𝑟𝑒𝑠𝑡 𝑎𝑛𝑑 𝑎𝑔𝑟𝑖𝑐𝑢𝑙𝑡𝑢𝑟𝑒 𝑣𝑢𝑙𝑛𝑒𝑟𝑎𝑏𝑖𝑙𝑖𝑡𝑦 of the different territories (e.g. different states of a country), scoring from 0 until 100 after normalizing:

𝛯 = 𝛥 × (100 -𝛱).
The value 100 means the territory is the most vulnerable. For instance, the values of 𝛯 for some regions are shown in Table 3 (www.amar.org.ir), they can be obtained from each country's statistics office.

Table 3:

Concentrating on the territories with high level of unemployment and with high vulnerability can lead to social advantages. In other words, if jobs with higher levels of employment are offered in the territories with high level of vulnerability, more social advantages can be obtained [START_REF] Rabbani | Optimal design for sustainable bioethanol supply chain considering the bioethanol production strategies: A case study[END_REF].

Depending on the job losses in the other production facilities for residents of territories due to the economic crisis, various job categories are proposed in the SC of bio-refineries that are relevant to the skills of the individuals in these territories.

For instance, the farmers lost jobs can be replaced by work in the combustion stations, and the pyrolysis technology stations can provide jobs for individuals previously working in the corporations relating to oil. For example, according to the Iranian statistics office ( www.amar.org.ir), a large number of farming jobs were destroyed in the last economic crisis, so their unemployment rate is high (equal to 11.23%). These farmers could be used in the combustion centers. If the social impact of the jobs created for local people is developed in this way, there will be social advantages.

After consulting the Renewable Energy and Energy Efficiency Organization (www.satba.gov.ir), the jobs created for local people by installing the bio-refinery are classed into three main categories depending on the average unemployment rate (𝛬 𝑤 ). There are jobs related to combustion, pelletizing, and the pyrolysis section (w), (see Table 4).

It should be mentioned that these unemployment rates can be obtained from the statistics office of each country, so Table 4 can be adapted to other case studies or countries.

Given the vulnerability and unemployment rate in the bio-refineries' territory, the social impact of the jobs created in the category w in the territory b could be obtained as follows:

𝛹 𝑤,𝑏 = 𝛬 𝑤 × 𝛯 𝑏 (S1)
Therefore, in order to maximize the social impact in the territories where bio-refineries will be established, the areas with high vulnerability indexes are considered using the statistics office of each country. These areas are used as input (digital map) for GIS. Then, by using the ring buffers as defined in the ArcGIS Software at different distances (e.g., 1.5, 4, 5, 17, 70, and 100 km from the central locations), the areas being analyzed are limited and those outside the ring buffers (spaces) are omitted. This method is also used for the areas with high rates of unemployment in order to obtain the second digital map layer of society criteria.

Table 4

The job class and its average unemployment. Average unemployment rate (𝛬 𝑤 ) Description Class (w)

11.23%

This class of jobs has a revenue between $50,000 and $55,000 per year. The revenue is able to change in the specific range considering the technologies' capacities and the requested variable and fixed work hours. For example, jobs related to burning of agriculture and forest biomass to generate heat and electricity, or periodic maintenance of combustion technology like the biomass boiler and steam turbine.

Combustion

6.55%

This class of jobs has a revenue between $55,000 and $60,000 per year. The revenue is able to change in the specific range considering the technologies' capacities and the requested variable and fixed work hours. For example, working with technologies which are specific to generate pellets, or preprocesses which are requested in each period before performing the main process of generating pellets.

2.Pelletizing

12.35%

This class of jobs has a revenue more than $60,000 per year. The revenue is able to change in the specific range considering the technologies' capacities and the requested variable and fixed work hours. For example, the hourly jobs for the generating process with pyrolysis technologies or the jobs with fixed hours for constant presence of the experts beside the facilities in each period.

3.Pyrolysis

The resources of the bioenergy supply network (BE-SN)

The resources required include forest residues and agricultural remains. The former involves harvesting residues such as non-merchantable, small diameter, low quality logs, tree tops, and branches (not suitable for either pulp production or lumber) and sawmill waste. The latter includes agricultural waste and non-food crops like corn stover and wheat straw.

These raw materials (biomass) could usually be gathered from many aggregated cutting blocks and agricultural lands. One of the signs of biomass availability is the presence of procurement centers/ forest product mills. Obviously, the farther the location of a bio-refinery is from the procurement centers/forest product mills, the higher the biomass accessibility cost will be. Accordingly, the proposed method can use the ring buffers at different distances (e.g., of 3, 12, 25, 75, and 100 km) around the existing procurement centers/forest product mills to make the biomass accessibility less expensive. It is worth mentioning that these residues ordinarily have no use in any other industry, and are usually disposed by burning or in landfill [START_REF] Zareei | Evaluation of biogas potential from livestock manures and rural wastes using GIS in Iran[END_REF][START_REF] Zhang | A GIS-based method for identifying the optimal location for a facility to convert forest biomass to biofuel[END_REF].

Supplying energy from resources is another issue for biomass conversion technologies in the biorefineries. The required energy can be supplied either by the bioenergy generated in the bio-refineries or from the electricity of the power plants that are the current energy sources.

Transferring electricity and energy from remote areas is costly. If energy sources are far from biorefineries, they will induce heavy energy costs for the SC [START_REF] Zhang | A GIS-based method for identifying the optimal location for a facility to convert forest biomass to biofuel[END_REF]. Hence, using the ring buffers (spaces) at different distances (e.g. 1.5, 4, 5, 17, 70, and 100 km) from the energy sources limits the areas being analyzed, and those outside the ring buffers (spaces) are omitted.

The economic criteria in the locations of bio-refineries

The total transportation cost in the bioenergy/biofuel SC is quite high. Connecting bio-refineries to the country roadways/railways networks is a significant problem that imposes a high cost on the SC which can make it economically unprofitable. To solve this problem, different spaces are used around the country's main roadways and railways to exclude areas outside these spaces [START_REF] Sultana | Optimal siting and size of bioenergy facilities using geographic information system[END_REF].

3.1.1.4. The environmental criteria of BE-SN  Land use: Considering environmental issues and other features of bio-refineries, lands that have less usage problems should be selected [15,[START_REF] Perpiña | Multicriteria assessment in GIS environments for siting biomass plants[END_REF]. For example, agriculture is an important element in the economy of many countries. Conversion of agricultural lands can be not allowed according to the laws of the country. Therefore, bio-refineries cannot be built on these lands. Hence, other remaining regions (barren lands, woodlands, pastures, shrubs, herbaceous) will have priority.

Note that these laws may differ from country to country, so by considering new conditions the remaining regions and their weights on the map layers may be changed.  Land slope: Sloping surfaces are not suitable for building bio-refineries because they increase construction problems due to the costs of such activities as cutting, filling, earthwork and erosion prevention [START_REF] Nas | Selection of MSW landfill site for Konya, Turkey using GIS and multicriteria evaluation[END_REF]. To reduce these costs, the study of suitable locations could be limited to land with less slopes (e.g. less than 5 degrees), the digital elevation model and the ''surface'' command in the ArcGIS Software can be used in this part.

The second phase of the proposed two-phase approach

The second phase is aimed at designing an optimal SC network (SCN) that produces bioenergy from biomass to ensure that all the SC decisions, from supplying biomass to the end products (biofuel and bioenergy) received by customers, are made and integrated optimally. The decisions made at this phase are:

 Determining the raw material flow between the suppliers and bio-refineries and that of the bioenergy and biofuels between bio-refineries and customers.

 Selecting biomass suppliers.  Determining the optimal locations of bio-refineries from the appropriate locations identified in the first phase.

 Determining the type/capacity of the biomass conversion technologies used in each bio-refinery.

 Proposing the biofuel production rate and inventory planning for production during the year.

These decisions are affected by uncertainties such as variable access to biomass due to seasonal variations, and uncertain cost factors due to large-scale bioenergy/biofuel production [START_REF] Dal-Mas | Strategic design and investment capacity planning of the ethanol supply chain under price uncertainty[END_REF][START_REF] Kostin | Design and planning of infrastructures for bioethanol and sugar production under demand uncertainty[END_REF].

Stochastic programming or robust optimization (RO) can be used in order to cope with these kinds of uncertainties in the optimization problems [START_REF] Dehghani | Resilient solar photovoltaic supply chain network design under business-as-usual and hazard uncertainties[END_REF]. Although stochastic programming (SP) is a powerful tool for dealing with uncertainties, it suffers from some obvious flaws such as: 1) it needs the probability distribution information for values of the parameters under uncertainty, but in real life, it is not usually possible to determine this distribution accurately because of the shortage of historical data; 2) it generally leads to complexity in the computations for models in real world problems because it needs many scenarios to model uncertainties [START_REF] Pishvaee | A robust optimization approach to closed-loop supply chain network design under uncertainty[END_REF]. Conversely, RO, which is capable of preserving the primary model's computational tractability [START_REF] Li | A comparative theoretical and computational study on robust counterpart optimization: I. Robust linear optimization and robust mixed integer linear optimization[END_REF], is a free distribution method aimed at finding the solution (worst case) according to a predetermined set of uncertainties. It could be used to prevent input data uncertainty in the problem, and stays robust against any perturbations. Furthermore, besides the lack of information to find the probability distributions for uncertain parameters considered in this study, there also are different fluctuating factors that can affect these uncertain parameters such as seasonality of biomass or different cost factors due to the large scale of the network. The nature of uncertainty for these parameters is characterized by deep uncertainty. This means for each uncertain parameter, a known interval is expressed. The interval is expressed without assuming a specific distribution of probabilities [START_REF] Bairamzadeh | Modelling different types of uncertainty in biofuel supply network design and planning: A robust optimization approach[END_REF].

