Keywords: Distribution management, Perishable fruit, Shelf life model, Multi-objective decision making, CO2 emission, NSGA II Gestion de la distribution, denrée périssable, durée de conservation, Prise de décision multiobjectif, Émissions de CO 2, NSGA II

Purpose: Adapting the distribution of fresh fruit to meet consumers' specifications and requirements for quality, safety and sustainability while controlling costs is a complex challenge. Fruit Distribution Management ( FDM) is characterized by long-distance transportation, continuous decline in fruit quality in various form combined with significant supply, demand, and price uncertainties, and relatively thin margins. For these reasons, Fruit Distribution Management needs modern decision-making tools to be effective. The main objective of this research is to propose a method for optimizing the logistics needed to export fresh fruit which takes into account the specific challenges of this kind of product. Design/methodology/approach: The methodology is divided into 3 phases. First, the input factors that constitute the logistics costs and determine the loss of quality due to mechanical injuries (MI) and natural decay (ND), as well as the CO2 emissions of each activity are developed. This phase is based on an extended analysis of the literature and the use of real data. Second, we have developed a multi-objective optimization model that integrates both the distribution and inventory planning of fresh fruit (DIP model). This model takes into account the logistics cost, the total greenhouse gas (GHG) emissions, as well as the quality loss due to MI and ND based on two models of kinetic shelf life: zero order (DIP). -ZO) and exponential decay (DIP-ED). The DIP model objective is to optimize the planning for the distribution and storage for fresh fruit. It is based on a bi objective function: maximizing the total net profit (NP) and the percentage of the remaining fruit quality (% QR). Finally, to address this issue, we have applied a Non-Dominated Sorting Genetic Algorithm II (NSGA-II). A numerical study allows us to analyze the solution spaces of the two kinetic shelf life models (DIP-ZO and DIP-ED) according to the variation of supply, demand, and the market price. This study also includes CO2 emissions analysis. The results based on the NSGA-II are then compared with the results of another genetic algorithm based on an adjusted weight-sum approach (AWS-GA) to evaluate the performance of the algorithm. Findings: t he results we obtained indicate the efficiency of the NSGA-II algorithm to solve the problem of fresh fruit distribution. Both optimal Pareto front curves of DIP-ZO and DIP-ED show a strong positive relationship between %RQ and NP. They also indicate a negative correlation between % RQ and CO2 emission: reduction of % RQ in both cases is correlated with an increase in CO2. The decision variables can be used to decide on the best schedule for transporting and storing fruit in order to optimize the net profit and remaining quality. Practical implications: The proposed model (DIP-model) allows a significant improvement in the benefits related to the export of fresh fruit while minimizing the loss of quality and the environmental impact. It is a decision support tool that allows exporters to better plan the transport and storage of exported fresh fruits. Originality/value: The distribution and inventory planning model developed in this thesis provides solutions that integrate the kinetics of degradation of fresh fruit. While the other operational research models found in the literature only focus on Natural Decay based on a zero order reaction, our model introduces mechanical injuries, natural decay (zero order and Exponential) and consumer evaluation in the optimization process. This is an innovative approach because former models do not reflect reality, in particular for the international trade in fresh fruit which requires long distance transport.

LIST OF TABLE

 Table 1:
J1(ui)

Fitness value of objective 1, so maximising at optimal solution i of weight w1 J1(ui + 1) Fitness value of objective 1, so maximising at optimal solution i+1 of weight w1 J2(ui) Fitness value of objective 2 so maximising at optimal solution i of weight w1 J2(ui + 1) Fitness value of objective 2 so maximising at optimal solution i+1 of weight w1 JIT Just in time

K

The number of days of fruit storage at the distribution centre

LCA

CHAPTER I INTRODUCTION

The management of fruit distribution is receiving more and more attention, both in practice and in the scientific literature. In this chapter, we review the characteristics of fresh fruit distribution management ( FDM) and challenges in the following. First, we introduce the importance of fresh fruit in 1.1. Second, we preview fruit-specific issues in FDM: quality, safety and sustainability in 1.2. Third, we describe the loss in the fruit distribution, including the difference in definitions of fruit loss, waste, and quality loss for FDM in 1.3. Fourth, we describe the consumer value in fruit quality and type of quality loss in fruit: MI and ND in 1. 4 Fifth, the specific characteristics of FDM are discussed. Finally, we discuss the application of operation models in FDM and summarize the overview of this research and expected outcome in 1.7.

Importance

Fruit is a seed-bearing structure in flowering plants ( also known as angiosperms) formed in the ovary after flowering (Lewis, 2001). Most people consume fruit in the form of fresh produce that has been minimally processed. The minimally processed fresh fruit is commonly defined as any fruit that has been subjected to different processing steps ( e. g. , peeling, trimming, cutting, washing, disinfecting, rinsing, etc.) to obtain a fully edible product while providing convenience and functionality to consumers and ensuring food safety (Artés and [START_REF] Artes | Minimal processing of fresh fruit, vegetables, and juices[END_REF]. Most fresh fruit is considered as a type of perishable food that can deteriorate quickly after harvest. Usually, it requires some sort of optimally refrigerated storage to preserve the quality [START_REF] Dudeja | Food safety in large organized eating establishments[END_REF].