The interval uncertainty in robust optimization was first presented in [START_REF] Soyster | Convex programming with set-inclusive constraints and applications to inexact linear programming[END_REF]. The author considered all the uncertain parameter values in the worst case to provide maximum protection against uncertainties. Nevertheless, this is not realistic, because at the same time the whole set of uncertain parameters may result in the worst value, so the idea was excessively over-conservative. This theory was then developed in [START_REF] Ben-Tal | Robust solutions of linear programming problems contaminated with uncertain data[END_REF][START_REF] El Ghaoui | Robust solutions to uncertain semidefinite programs[END_REF] and, under an ellipsoid uncertainty set, a robust counterpart formulation to control the solution's conservatism level was presented. The authors developed a robust optimization methodology in which the linear program (LP) is changed to a convex nonlinear program (NLP), which is more complicated as regards the computations. Next, in [START_REF] Bertsimas | The price of robustness[END_REF] an approach was developed that can control the conservatism level and preserve the linearity of the model as well.

It will be used in this study, i.e. for the design of the bio-energy SC, the two-phase approach proposed in this paper is based on a robust model adopting the Bertsimas-Sim ideas [START_REF] Bertsimas | The price of robustness[END_REF].

Analytical Hierarchy Process (AHP)

The Analytical Hierarchy Process is a decision-making technique for extracting the weights of criteria in the problems involving competitive and multiple objectives (a complex decision-making problem). It generally involves three phases [START_REF] Saaty | What is the analytic hierarchy process?[END_REF]: 1) the problem is broken down into a descending hierarchical structure where the objective stands at the upper level, the criteria lie below it, and then sub-criteria are categorized; 2) the paired comparison matrix is computed for this hierarchy at each level, in such a way that, based on the 9-point scale, each element lies in a 1 to 9 interval (from the importance of the row criterion in relation to its column criterion), 1 means equal preference and 9 means strongly preferred; and, finally, 3) the principal eigenvalue and also the corresponding normalized eigenvector of the matrix are calculated to derive the relative importance weights of the criteria being compared [START_REF] Sultana | Development of agri-pellet production cost and optimum size[END_REF].

It is necessary to justify the consistency of the judgments in order to ensure the results of the weighting process. For a paired comparison matrix, the consistency index is obtained using the following equation:

𝐶𝐼 = (𝜆 𝑚𝑎𝑥 -𝑛) (𝑛 -1) ⁄ 𝐶𝑅 = 𝐶𝐼 𝑅𝐼 ⁄
where CI is the consistency index, 𝜆 𝑚𝑎𝑥 is the largest matrix eigenvalue, and n is the matrix order.

CR (the acronym of consistency rate) compares CI with RI (the acronym of random index). CR is used for a better understanding of the CI value. CR < 0.1 means consistency of the formed matrix and reliability of the calculated weights. Otherwise, reformation, from the beginning, of the pair-wise comparison matrix would be necessary.

Robust optimization approach

To briefly describe the Bertsimas-Sim's approach [START_REF] Bertsimas | The price of robustness[END_REF], let us examine the following LP:

𝑀𝑖𝑛

Model formulation

This section has two objectives. Firstly, it shows the development of a deterministic mixed integer linear programming model (MILP) to optimize the strategic design of the bioenergy SC. Secondly, it presents the MILP robust model considering uncertain parameters. Before formulating the problem, a verbal description is presented to understand the model better.

Deterministic Bioenergy Supply Network (DBE-SN) model

Using Table 2, the following DBE-SN model is formulated.

Objective function

The objective function (1) minimizes the total costs of the SC throughout the planning horizon, including costs of supplying biomass (purchasing/collecting), transportation of biomass to biorefineries, transportation of biofuel from bio-refineries to markets, fixed costs (annual investments), variable production costs, and energy costs for launching technologies, i.e. that part of the energy required by the bio-refinery supplied by the available energy sources. Also, the inventory holding costs of different biofuel types are also considered in the objective function. It is worth noting that the biomass is not stocked in this case to prevent its deterioration and dehydration from one year to another. Bioenergy storage is also dismissed because it is either impossible or not economical.

𝑀𝑖𝑛 𝑇𝑜𝑡𝑎𝑙 𝐶𝑜𝑠𝑡 = ∑ ∑ ∑ ∑ 𝜍 𝑟,
Constraints ( 11) make sure that the biofuel's amount for the markets should be equal to the amount produced at location b in any period.

∑ 𝑃 𝑓,𝑏,𝑐,𝑡 𝑀 = ∑ 𝑃 𝑓,𝑏,𝑎,𝑡 𝑎∈𝐴 𝑐∈𝐶 ∀𝑏 ∈ 𝐵, 𝑓 ∈ 𝐹, 𝑡 ∈ 𝑇 [START_REF] You | Optimal design of sustainable cellulosic biofuel supply chains: multiobjective optimization coupled with life cycle assessment and input-output analysis[END_REF] Constraints [START_REF] Awudu | Stochastic production planning for a biofuel supply chain under demand and price uncertainties[END_REF] ensure that the bioenergy used by the technology installed in each bio-refinery, plus the amount sold to customers (outside of the bio-refinery), should equal the total amount produced in the bio-refinery in each period. Constraints ( 13) and [START_REF] Demirbaş | Biomass resource facilities and biomass conversion processing for fuels and chemicals[END_REF] show the demand limitations for bioenergy and biofuel products.

𝛿
Constraints [START_REF] Soren | Resilient design of biomass to energy system considering uncertainty in biomass supply[END_REF] ensure persistence in the conversion processes after the bio-refineries are installed.

𝑌 𝑏,𝑎,𝑡 ≥ 𝑌 𝑏,𝑎,(𝑡-1) ∀𝑎 ∈ 𝐴, 𝑏 ∈ 𝐵, 𝑡 ∈ 𝑇 [START_REF] Soren | Resilient design of biomass to energy system considering uncertainty in biomass supply[END_REF] Constraints ( 19) and ( 20) are to prevent the model from selecting more than one technology for generating any kind of biofuel and bioenergy. Index 𝑎 𝑒 presents a subset of the technologies which can produce the bioenergy of type e, index 𝑎 𝑓 presents one that can produce type f bioenergy. It is worth noting that, when the installed technologies' numbers are limited to the available biomass or to the demand for products, constraints [START_REF] Schmidt | Potential of biomass-fired combined heat and power plants considering the spatial distribution of biomass supply and heat demand[END_REF] and ( 20) could be eliminated. Therefore, when the objective function does not consider such limiting factors as high costs, the total number of technologies installed in each bio-refinery may not be limited for samples with large available biomass and high product demand.

∑ 𝑌 𝑏,𝑎,𝑡 ≤ 1

Robust Bioenergy Supply Network (RBE-SN) model

Costs, amount of resources, production, and the demand for bioenergy/biofuel products are considered as uncertain parameters. Then, by developing the DBE-SN model into its robust counterpart, these parameters are considered as random variables that acquire value from a symmetric distribution according to a nominal value. For instance, 𝛽 𝑟,𝑠,𝑡 ̃ belongs to the interval [𝛽 𝑟,𝑠,𝑡 -𝛽 𝑟,𝑠,𝑡 ̂ , 𝛽 𝑟,𝑠,𝑡 + 𝛽 𝑟,𝑠,𝑡 ̂] , where 𝛽 𝑟,𝑠,𝑡 is its nominal value and 𝛽 𝑟,𝑠,𝑡 ̂ is the variation amplitude.

Accordingly, the following robust method is proposed.

Objective function

The objective function presented in ( 1) is converted to ( 23) and ( 24). Since the model looks for the worst case, the whole expression ( 1) is considered equal to the maximum possible value (i.e. value of Z). Then, ( 1) is converted to the robust counterpart model presented in [START_REF] Santibañez-Aguilar | Sequential Use of Geographic Information System and Mathematical Programming for Optimal Planning for Energy Production Systems from Residual Biomass[END_REF]

Constraints:

According to Section 3.2 (Robust optimization approach) into each of the constraints (2), ( 9), ( 10), ( 13) -( 14), and ( 17), the budget parameters are introduced, and these constraints are changed to constraints (32), ( 39), ( 40), ( 43)- [START_REF] Wheeler | Combining multi-attribute decision-making methods with multiobjective optimization in the design of biomass supply chains[END_REF], and (49), respectively. It can be observed that when perturbations are larger, these constraints become tighter.

Case study

To illustrate how this approach can be used in practice, a case study from Iran is considered. Due to high climate diversity across the Iranian territory, there are many AF areas where the residues are left idle and sometimes incur costs and create environmental pollution for the inhabitants because the normal methods of disposal are burning or transportation to remote landfill sites.

Two main kinds of raw material (biomass) are considered for changing: 1) forest residues from operation processes in the forests and sawmill wastes such as chips, branches, shavings, leaves, sawdust, tree tops, hog fuel; 2) agricultural residues coming from grain harvesting of plants such as corn and wheat.

These residues can be changed to bioenergy like electricity and heat, be used to produce biofuel like ethanol, biodiesel, or converted to other products with a bio-base, e.g. plastics, and chemicals [START_REF] Demirbas | Potential contribution of biomass to the sustainable energy development[END_REF]. The basic processes for converting the biomass are thermochemical, biochemical, and chemical. The biochemical and thermochemical are appropriate methods for treating AF biomass, the former involves fermentation and hydrolysis and the latter involves pyrolysis, combustion, and gasification [START_REF] Mckendry | Energy production from biomass (part 2): conversion technologies[END_REF].