Fresh fruit is one of the most important food categories in supermarkets around the world. Everyone across the globe purchases them, but the consumption varies considerably among and within countries, in large part reflecting the prevailing economic, cultural, and agricultural environments. The fresh fruit sector has the highest proportion of sales, contributing to 86 per cent of total agricultural products [START_REF] Vasileska | Global and regional food consumption patterns and trends[END_REF]. A rising fresh fruit consumption around the world is mainly motivated by the recommendations made by different organizations, such as the World Health Organization (WHO), the Food and Agricultural Organization (FAO), the US Department of Agriculture, and the European Food and Safety Authority, etc., because of their healthy properties [START_REF] Allende | Minimal processing for healthy traditional foods[END_REF][START_REF] Warriner | Recent advances in the microbial safety of fresh fruits and vegetables[END_REF]. Fruits are essential sources of a wide range of vital micronutrients, phytochemicals (e.g., anthocyanins and other phenolic compounds), and fibre of great importance from the human nutritional point of view [START_REF] Tomás-Callejas | Survival and distribution of Escherichia coli on diverse fresh-cut baby leafy greens under preharvest through postharvest conditions[END_REF]. Sufficient daily consumption of fruit could help prevent major diseases, such as cardiovascular diseases and certain cancers.

Roughly 16.0 million (1.0%) disability-adjusted life years (DALYs, a measure of the potential life lost due to premature mortality and the years of productive life lost due to disability) and 1.7 million (2.8%) of deaths worldwide are attributable to low fruit and vegetable consumption. Furthermore, insufficient intake of fruit and vegetables is estimated to cause around 14% of gastrointestinal cancer deaths, about 11% of ischaemic heart disease deaths, and about 9% of stroke deaths globally.

Global fruit trade is increasing to meet consumer demand for the regular supply of good quality, safe, and nutritious fresh food products. [START_REF] Opara | Assessment of what the consumer values in fresh fruit quality: case study of Oman[END_REF]. At the same time, there has been mounting evidence in both medical and other scientific literature on the functionality of some types of fresh fruit. [START_REF] Bramley | Is lycopene beneficial to human health?[END_REF][START_REF] Canene-Adams | The tomato as a functional food[END_REF][START_REF] Franke | Vitamin C and flavonoid levels of fruits and vegetables consumed in Hawaii[END_REF][START_REF] Southon | Increased fruit and vegetable consumption within the EU: potential health benefits[END_REF]. Consequently, relevant health agencies and non-governmental aid organisations have continued to promote increased consumption of fresh fruit.

During the last five years, international trade in fresh fruit and vegetable increased every year, as shown in Figure1. By 2018, the total import value of fruits and vegetables in the EU was worth about 59.8 billion Euros, which increased to 16.3 per cent from 2014. In this same year, the United States of America had about 33.0 billion Euros of the total import value of fruits and vegetable, which combined share of fruit exports increased to 18.71 per cent from 2014, while the rest of the world rose to 59.7 per cent of total import value from 2014 to 2018. Europe is the largest market, with a population of more than 500 million consumers. They are responsible for 45% of the total global trade value of fresh fruit and vegetables.

Quality, safety, and sustainability in FDM

FDM has received a great deal of attention lately in both government and private sectors due to consumers' concerns in quality, health, and safety, as well as environmental and social responsibility [START_REF] Akkerman | Quality, safety and sustainability in food distribution: a review of quantitative operations management approaches and challenges[END_REF]. In the global fresh fruit distribution, it is evident that each export company must be held responsible for fruit quality, safety, and sustainability under an economic point of view. Many companies try to reduce unnecessary distribution costs based on the number of vehicles used, total distance travelled, and overall lead time. At the same time, the loss of quality is also reduced indirectly. The crucial challenge for managing fresh fruit is that fruit value deteriorates significantly over time in the fruit distribution at higher rates depending on temperature and humidity [START_REF] Brasil | Postharvest quality of fruits and vegetables: An overview[END_REF]. For a wide variety of fruits, the optimal temperature control is essential for controlling fruit quality and fruit safety.

However, it leads to additional energy consumption and the increase in greenhouse gas emissions (GHG emission). As such, temperature-controlled fruit distribution is related to all three fruit-specific aspects that are the focus in our discussion: quality, safety, and sustainability.

In the following sections, we discuss three main aspects of fresh fruit: fruit quality in 1. 2. 1, fruit safety in 1. 2. 2, fruit sustainability in 1. 2. 3, and finally, the interdependence between quality, safety, and sustainability is concluded in 1.2.4.