In this case study, the following four categories of the technologies for the biorefineries are considered: 1) gasification for producing heat and electricity; 2) combustion for producing heat and electricity; 3) generation of bio-oil through fast pyrolysis; and 4) pelletization, i.e. the production of pellets. Table 5 shows the different kinds of biomass needed for each technology [START_REF] Campbell | A feasibility study guide for an agricultural biomass pellet company[END_REF][START_REF] Rogers | Estimation of the production cost of fast pyrolysis bio-oil[END_REF][START_REF] Lehtikangas | Quality properties of pelletised sawdust, logging residues and bark[END_REF]. Note that the processes of fast pyrolysis and combustion are able to convert all kinds of the biomass, in contrast, the processes of pelletization and gasification need biomass which is clean with low ash in content. Therefore, two kinds of the biomass can be used for the technologies of pelletization and gasification. These are the stem chips coming from harvesting residues of damaged mountain pines, and wood chips from sawmill waste [START_REF] Rogers | Estimation of the production cost of fast pyrolysis bio-oil[END_REF][START_REF] Yue | Stackelberg-game-based modeling and optimization for supply chain design and operations: A mixed integer bilevel programming framework[END_REF]. Four capacities (0.5, 2, 3, and 5 MW) are considered for the combustion technologies. Table 6 reports the efficiency of these technologies for the biorefineries [START_REF] Mckendry | Energy production from biomass (part 1): overview of biomass[END_REF][START_REF] Tong | Stochastic programming approach to optimal design and operations of integrated hydrocarbon biofuel and petroleum supply chains[END_REF][START_REF] Heat | Power Catalog of Technologies[END_REF]. Consulting the Renewable Energy and Energy Efficiency Organization (www.satba.gov.ir), for different capacities of burning technologies, there are a variety of electrical and thermal efficiencies. For pyrolysis technology at three capacities (200, 400, 600 ton/day), the efficiency depends on the type of biomass, see Table 5. For technology of pellet at three capacities (15000, 30000, 45000 ton/year), the efficiency is assumed to be 92%. [START_REF] Mckendry | Energy production from biomass (part 2): conversion technologies[END_REF][START_REF] Heat | Power Catalog of Technologies[END_REF].

Table 5:

Table 6 Four products, namely electricity, heat, bio-oil, and pellet are considered in this study: the electricity is either sold to the local electrical grid in the bio-refinery area or used inside the bio-refinery; heat is used both inside the bio-refinery and sold to the nearby factories/industries or houses around the biorefinery area; bio-oil and pellets are stored to meet the local demand of the region as well as that from other regions or provinces.

Iran has a cross-country railroad network throughout most of the country and many highways and local roads. Since long-distance transportation is usually less expensive by train, most of the long-haul freight is transported to the railway station by trucks, from where it is transported by train to distant areas. Trucks usually travel at 70-80 km/hour while the train speed is about 60 km/hour. This case study used the expertise and GIS data from National Cartographic Center of Iran (www.ncc.ir), the national mapping agency, and also considered four 5-year periods.

Results and discussion

Results of the first phase of the proposed two-phase approach

The GIS data and the criteria/sub-criteria maps obtained from the national mapping agency were used as inputs for GIS software. Then, after digitalizing the maps, they were changed to the raster form (e.g. 95 m resolution). When this was achieved, a group of experts from the national mapping agency specializing in this field was asked to use the AHP method as a Multi-Criteria Decision Making (MCDM) technique to weight each map from an economic-engineering perspective.

According to [START_REF] Malczewski | GIS-based land-use suitability analysis: a critical overview[END_REF], the map overlaying in a GIS is usually done either by the Boolean overlay method, which is applied to non-compensatory cumulative operators such as "union" (OR logic) with only one criterion and "intersection" (AND logic) with every criterion [START_REF] Gorsevski | Integrating multi-criteria evaluation techniques with geographic information systems for landfill site selection: a case study using ordered weighted average[END_REF], or the weighted overlay method in which a relative importance weight is allocated to each evaluation criterion (or map layer) based on compensatory combinatorial rules. Hence, the weighted overlay method is more flexible than the Boolean method in selecting the appropriate locations of bio-refineries.

Table 7 shows the main types, the categories and the subcategories of different criteria and subcriteria used in the decision-making problem considered in this study. They are considered as a descending hierarchical structure. Four main category types (societal, resource, economic, and environmental) are considered at the upper level, subdivided into eight categories, and then the subcategories are considered for the next level of the descending hierarchical structure. For each level of this hierarchy, the paired comparison matrix is computed by the experts (e.g. from National Cartographic Center of Iran; www.ncc.ir). For example, in the third row of Table 7, the economic criteria are divided into distance to the road and distance to the rail. In the experts' opinion, these two criteria can be divided into five sub-criteria (i.e. 0-3, 3-6, 6-20, 20-50, 50-100 km for distance to the road, and 0-5, 5-10, 10-25, 25-45, 45-100 km for distance to the rail). Using AHP, their weights can be obtained. Table 7 shows that all consistency ratios (CR) obtained from the weights are less than 0.1, this indicates the consistency of the formed matrix and the reliability of the calculated weights.

Figure 3: Final map of suitable locations for the selection of bio-refinery sites Table 7:

All the digital map layers are weighted by using the weights computed in Table 7 and are combined with the GIS analyzer. The final map for the proposed locations is calculated using the suitability index.

The map is presented in Figure 3. Finally, 23 candidate locations with a high-suitability level are selected by using the equal-distance classification method. These suitable locations are considered as inputs for the second phase.

Results of the second phase

For this part of case study, both the proposed MILP models were coded in GAMS 24, and solved by using the CPLEX solver. All empirical experiments were implemented with an Intel Core i3, 2.13 GHz processor with 4GB of RAM. The robust model's efficiency and performance were examined and compared with the deterministic model.

Effects of uncertainty on total costs of the bioenergy SC

The uncertainty's effect on the total SC costs is examined by changing the robust model's conservatism level and the perturbation amplitude of uncertain parameters. Levels considered for the perturbation amplitude (𝑎 𝑖𝑗 ̂) are 5, 10, 20 and 30% and those for the reliability and conservatism levels, controlled by the budget parameter 𝛤, are 68, 83, and 99%. Table 8 presents the different results obtained by adjusting each perturbation amplitude/reliability level of the model. It can be seen that the robust model costs are higher than the deterministic one at all uncertainty levels, due to the increase in the costs of improving the bioenergy SC stability. This increase becomes more significant as the conservatism/perturbation level increases. For instance, at high conservatism and risk aversion levels of the model (99% reliability and 30% amplitude), the total SC cost increases by 49.3% compared to the deterministic case. At lower uncertainty levels, it is possible, of course, to pay more reasonable costs, by creating a trade-off between robustness and the corresponding cost.

Table 8:

Examining and comparing the problem solution times is another outcome of solving the robust model with different conservatism/risk levels. As shown in Table 9, although the new constraints and variables are defined in the model (robust), it is still tractable from computational point of view, and the techniques used prevents elongation of the solution time compared with the deterministic model.

Table 9:

To study the differences in the costs of the deterministic and robust models, we first study each set of uncertain parameters at different perturbation and conservatism levels, and then check the effects on the increase in the total cost of the bioenergy SC by examining the normalized deviation, i.e.,

(𝑍 -𝑀𝑖𝑛 𝑇𝑜𝑡𝑎𝑙 𝐶𝑜𝑠𝑡) 𝑀𝑖𝑛 𝑇𝑜𝑡𝑎𝑙 𝐶𝑜𝑠𝑡 ⁄

where Z and 𝑀𝑖𝑛 𝑇𝑜𝑡𝑎𝑙 𝐶𝑜𝑠𝑡 are the optimum values of the robust and deterministic models, respectively.

Figures 4 to 8 show the values of the responses to various perturbations and uncertainties. At 30% perturbation, changes in the data of the biomass accessibility and transportation costs of the SC lead to increases of about 3.75% and 2.35%, respectively, in the total SC cost, while changes in the demand data, bio-refinery investment costs, and operation costs of conversion technologies would each increase the total SC cost by 5.1%, 9.3%, and 11%, respectively. These results suggest that efforts should be made to estimate the bio-refinery investment costs and the operation costs of conversion technologies more accurately.

Another point worth mentioning here is that, as shown in the demand graph (Figure 4), if the reliability is enhanced, the change in the total cost reaches its worst value more rapidly, while in Figures 5 to 8, the worsening rates enhance more slowly (gradually). This means that the change in the total cost shows a strong reaction to changes in the demand data, even at a low conservatism level. Hence, it is necessary that the demand data uncertainty be examined precisely, even regarding a risk-taking decision-maker who usually accepts a relatively high level for violation of the constraints. 10 report the optimal designs obtained by the two models (Robust and Deterministic) for 4 data perturbation levels. Figures 910111213show that both models suggest almost identical locations for bio-refineries meaning that the strategic location decisions are reasonably robust and do not become invalid due to small data noise. In contrast, they perform differently in determining the type of conversion technologies and their capacities inside bio-refineries. In general, the robust approach creates a greater number of facilities (a spread form) or a lower number of highercapacity facilities (centralized configuration) comparing the deterministic approach, so that the system can satisfy all (most) of the constraints in the worst scenarios [START_REF] Pishvaee | A robust optimization approach to closed-loop supply chain network design under uncertainty[END_REF]. For the specific SC in this study, the robust approach suggests fewer, but higher capacity facilities. This is shown in Figures 12 and13 where bio-refineries b15 and b16 are eliminated.

Table 10 shows that in the biorefinery areas b2, b8-b10, b12-b14, b19 and b21 at least one technology is installed under both the deterministic and robust models. Only location b15 is not selected for any technology under the robust model with 20% perturbation, and locations b15 and b16 are not selected for any technology under the robust model with 30% perturbation; other locations are identical (in the deterministic and robust models). This means that if there is small data noise, the strategic decisions related to the biorefineries locations where the technologies are installed will not be invalidated, and they are reasonably robust against the uncertainty. On the other hand, Table 10 shows that, under uncertainty, different technologies as well as various capacities are selected. For example, in location b2 the robust model under 20% perturbation suggests installing the technology to produce pellets with a capacity of 30,000 t/year while the deterministic model suggests the same technology but different capacity (15,000 t/year).

Similarly, the deterministic model suggests installing the biomass boiler and steam turbine with 3MW capacity in location b10, but the robust model, under 20% perturbation, suggests a different technology (pellet 45,000 t/y). In Table 10, the robust model suggests equal to or higher than the capacity of each technology proposed with the deterministic model (e.g. under perturbation 30%, the robust model suggests a pellet plant at 30,000 instead of 15,000 t/year suggested by the deterministic model in b2). However, the total number of technologies is reduced when the robust model is used (e.g. the robust model under 30% perturbation suggests 14 technologies, instead of 20 technologies suggested by the deterministic model). Compared with the deterministic model, the robust model in this study tends to a centralized configuration (a lower number of higher-capacity facilities), so the system can satisfy all (most) of the constraints in the worst scenarios [START_REF] Pishvaee | A robust optimization approach to closed-loop supply chain network design under uncertainty[END_REF]. The reason can be understood better by looking at Figures 5 and7. These figures show that the changes in data of the bio-refinery's investment cost and the operation cost of the conversion technology significantly affect the objective function of the model. Therefore, the robust model tries to weaken this undesirable impact by offering fewer bio-refineries with higher technological capacities (due to their more affordable economic scale). It is worth mentioning that when the technological capacity increases, the variable production cost decreases relative to the total production.

In addition, Figures 9-13 demonstrate that the bio-oil and pellet demands are satisfied with, respectively, three yellow and green colors (pale to dark). The point is that the provinces selected as pilot markets are not equal, whether for products in the deterministic and robust models or for their demands. However, 5 provinces (C1 to C5 in Figure 9) appear as optimal markets in all cases, and since they stay optimal even with data perturbation, they can be considered as reliable options in the early steps of the development process in the biofuel market. The sensitivity is performed using the following conditions: reliability and perturbation level are set to 99% and 30% respectively (base case model), and then nominal values of the 8 parameters are changed over reasonable ranges ( 20% -+

). Figure 14 reports the sensitivity analysis results. It shows that the total cost is very sensitive to the costs of investment and production. If the capital costs and production costs are increased by +20%, for each of the costs, the total cost increases by more than 44% and 42% respectively.

As shown in Figure 14, the conversion technology's transformation yields have a greater effect on the total cost in negative changes than positive ones. The biomass mix in the base case model is often made of forest and sawmill residues. If the transformation yield of the conversion technology is enhanced to 20%, the use of forest residues is reduced, which means the cost of biomass will have a proportional reduction. Nevertheless, if the transformation yield decreases by 20%, more wheat straw and corn stover (residues of agriculture) have to be supplied, and these cost more than forest residues. Consequently, the total cost increases by more than 32%.

In addition, when there are variations in demand for bio-oil, the change of total cost can vary approximately in a range from -14% to +13%. The investigation indicates that when demand of bio-oil rises to 20%, this leads to a centralized configuration in which one larger pyrolysis plant (600 ton/day) is installed in location b9 instead of the two smaller pyrolysis plants (one 200 ton/day in location b10, and one 200 ton/day in location b9) in the base case model, see Figure 13 and the last column of Table 10. This reduces the total cost. Moreover, the total cost changes of the bioenergy SC are proportional to the changes in the biomass cost, and the total cost of the supply chain is relatively insensitive to variations in other parameters like the availability of biomass, heat demand and the cost of transportation.

The social effects of the bioenergy SC on the territories

In this section, the effect of the bioenergy supply chain on the society in the territories where biorefineries are established, is investigated. To do so, we define the social profit of creating job w (the work hours) in territory b as follows: The social profits obtained from the optimal design of the bioenergy supply chain (by using the deterministic and robust models with 99% reliability level) are calculated and presented in Table 12 (using Table 10, Table 11 and equation (S2)). In order to obtain the number of jobs, value 1 is substituted instead of the social impact (𝛹 𝑤,𝑏 ) in (S2). Table 12 shows the social profit generated by the optimal design (considering Table 10) obtained with the deterministic model and robust model with 99% reliability and 5%, 10%, 20%, 30% perturbation. Considering the last row of Table 12, the maximum social profit and created jobs belong to the deterministic model (48.84 M points and 263 jobs respectively), and the minimum belongs to the robust model under 30% perturbation. As mentioned in Section 6.2.2, in this case, comparing the deterministic model, the robust model tends to give a centralized configuration (a lower number of higher-capacity facilities). Therefore, fewer work hours are created in the robust design under 30% perturbation compared with the deterministic model. The robust model under 99% reliability and 30% perturbation designs a supply chain giving social benefit (up to 31.79 M points) and 171 jobs. Table 12 shows that at lower perturbation levels, it is of course possible, to have more social profit and jobs. If the robust model with 10% perturbation and 99% reliability is considered, it leads to the creation of social benefit (up to 45.89 M points) and 262 jobs under uncertain conditions. These jobs are created in the areas with high rates of unemployment and high vulnerability to the variation in the markets in an economic crisis, so the jobs have a very significant impact on the local society.

The performance analysis

In order to show the advantage of the suggested approach and model compared with conventional ones some tests are implemented here.

In type 1 tests, instead of using the locations introduced by the first phase, some arbitrarily chosen locations are used (three diverse sets). A basic case mode, reliability 99% and perturbation 30%, is considered for the robust model, which is then run. The total cost of the bioenergy supply chain and time of the computations are considered to evaluate the performance, see Figure 15.

Figure 15 shows if the robust model is employed, the cost is smaller (as well as the computational time) for the case of high-suitability candidate locations, than for arbitrarily chosen candidate locations used. If 23 arbitrary chosen candidate locations are selected, this increases the total bioenergy SC cost to 1361M$ (42% more than the optimal cost). Figure 15 also shows that when 33 or 43 arbitrary chosen candidate locations are considered, although the total bioenergy SC cost is reduced compared with 23 arbitrary chosen candidate locations, the computation time increases significantly. Furthermore, when more candidate locations are used, it does not necessarily mean that it is possible to build a bio-refinery in a feasible region while meeting all the environmental, economic, social, and technological constraints. Thus, the first phase of the proposed approach which selects the candidate locations to build bio-refineries with high suitability ranking, increases both the performance as well as the tractability of the bioenergy supply chain design model. The mean value indicates the model (robust) performs better than the deterministic one, for every case of different perturbation and reliability levels, and this superiority is more important when the perturbation level is increased meaning that when the supply chain suffers from insufficient historical data, the model (robust) is coordinated more effective with it, especially in greater levels of perturbation.

Results also show that when the conservatism level increases, the distance between the performances of the two approaches increases as well. In fact, one advantage of the robust solution is that at different possible values for uncertain parameters, it stays feasible with a cost increase. Consequently, here in this particular case, the preferred option is the biggest values for reliability and perturbation levels, which offers greater safety and immunity. Nevertheless, 30% perturbation and 99% reliability may not be the best option, the final decision depends on the level of acceptability of the risk by the decision-maker. As shown in Figures 16 to 18

Conclusions

In this paper, a two-phase approach was proposed in order to design bioenergy SCs. The first phase, by integrating geographical information, social aspects, and by using multi-criteria decision-making techniques, aimed to find the appropriate locations for the bio-refineries in a geographical area. High rates of unemployment and high vulnerability of the territtories to variations in the markets during an economic crisis are considered as social concerns. The first phase enhances the practicality of the supply chain design, reduces its computational complexity, and help set up a sustainable development. The selected locations serve as input for the second phase. In the second phase, in order to cope with the uncertainties, a robust model is used to reduce the sensitivity to inaccurate input data. The use of the robust model leads to solutions which stay optimal, even when the parameters change slightly. In order to validate the two-phase sequential approach, a case study was carried out which showed that the proposed approach outperformed the traditional models, and for the case considered, led to creating 262 jobs. The jobs will be created in the areas with high rates of unemployment, and high vulnerability, so the jobs have a significant impact on the local society.

This work can be expanded in various ways. In future research, firstly, additional decisions could be integrated into the SC design: for instance, the new model could include some supplementary costs in order to provide insurance for the bio-refinery workers. Secondly, initial capacities or high technologies could be considered to improve the conversion productivity. Thirdly, product recycling after use by the customer can be considered. Fourth, decisions related to carbon trading and carbon pricing policies can be used. Finally, a column-wise version of the robust optimization can be used in order to tackle uncertainty better [START_REF] Ghelichi | A novel robust optimization approach for an integrated municipal water distribution system design under uncertainty: A case study of Mashhad[END_REF].

Appendix

Figure 1 :

 1 Figure 1: Configuration of the bioenergy supply chain network.

  𝑒,𝑏,𝑎,𝑡 𝑎∈𝐴 ∀𝑒 ∈ 𝐸, 𝑏 ∈ 𝐵, 𝑡 ∈ 𝑇[START_REF] Awudu | Stochastic production planning for a biofuel supply chain under demand and price uncertainties[END_REF]

Figure 4 :Figure 5 :Figure 6 :Figure 7 :Figure 8 :

 45678 Figure 4: Bioenergy SC cost response to demand data variations

Figures 9 -

 9 Figures 9-13 and Table10report the optimal designs obtained by the two models (Robust and Deterministic) for 4 data perturbation levels. Figures9-13show that both models suggest almost identical locations for bio-refineries meaning that the strategic location decisions are reasonably robust and do not become invalid due to small data noise. In contrast, they perform differently in determining the type of conversion technologies and their capacities inside bio-refineries. In general, the robust approach creates a greater number of facilities (a spread form) or a lower number of highercapacity facilities (centralized configuration) comparing the deterministic approach, so that the system can satisfy all (most) of the constraints in the worst scenarios[START_REF] Pishvaee | A robust optimization approach to closed-loop supply chain network design under uncertainty[END_REF]. For the specific SC in this study, the robust approach suggests fewer, but higher capacity facilities. This is shown in Figures12 and 13where bio-refineries b15 and b16 are eliminated.

Figure 9 :

 9 Figure 9: Deterministic model

Figure 10 :

 10 Figure 10: Robust model (with 99% reliability and 5% perturbation)

Figure 11 :Figure 12 :Figure 13 :

 111213 Figure 11: Robust model (with 99% reliability and 10% perturbation)

Figure 14 :

 14 Figure 14: Sensitivity analysis under robust model (with respect to the base case model: perturbation= 30%, reliability =99%).

Figure 15 :

 15 Figure 15: Effects of using the locations introduced by the first phase vs. ignoring the first phase

  .

  , the deterministic model's standard deviations are much larger than the model (robust). It means when the parameters are affected by small perturbation, the solution coming from the deterministic model has deviated considerably but the solutions of the model (robust) stay close to the optimal solution.

Figure 16 :Figure 17 :Figure 18 :

 161718 Figure 16: The two models' performance (68% reliability)

Table 1 :

 1 This study vs. the bio-energy supply chain literature

	Conversion technology A can be used at any candidate

  where 𝑎 ̃𝑖𝑗 can be uncertain and 𝐽 𝑖 is the set of uncertain parameters of row i.The 𝑎 ̃𝑖𝑗 is a random variable on a support [𝑎 𝑖𝑗 -𝑎 𝑖𝑗 ̂ , 𝑎 𝑖𝑗 + 𝑎 𝑖𝑗 ̂ ] where 𝑎 𝑖𝑗 is the nominal value and 𝑎 𝑖𝑗 ̂ is the perturbation amplitude. The parameter 𝛤 𝑖 (uncertainty budget), that may not be integer, can be used in each constraint i in order to make a trade-off for the solution's conservatism level and the model's robustness. It takes values between [0, |𝐽 𝑖 |] where|𝐽 𝑖 | shows the cardinality of set 𝐽 𝑖 , and aims at forcing ⌊𝛤 𝑖 ⌋ parameters to acquire their values at worst case, then goes for next one (𝑎 ̃𝑖𝑡 ) and moves the next one to its worst value from its nominal value by (𝛤 𝑖 -⌊𝛤 𝑖 ⌋)𝑎 𝑖𝑡 ̂. Hence, the following form, which is nonlinear, can be considered as the model's robust counterpart mentioned in (R1): 𝑖 ∪{𝑡 𝑖 }|𝑆 𝑖 ⊆𝐽 𝑖 ,|𝑆 𝑖 |=⌊𝛤 𝑖 ⌋, 𝑡 𝑖 ∈𝐽 𝑖 \𝑆 𝑖 }where 𝑆 𝑖 shows coefficients which take the worst value and 𝑡 𝑖 demonstrates the one that varies if 𝛤 𝑖 is not an integer.The constraint i's protection function, (𝑚𝑎𝑥 {𝑆 𝑖 ∪{𝑡 𝑖 }|𝑆 𝑖 ⊆𝐽 𝑖 ,|𝑆 𝑖 |=⌊𝛤 𝑖 ⌋,𝑡 𝑖 ∈𝐽 𝑖 \𝑆 𝑖 } {∑ 𝑎 ̂𝑖𝑗Due to the feasibility of the problem (R3), and also because it is bounded for all 𝛤 𝑖 , its dual pair is also bounded and feasible with the identical objective value according to the strong duality property. If 𝜚 𝑖 and 𝛶 𝑖𝑗 (dual variables) are defined, the dual problem for (R3) can be shown as follows:It is worth noting that when 𝛤 𝑖 ′ = 0, there is no protection against uncertainty, and when 𝛤 𝑖 ′ = 1, there is full protection against uncertainty. When 𝛤 𝑖 ′ varies between 0 and 1, it can control the solution's conservatism level. Bertsimas and Sim[START_REF] Bertsimas | The price of robustness[END_REF] suggest that if decision makers change the value of 𝛤 𝑖 by considering an upper bound for the constraint violation's probability [𝑒𝑥𝑝(-𝛤 𝑖 2 2|𝐽 𝑖 | ⁄ )], they can adjust constraint i's conservatism/reliability level.

	𝑀𝑖𝑛 𝛤 𝑖 𝜚 𝑖 + ∑ 𝛶 𝑖𝑗
		𝑗∈𝐽 𝑖
	𝑐𝑥 𝑠𝑡: 𝜚 𝑖 + 𝛶 𝑖𝑗 ≥ 𝑎 ̂𝑖𝑗 |𝑥 𝑗 * |		∀ 𝑖, 𝑗 ∈ 𝐽 𝑖	(R4)
	𝛶 𝑖𝑗 ≥ 0					∀ 𝑖, 𝑗 ∈ 𝐽 𝑖
	𝑠𝑡: ∑ 𝑎 ̃𝑖𝑗 𝑥 𝑗 ≥ 𝑏 𝑖 𝑗 𝜚 𝑖 ≥ 0			∀ 𝑖	∀ 𝑖	(R1)
	𝑥 ∈ 𝑋 Substituting (R4) in (R2), the linear robust counterpart will be as follows:
	𝑀𝑖𝑛 𝑐𝑥
	𝑠𝑡: ∑ 𝑎 𝑖𝑗	𝑥 𝑗 -𝛤 𝑖 𝜚 𝑖 -∑ 𝛶 𝑖𝑗	≥ 𝑏 𝑖	∀ 𝑖	(R5)
	𝑗		𝑗∈𝐽 𝑖
	𝛶 𝑖𝑗 , 𝜚 𝑖 , 𝑥 𝑗 ≥ 0				∀ 𝑖, 𝑗 ∈ 𝐽 𝑖 ̂ , 𝑏 𝑖 + 𝑏 𝑖 ̂ ] meaning that the distribution
	of each uncertain parameter is symmetric and bounded, but 𝛤 𝑖	′ (uncertainty budget) takes values
	𝑀𝑖𝑛 𝑐𝑥 between 0 and 1. Considering these definitions, problem (R1)'s robust counterpart can be written as
	follows:
	𝑠𝑡: ∑ 𝑎 𝑖𝑗 𝑥 𝑗 -		𝑚𝑎𝑥	{∑ 𝑎 ̂𝑖𝑗	𝑥 𝑗 + (𝛤 𝑖 -⌊𝛤 𝑖 ⌋)𝑎 𝑖𝑡 𝑖 ̂ 𝑥 𝑗 } ≥ 𝑏 𝑖	∀ 𝑖 (R2)
	𝑗 𝑀𝑖𝑛 𝑐𝑥					𝑗∈𝑆 𝑖
	𝑋 ≥ 0 𝑠𝑡: ∑ 𝑎 ̃𝑖𝑗	𝑥 𝑗 ≥ 𝑏 𝑖 + 𝑚𝑎𝑥 𝑏 𝑖 ̂𝜐𝑖	∀ 𝑖	(R6)
	𝑗
	0 ≤ 𝜐 𝑖 ≤ 𝛤 𝑖	′				∀ 𝑖
	𝑥 ≥ 0
						𝑗∈𝑆 𝑖	|𝑥 𝑗 * | + (𝛤 𝑖 -
	⌊𝛤 𝑖 ⌋)𝑎 𝑖𝑡 𝑖 ̂ |𝑥 𝑗 * |}), considering 𝑥 𝑗 * as optimal solution could be rewritten in the linear form as follows: The equivalent of equation (R6) is the following linear optimization problem:
	𝑀𝑎𝑥 ∑ 𝑎 𝑖𝑗 ̂|𝑥 𝑗 * |𝜐 𝑖𝑗 𝑀𝑖𝑛 𝑐𝑥
	𝑗∈𝐽 𝑖 𝑠𝑡: ∑ 𝜐 𝑖𝑗 ≤ Γ 𝑖 𝑗 𝑠𝑡: ∑ 𝑎 ̃𝑖𝑗 𝑥 𝑗 ≥ 𝑏 𝑖	+ 𝛤 𝑖	′ 𝑏 𝑖 ̂		∀ 𝑖 ∀ 𝑖	(R3) (R7)
	𝑗∈𝐽 𝑖
	0 ≤ 𝜐 𝑖𝑗 ≤ 1 𝑥 ≥ 0				∀ 𝑖, 𝑗 ∈ 𝐽 𝑖

{𝑆 𝑖

To apply the robust equation to constraints where uncertainties only affect the right-hand side (RHS), consider that of (R1). Here, also, there is the interval [𝑏 𝑖 -𝑏

  Constraints[START_REF] D'amore | Strategic optimisation of biomass-based energy supply chains for sustainable mobility[END_REF] ensure that amount of the biomass r coming from supplier s could not be more than the available biomass.∑ 𝑈 𝑟,𝑠,𝑏,𝑡 ≤ 𝛽 𝑟,𝑠,𝑡 b∈𝐵 ∀𝑟 ∈ 𝑅, 𝑠 ∈ 𝑆, 𝑡 ∈ 𝑇 (2)Constraints (3) ensure that the total biomass shipped from various resources is equal to that used by all conversion technologies at any location and in any period. ) guarantee that the total bioenergy and biofuel produced by each technology is equal to its conversion efficiency. Types of technologies and biomass are considered in this conversion efficiency because, depending on the quality and amount of energy involved, various biomass types have different efficiencies and can be converted through different conversion methods.

	+ ∑ ∑ ∑ ∑ 𝜍 𝑏,𝑎,𝑡 𝑉 t∈𝑇 𝑃 𝑓,𝑏,𝑎,𝑡 ≤ 𝜉 𝑎,𝑓 𝑀 . 𝑌 𝑏,𝑎,𝑡	. 𝑈 𝑟,𝑏,𝑎,𝑡 𝑈	∀𝑓 ∈ 𝐹, 𝑏 ∈ 𝐵, 𝑎 ∈ 𝐴, 𝑡 ∈ 𝑇 (7)
	𝑎∈𝐴 𝐺 𝑒,𝑏,𝑎,𝑡 ≤ 𝜉 𝑎,𝑒 𝑏∈𝐵 𝑟∈𝑅 𝑀 . 𝑌 𝑏,𝑎,𝑡	∀𝑒 ∈ 𝐸, 𝑏 ∈ 𝐵, 𝑎 ∈ 𝐴, 𝑡 ∈ 𝑇 (8)
	+ ∑ ∑ ∑ 𝜍 𝑒,𝑏,𝑡 𝐸 ̃	. 𝐽 𝑒,𝑏,𝑡 𝐶
	𝑒∈𝐸	𝑏∈𝐵	𝑡∈𝑇
	+ ∑ ∑ ∑ 𝜍 𝑓,𝑏 𝐻 ̃ 𝑡∈𝑇 𝑏∈𝐵 𝑓∈𝐹 Constraints (9) and (10) permit that, in each period, biofuel and bioenergy should exceed a minimum 𝐵 (1) . 𝐼 𝑓,𝑏,𝑡 utilization capacity and prevent the installation of idle technologies.
	𝑃 𝑓,𝑏,𝑎,𝑡 ≥ 𝜉 𝑎,𝑓 𝑀	. 𝑌 𝑏,𝑎,𝑡 . 𝜇 𝑓 𝑚 ̃	∈ 𝑇 ∀𝑓 ∈ 𝐹, 𝑏 ∈ 𝐵, 𝑎 ∈ 𝐴, 𝑡	(9)
	4.1.2. Constraints 𝐺 𝑒,𝑏,𝑎,𝑡 ≥ 𝜉 𝑎,𝑒 𝑀 . 𝑌 𝑏,𝑎,𝑡 . 𝜇 𝑒 𝑚 ̃	∀𝑒 ∈ 𝐸, 𝑏 ∈ 𝐵, 𝑎 ∈ 𝐴, 𝑡
							∈ 𝑇
						𝑈	∀𝑟 ∈ 𝑅, 𝑏 ∈ 𝐵, 𝑡 ∈ 𝑇 (3)
	𝑠∈𝑆			𝑎∈𝐴
	Constraints (4) ensure the type of biomass required for each technology.
	𝑈 𝑟,𝑏,𝑎,𝑡 𝑈	≤ 𝜑 . 𝜓 𝑟,𝑎	∀𝑟 ∈ 𝑅, 𝑏 ∈ 𝐵, 𝑡 ∈ 𝑇 (4)
	𝑟∈𝑅 Constraints (5) and (6𝑃 𝑓,𝑏,𝑎,𝑡 = ∑ 𝛾 𝑓,𝑟,𝑎	𝑏∈𝐵 . 𝑈 𝑟,𝑏,𝑎,𝑡 𝑠∈𝑆 𝑟∈𝑅 𝑈	t∈𝑇	𝑠,𝑡 𝐵	. 𝑈 𝑟,𝑠,𝑏,𝑡	∀𝑓 ∈ 𝐹, 𝑏 ∈ 𝐵, 𝑎 ∈ 𝐴, 𝑡 ∈ 𝑇 (5)
	+ ∑ ∑ ∑ ∑ 𝜍 𝑟,𝑠,𝑏,𝑡 𝐵,𝑇 t∈𝑇 𝑏∈𝐵 𝑠∈𝑆 𝑟∈𝑅 𝑟∈𝑅 𝐺 𝑒,𝑏,𝑎,𝑡 = ∑ 𝛾 𝑒,𝑟,𝑎 . 𝑈 𝑟,𝑏,𝑎,𝑡 . 𝑈 𝑟,𝑠,𝑏,𝑡 𝑈	∀𝑒 ∈ 𝐸, 𝑏 ∈ 𝐵, 𝑎 ∈ 𝐴, 𝑡 ∈ 𝑇 (6)
	+ ∑ ∑ ∑ ∑ 𝜍 𝑓,𝑏,𝑐,𝑡 𝐵,𝑇 t∈𝑇	. 𝑃 𝑓,𝑏,𝑐,𝑡 𝑀
	𝑓∈𝐹	𝑏∈𝐵	𝑐∈𝐶
	+ ∑ ∑ ∑ 𝜍 𝑎,𝑏,𝑡 𝐹 ̃	. 𝑌 𝑏,𝑎,𝑡
	𝑎∈𝐴	𝑏∈𝐵	𝑡∈𝑇

∑ 𝑈 𝑟,𝑠,𝑏,𝑡 = ∑ 𝑈 𝑟,𝑏,𝑎,𝑡 Constraints (

7

) and (8) ensure the maximum throughout for final products producing by different technologies in each period, and show that production will continue in bio-refinery b if technology a is installed and works there (𝑌 𝑏,𝑎,𝑡 = 1).

  Constraints[START_REF] Nguyen | Supplier selection and operation planning in biomass supply chains with supply uncertainty[END_REF] ensure that all the biofuel distributed to the markets throughout each period (i.e.∑ 𝑃 𝑓,𝑏,𝑐,𝑡 𝑀 𝑐∈𝐶) , plus the biofuel inventory at the end of period t (i.e. 𝐼 𝑓,𝑏,𝑡 𝐵 ) should not exceed the biofuel produced by technology a in period t (i.e. ∑ 𝑃 𝑓,𝑏,𝑎,𝑡𝑎∈𝐴) plus the inventory at the end of period t-1 (i.e.

	𝐼 𝑓,𝑏,(𝑡-1) 𝐵	).
	∑ 𝑃 𝑓,𝑏,𝑎,𝑡	+ 𝐼 𝑓,𝑏,(𝑡-1) 𝐵	≥ ∑ 𝑃 𝑓,𝑏,𝑐,𝑡 𝑀	+ 𝐼 𝑓,𝑏,𝑡 𝐵	∀𝑓 ∈ 𝐹, 𝑏 ∈ 𝐵, 𝑡 ∈ 𝑇 (16)
	𝑎∈𝐴					𝑐∈𝐶
	Constraints (17) indicate that the total biofuel produced in all bio-refineries in each period should be
	at least equal to the total targeted demand in each period (throughout the considered country or
	geographical area).
	∑ ∑ 𝑃 𝑓,𝑏,𝑐,𝑡 𝑀	≥ 𝜛 𝑓,𝑡 𝑇 ̃	∀𝑓 ∈ 𝐹, 𝑡 ∈ 𝑇
	𝑏∈𝐵	𝑐∈𝐶
	𝑓,𝑐,𝑡 𝑚 ̃ . 𝑀 𝑓,𝑐 ≤ ∑ 𝑃 𝑓,𝑏,𝑐,𝑡 𝑀	≤ 𝛿 𝑓,𝑐,𝑡 𝑀 ̃ . 𝑀 𝑓,𝑐	∀𝑓 ∈ 𝐹, 𝑐 ∈ 𝐶, 𝑡 ∈ 𝑇 (13)
					𝑏∈𝐵
	𝛿 𝑒,𝑏,𝑡 𝐸,𝑚 ̃≤ 𝐺 𝑒,𝑏,𝑡 𝑆	≤ 𝛿 𝑒,𝑏,𝑡 𝐸,𝑀 ̃	∀𝑒 ∈ 𝐸, 𝑏 ∈ 𝐵, 𝑡 ∈ 𝑇 (14)
	Constraints (15) guarantee that the energy required for conversion technologies in each bio-refinery
	is equal to the energy that can be met by the bioenergy produced in the bio-refinery plus that supplied
	from other currently used sources of energy at that location.
	∑ ∑ 𝜗 𝑒,𝑟,𝑎 𝐼,𝐶	. 𝑈 𝑟,𝑏,𝑎,𝑡 𝑈	= 𝐺 𝑒,𝑏,𝑡 𝑈	+ 𝐽 𝑒,𝑏,𝑡 𝐶	∀𝑒 ∈ 𝐸, 𝑏 ∈ 𝐵, 𝑡 ∈ 𝑇 (15)
	𝑟∈𝑅	𝑎∈𝐴

  and a budget parameter𝛤 𝑍 . It is worth mentioning here that 𝛤 𝑍 acquires values in the range 0 to the sum of the number of uncertain parameters in[START_REF] Mohseni | Robust design and planning of microalgae biomass-to-biodiesel supply chain: A case study in Iran[END_REF].

	+ ∑ ∑ ∑ 𝑑 𝑎,𝑏,𝑡 1		+ ∑ ∑ ∑ ∑ 𝑒 𝑟,𝑏,𝑎,𝑡 1	+ ∑ ∑ ∑ 𝑔 𝑒,𝑏,𝑡 1
	𝑎∈𝐴	𝑏∈𝐵	𝑡∈𝑇			𝑟∈𝑅	𝑏∈𝐵	𝑎∈𝐴	𝑡∈𝑇	𝑒∈𝐸	𝑏∈𝐵	𝑡∈𝑇
	+ ∑ ∑ ∑ 𝑙 𝑓,𝑏,𝑡 1	+ 𝛤 𝑍 . 𝛲 𝑍 ≤ 𝑍	(24)
	𝑓∈𝐹	𝑏∈𝐵	𝑡∈𝑇
	𝛲 𝑍 + 𝑎 𝑟,𝑠,𝑏,𝑡 1	≥ 𝜍 𝑟,𝑠,𝑡 𝐵 ̂ . 𝑈 𝑟,𝑠,𝑏,𝑡	∈ 𝑇 ∀𝑟 ∈ 𝑅, 𝑠 ∈ 𝑆, 𝑏 ∈ 𝐵, 𝑡	(25)
	𝛲 𝑍 + 𝑏 𝑟,𝑠,𝑏,𝑡 1	≥ 𝜍 𝑟,𝑠,𝑏,𝑡 𝐵,𝑇 ̂ . 𝑈 𝑟,𝑠,𝑏,𝑡	∈ 𝑇 ∀𝑟 ∈ 𝑅, 𝑠 ∈ 𝑆, 𝑏 ∈ 𝐵, 𝑡	(26)
	𝛲 𝑍 + 𝑐 𝑓,𝑏,𝑐,𝑡 1		≥ 𝜍 𝑓,𝑏,𝑐,𝑡 𝐵,𝑇 ̂ . 𝑃 𝑓,𝑏,𝑐,𝑡 𝑀	∈ 𝑇 ∀𝑓 ∈ 𝐹, 𝑏 ∈ 𝐵, 𝑐 ∈ 𝐶, 𝑡	(27)
	𝛲 𝑍 + 𝑑 𝑎,𝑏,𝑡 1	≥ 𝜍 𝑎,𝑏,𝑡 𝐹 ̂ . 𝑌 𝑏,𝑎,𝑡	∀𝑎 ∈ 𝐴, 𝑏 ∈ 𝐵, 𝑡 ∈ 𝑇	(28)
	vectors 𝛲 𝑍 , 𝑎 𝑟𝑠𝑏𝑡 1 𝛲 𝑍 + 𝑒 𝑟,𝑏,𝑎,𝑡 1 ≥ 𝜍 𝑏,𝑎,𝑡 , 𝑏 𝑟𝑠𝑏𝑡 1 , 𝑐 𝑓𝑏𝑐𝑡 1 , 𝑑 𝑎𝑏𝑡 1 , 𝑒 𝑟𝑏𝑎𝑡 1 𝑉 ̂ . 𝑈 𝑟,𝑏,𝑎,𝑡 𝑈 1 𝑀𝑖𝑛 𝑍 , 𝑔 𝑒𝑏𝑡 1 , 𝑙 𝑓𝑏𝑡 𝛲 𝑍 + 𝑔 𝑒,𝑏,𝑡 1 ≥ 𝜍 𝑒,𝑏,𝑡 𝐸 ̂ . 𝐽 𝑒,𝑏,𝑡 𝐶	to (31) by defining dual ∀𝑟 ∈ 𝑅, 𝑏 ∈ 𝐵, 𝑎 ∈ 𝐴, 𝑡 ∈ 𝑇 (29) ∀𝑒 ∈ 𝐸, 𝑏 ∈ 𝐵, 𝑡 ∈ 𝑇 (30)
	St: 𝛲 𝑍 + 𝑙 𝑓,𝑏,𝑡 1	≥ 𝜍 𝑓,𝑏 𝐻 ̂ . 𝐼 𝑓,𝑏,𝑡 𝐵	∀𝑓 ∈ 𝐹, 𝑏 ∈ 𝐵, 𝑡 ∈ 𝑇	(23) (31)
	∑ ∑ ∑ ∑ 𝜍 𝑟,𝑠,𝑡 𝐵	. 𝑈 𝑟,𝑠,𝑏,𝑡
	𝑟∈𝑅	𝑠∈𝑆	𝑏∈𝐵	𝑡∈𝑇
	+ ∑ ∑ ∑ ∑ 𝜍 𝑟,𝑠,𝑏,𝑡 𝐵,𝑇	. 𝑈 𝑟,𝑠,𝑏,𝑡
	𝑟∈𝑅	𝑠∈𝑆	𝑏∈𝐵	𝑡∈𝑇
	+ ∑ ∑ ∑ ∑ 𝜍 𝑓,𝑏,𝑐,𝑡 𝐵,𝑇	. 𝑃 𝑓,𝑏,𝑐,𝑡 𝑀
	𝑓∈𝐹	𝑏∈𝐵	𝑐∈𝐶	𝑡∈𝑇
	+ ∑ ∑ ∑ 𝜍 𝑎,𝑏,𝑡 𝐹		. 𝑌 𝑏,𝑎,𝑡
	𝑎∈𝐴	𝑏∈𝐵	𝑡∈𝑇
	+ ∑ ∑ ∑ ∑ 𝜍 𝑏,𝑎,𝑡 𝑉	. 𝑈 𝑟,𝑏,𝑎,𝑡 𝑈
	𝑟∈𝑅	𝑏∈𝐵	𝑎∈𝐴	𝑡∈𝑇
	+ ∑ ∑ ∑ 𝜍 𝑒,𝑏,𝑡 𝐸		. 𝐽 𝑒,𝑏,𝑡 𝐶
	𝑒∈𝐸	𝑏∈𝐵	𝑡∈𝑇
	+ ∑ ∑ ∑ 𝜍 𝑓,𝑏 𝐻	. 𝐼 𝑓,𝑏,𝑡 𝐵
	𝑓∈𝐹	𝑏∈𝐵	𝑡∈𝑇
	+ ∑ ∑ ∑ ∑ 𝑎 𝑟,𝑠,𝑏,𝑡 1	+ ∑ ∑ ∑ ∑ 𝑏 𝑟,𝑠,𝑏,𝑡 1	+ ∑ ∑ ∑ ∑ 𝑐 𝑓,𝑏,𝑐,𝑡 1
	𝑟∈𝑅	𝑠∈𝑆	𝑏∈𝐵	𝑡∈𝑇				𝑟∈𝑅	𝑠∈𝑆	𝑏∈𝐵	𝑡∈𝑇	𝑓∈𝐹	𝑏∈𝐵	𝑐∈𝐶	𝑡∈𝑇

  ∑ 𝑈 𝑟,𝑠,𝑏,𝑡 ≤ 𝛽 𝑟,𝑠,𝑡 -𝛤 𝑟,𝑠,𝑡 . 𝛽 𝑟,𝑠,𝑡 ̂ 𝐺 𝑒,𝑏,𝑎,𝑡 ≤ 𝜉 𝑎,𝑒 𝑀 . 𝑌 𝑏,𝑎,𝑡 ∀𝑒 ∈ 𝐸, 𝑏 ∈ 𝐵, 𝑎 ∈ 𝐴, 𝑡 ∈ 𝑇 (38)

	𝑃 𝑓,𝑏,𝑎,𝑡 ≤ 𝜉 𝑎,𝑓 𝑀 . 𝑌 𝑏,𝑎,𝑡	∀𝑓 ∈ 𝐹, 𝑏 ∈ 𝐵, 𝑎 ∈ 𝐴, 𝑡	(37)
	𝐺 𝑒,𝑏,𝑡 𝑆 , 𝐺 𝑒,𝑏,𝑡 𝑈	≥ 0	∈ 𝑇
	𝑃 𝑓,𝑏,𝑎,𝑡 ≥ 𝜉 𝑎,𝑓 𝑀 . 𝑌 𝑏,𝑎,𝑡 . 𝜇 𝑓 𝑚 + 𝛤 𝑓,𝑏,𝑎,𝑡 . 𝜉 𝑎,𝑓 𝑀 𝑌 𝑏,𝑎,𝑡 , 𝑀 𝑓,𝑐 ∈ {0,1} 𝛲 𝑍 , 𝑎 𝑟𝑠𝑏𝑡 1 , 𝑏 𝑟𝑠𝑏𝑡 1 , 𝑐 𝑓𝑏𝑐𝑡 1 , 𝑑 𝑎𝑏𝑡 1 , 𝑒 𝑟𝑏𝑎𝑡 1 , 𝑔 𝑒𝑏𝑡 1 , 𝑙 𝑓𝑏𝑡 1 ∈ 𝑅 + . 𝑌 𝑏,𝑎,𝑡 . 𝜇 𝑓 𝑚 ̂ ∀ 𝑟 ∈ 𝑅, 𝑠 ∈ 𝑆, 𝑏 ∈ 𝐵, 𝑎 ∈ 𝐴, ∀𝑓 ∈ 𝐹, 𝑏 ∈ 𝐵, 𝑎	(54) (39) (55)
						∈ 𝐴, 𝑡 ∈ 𝑇 𝑓 ∈ 𝐹, 𝑐 ∈ 𝐶, 𝑒 ∈ 𝐸, 𝑡 ∈ 𝑇
	𝐺 𝑒,𝑏,𝑎,𝑡 ≥ 𝜉 𝑎,𝑒 𝑀 . 𝑌 𝑏,𝑎,𝑡 . 𝜇 𝑒 𝑚 + 𝛤 𝑒,𝑏,𝑎,𝑡 . 𝜉 𝑎,𝑒 𝑀 . 𝑌 𝑏,𝑎,𝑡 . 𝜇 𝑒 𝑚 ̂	∀𝑒 ∈ 𝐸, 𝑏	(40)
						∈ 𝐵, 𝑎 ∈ 𝐴, 𝑡
						∈ 𝑇
	∑ 𝑃 𝑓,𝑏,𝑐,𝑡 𝑀	= ∑ 𝑃 𝑓,𝑏,𝑎,𝑡	∀𝑏 ∈ 𝐵, 𝑓 ∈ 𝐹, 𝑡 ∈ 𝑇	(40)
	𝑐∈𝐶					𝑎∈𝐴
	𝐺 𝑒,𝑏,𝑡 𝑆	+ 𝐺 𝑒,𝑏,𝑡 𝑈	= ∑ 𝐺 𝑒,𝑏,𝑎,𝑡	∀𝑒 ∈ 𝐸, 𝑏 ∈ 𝐵, 𝑡 ∈ 𝑇	(42)
						𝑎∈𝐴
	𝛿 𝑓,𝑐,𝑡 𝑚	. 𝑀 𝑓,𝑐 + 𝛤 𝑓,𝑐,𝑡 1	. 𝛿 𝑓,𝑐,𝑡 𝑚 ̂ . 𝑀 𝑓,𝑐 ≤ ∑ 𝑃 𝑓,𝑏,𝑐,𝑡 𝑀	∀𝑓 ∈ 𝐹, 𝑐 ∈ 𝐶, 𝑡 ∈ 𝑇	(43)
						𝑏∈𝐵
	∑ 𝑃 𝑓,𝑏,𝑐,𝑡 𝑀	≤ 𝛿 𝑓,𝑐,𝑡 𝑀	. 𝑀 𝑓,𝑐 -𝛤 𝑓,𝑐,𝑡 2	. 𝛿 𝑓,𝑐,𝑡 𝑀 ̂ . 𝑀 𝑓,𝑐	∀𝑓 ∈ 𝐹, 𝑐 ∈ 𝐶, 𝑡 ∈ 𝑇 (44)
	𝑏∈𝐵
	𝛿 𝑒,𝑏,𝑡 𝐸,𝑚 + 𝛤 𝑒,𝑏,𝑡 1	. 𝛿 𝑒,𝑏,𝑡 𝐸,𝑚 ̂ ≤ 𝐺 𝑒,𝑏,𝑡 𝑆	∀𝑒 ∈ 𝐸, 𝑏 ∈ 𝐵, 𝑡 ∈ 𝑇	(45)
	𝐺 𝑒,𝑏,𝑡 𝑆	≤ 𝛿 𝑒,𝑏,𝑡 𝐸,𝑀 -𝛤 𝑒,𝑏,𝑡 2	. 𝛿 𝑒,𝑏,𝑡 𝐸,𝑀 ̂	∀𝑒 ∈ 𝐸, 𝑏 ∈ 𝐵, 𝑡 ∈ 𝑇	(46)
	∑ ∑ 𝜗 𝑒,𝑟,𝑎 𝐼,𝐶	. 𝑈 𝑟,𝑏,𝑎,𝑡 𝑈	= 𝐺 𝑒,𝑏,𝑡 𝑈	+ 𝐽 𝑒,𝑏,𝑡 𝐶	∀𝑒 ∈ 𝐸, 𝑏 ∈ 𝐵, 𝑡 ∈ 𝑇 (47)
	𝑟∈𝑅	𝑎∈𝐴
	∑ 𝑃 𝑓,𝑏,𝑎,𝑡	+ 𝐼 𝑓,𝑏,(𝑡-1) 𝐵	≥ ∑ 𝑃 𝑓,𝑏,𝑐,𝑡 𝑀	+ 𝐼 𝑓,𝑏,𝑡 𝐵	∀𝑓 ∈ 𝐹, 𝑏 ∈ 𝐵, 𝑡 ∈ 𝑇 (48)
	𝑎∈𝐴					𝑐∈𝐶
	𝑐∈𝐶 ∑ ∑ 𝑃 𝑓,𝑏,𝑐,𝑡 𝑏∈𝐵 𝑀	≥ 𝜛 𝑓,𝑡 𝑇 + 𝛤 𝑓,𝑡 . 𝜛 𝑓,𝑡 𝑇 ̂	∀𝑟 ∈ 𝑅, 𝑠 ∈ 𝑆, 𝑡 ∈ 𝑇 ∀𝑓 ∈ 𝐹, 𝑡 ∈ 𝑇	(32) (49)
	𝑏∈𝐵
	𝑈 ∑ 𝑈 𝑟,𝑠,𝑏,𝑡 = ∑ 𝑈 𝑟,𝑏,𝑎,𝑡 𝑌 𝑏,𝑎,𝑡 ≥ 𝑌 𝑏,𝑎,(𝑡-1) 𝑎∈𝐴 𝑠∈𝑆 ∑ 𝑌 𝑏,𝑎,𝑡 ≤ 1	∀𝑟 ∈ 𝑅, 𝑏 ∈ 𝐵, 𝑡 ∈ 𝑇 ∀𝑎 ∈ 𝐴, 𝑏 ∈ 𝐵, 𝑡 ∈ 𝑇 ∀𝑒 ∈ 𝐸, 𝑏 ∈ 𝐵, 𝑡 ∈ 𝑇	(50) (33) (51)
	𝑈 𝑟,𝑏,𝑎,𝑡 𝑈 𝑎 𝑒 ∈𝐴	≤ 𝜑 . 𝜓 𝑟,𝑎	∀𝑟 ∈ 𝑅, 𝑏 ∈ 𝐵, 𝑡 ∈ 𝑇	(34)
	𝑃 𝑓,𝑏,𝑎,𝑡 = ∑ 𝛾 𝑓,𝑟,𝑎 𝑟∈𝑅 𝑎 𝑓 ∈𝐴 ∑ 𝑌 𝑏,𝑎,𝑡 ≤ 1	. 𝑈 𝑟,𝑏,𝑎,𝑡 𝑈	∀𝑓 ∈ 𝐹, 𝑏 ∈ 𝐵, 𝑎 ∈ 𝐴, 𝑡 ∈ 𝑇 ∀𝑓 ∈ 𝐹, 𝑏 ∈ 𝐵, 𝑡 ∈ 𝑇	(35) (52)
	𝐺 𝑒,𝑏,𝑎,𝑡 = ∑ 𝛾 𝑒,𝑟,𝑎 𝑟∈𝑅	. 𝑈 𝑟,𝑏,𝑎,𝑡 𝑈	∈ 𝑇 ∀𝑒 ∈ 𝐸, 𝑏 ∈ 𝐵, 𝑎 ∈ 𝐴, 𝑡	(36)

𝑈 𝑟,𝑠,𝑏,𝑡 , 𝑈 𝑟,𝑏,𝑎,𝑡 𝑈 , 𝐽 𝑒,𝑏,𝑡 𝐶 , 𝑃 𝑓,𝑏,𝑎,𝑡 , 𝐼 𝑓,𝑏,𝑡 𝐵 , 𝑃 𝑓,𝑏,𝑐,𝑡 𝑀 , 𝐺 𝑒,𝑏,𝑎,𝑡 , ∀ 𝑟 ∈ 𝑅, 𝑠 ∈ 𝑆, 𝑏 ∈ 𝐵, 𝑎 ∈ 𝐴, 𝑓 ∈ 𝐹, c ∈ 𝐶, 𝑒 ∈ 𝐸, 𝑡 ∈ 𝑇 (53)

  𝑺𝒐𝒄𝒊𝒂𝒍 𝒑𝒓𝒐𝒇𝒊𝒕 𝒘,𝒃 = 𝜳 𝒘,𝒃 × 𝑻𝒉𝒆 𝒓𝒆𝒒𝒖𝒊𝒓𝒆𝒅 𝒉𝒐𝒖𝒓𝒔 𝒘,𝒃 (𝑯𝒐𝒖𝒓𝒍𝒚 𝒘𝒂𝒈𝒆 𝒘𝒐𝒓𝒌 + 𝑺𝒂𝒍𝒂𝒓𝒊𝒆𝒅 𝒘𝒐𝒓𝒌) (S2)Where hourly wage work refers the work involved in transforming the biomass to bioenergy and biofuel, and salaried work refers to the work of keeping the bio-refinery open (jobs with a fixed salary). The work hours needed to convert the biomass using the different technologies can vary depending on the capacities. Table11shows the assumptions related to the work (hours of work) for the different technologies of combustion, pellet and pyrolysis. The total requested jobs (in terms of whole hours needed for work) for the different types of technologies with the different capacities come from the reports presented in[START_REF] Heat | Power Catalog of Technologies[END_REF][START_REF] Thornley | Quantification of employment from biomass power plants[END_REF], and from consultation with the Renewable Energy and Energy Efficiency Organization (www.satba.gov.ir). In addition, the work (the work hours) requested for technologies related to pyrolysis and pellet with different capacities, hourly-wage work, and salaried work hours also come from different previous studies[START_REF] Campbell | A feasibility study guide for an agricultural biomass pellet company[END_REF][START_REF] Rogers | Estimation of the production cost of fast pyrolysis bio-oil[END_REF][START_REF] Sultana | Development of agri-pellet production cost and optimum size[END_REF].

	The percentage of variation in the total cost with respect to the
		base case model
	20% change in the parameter	-20% change in the parameter
		Capital costs
		50%
		40%
	Transportation costs	20% 30%	Production costs
		10%
		0%
		-10%
		-20%
		-30%
		-40%
	heat demand	-50%	Transformation yield
	Biomass availibility		Bio-oil demand
		Biomass costs

Table 11 :

 11

X X X X X X X X X X X Scenario-based stochastic programming X (Kostin et al., 2012) X

3,4 X X X X X X X X Two-stage stochastic programming X (Saghaei et al., 2020) X 1 X X X X X X X Two-stage stochastic programming X (Balaman and Selim, 2015) X 2-7 X X X X X X X X Fuzzy multi-objective modeling approach X (Awudu and Zhang, 2013) X 2 X X X X X X Stochastic programming X (Santibañez-Aguilar et al., 2019) X X 2 X X X X X X X X X -X X X (Mohseni et al., 2016) X X 1 X X X X X X X X X X X Robust convex Programming (Bertsimas & sim's approach) X (Chen and Fan, 2012) X X 1 X X X X X X X Two-stage stochastic programming X (Marvin et al., 2012) X X 3 X X X X X X X Sensitivity analysis X (Razm et al., 2019b) X 3 X X X X X X X X Two-stage stochastic programming X X X X (Osmani and Zhang, 2013) X 2 X X X X X X X X X Two-stage stochastic programming X (Khishtandar, 2019) X 1 X X X Fuzzy chance-constrained programming X Proposed model X X 1 X X X X X X X X X X X X X Robust convex Programming (Bertsimas & sim's approach) X X X X