Fruit quality

Quality of fruit refers typically not only to the physical properties of food products but also to the way the final consumer perceives the product. The physical properties in the fruit include not only microbial aspects but also texture or flavour. Fruit quality has several interpretations and perceptions among producers, marketers, and consumers (Kader, 2001;[START_REF] Opara | Assessment of what the consumer values in fresh fruit quality: case study of Oman[END_REF]. Shewfelt [START_REF] Shewfelt | What is quality?[END_REF] stated that fruit quality is often defined from a product or consumer orientation and that the combinations of product attributes constitute quality while the consumer's perception and response to those attributes to be referred to as acceptability. [START_REF] Kyriacou | Towards a new definition of quality for fresh fruits and vegetables[END_REF] consider that the quality of fruits and vegetables constitutes a dynamic composite of the physicochemical properties pertaining to horticultural commodities and consumer perception. The components of quality attributes vary with the context of space and time in the fruit supply chain, while the concept of quality encompasses both perception and acceptability.

The fruit quality has always been a strong selling point for fresh fruit. The colour, flavour, texture, and the nutritional value of fresh fruit are factors critical to consumer acceptance and the success of these products [START_REF] Barrett | Color, flavor, texture, and nutritional quality of fresh-cut fruits and vegetables: desirable levels, instrumental and sensory measurement, and the effects of processing[END_REF], which they also related to the fruit quality assessment of consumers in both healthier diets and fruit taste. The appearance of the fruit usually determines whether the fruit is accepted or rejected; therefore, this is one of the most critical quality attributes. Fruits are rich wellsprings of vitamins and minerals, dietary fibre, and a host of beneficial non-nutrient substances, including plant sterols, flavonoids, and other antioxidants. Nutritional value is a hidden character that affects our bodies in ways that we cannot perceive. Still, this quality attribute is increasingly becoming valued by consumers, scientists, and the medical profession.

Understanding consumer perceptions and mentalities towards fruit quality are fundamental in setting quality specifications for marketing as well as providing a useful guide for postharvest research aimed at quality improvement of fresh fruit. It is also a vital issue for breeding research to improve fruit quality and acceptability, as well as in market-oriented fruit production. [START_REF] Wismer | Identifying flavour targets for fruit breeding: a kiwifruit example[END_REF]. Researchers have looked for a superior comprehension of the mechanisms of fruit development and ripening, which underpin quality evolution [START_REF] White | Recent advances in fruit development and ripening: an overview[END_REF]. Renewed and increasing interest in the health and nutritional benefits of consuming fresh fruit and other horticultural produce has been matched by efforts among researchers to gain a better understanding of the synthesis, accumulation, and degradation of nutritional aspects of fruit quality [START_REF] Franke | Vitamin C and flavonoid levels of fruits and vegetables consumed in Hawaii[END_REF].

FDM is different from other products because it shows continuous quality change throughout the supply chain, all the way until final consumption due to the perishable nature of the fruit. These distinctions have also affected the limitation of the feasibility of the fruit quality integration in food supply chain management. Most fruit is considered perishable food, which is a type of food that spoils the most quickly, and it requires refrigeration [START_REF] Dudeja | Food safety in large organized eating establishments[END_REF]. Temperature control is an essential factor which affects fruit quality by influencing the level of quality degradation and affects fruit safety by influencing the growth of potentially harmful bacteria such as Salmonella and Escherichia coli [START_REF] Brasil | Postharvest quality of fruits and vegetables: An overview[END_REF]. At the same time, insufficient temperature control may even lead to chemical reactions that could change a fruit' s appearance or texture. These undesirable changes in product characteristics determine the shelf life of the fruit product, which is hence often linked to a temperature requirement [START_REF] Zhang | Critical factors for shelf life prediction of commercial fruit product[END_REF]. Nowadays, new innovative advancements, for example, post-harvest technology, packaging system, and time-temperature indicators, are used to manage fruit quality in the fruit distribution [START_REF] Giannakourou | Application of a TTI based distribution management system for quality optimization of frozen vegetables at the consumer end[END_REF]. However, the cold chain system is still an essential and the most effective method in delaying quality losses in the fruit distribution supply chain when compared to the other technologies.

Fruit safety

Fruit safety generally refers to the prevention of illnesses resulting from the consumption of contaminated food. Three generally recognised categories of hazards are associated with all fruits, including fresh produce: biological, chemical, and physical hazards [START_REF] Bennett | Produce-associated foodborne disease outbreaks, USA, 1998-2013[END_REF]. For FDM practices, the occurrence of the chemical and physical hazards is favoured over any type of remedial action to correct a problem after they have occurred. Still, the biological hazard microorganisms cannot take action because there is no kill step for inactivation of all microbes that can be present on fresh produce [START_REF] Fan | Global Initiative on Food Loss and Waste Reduction[END_REF]. Most microorganisms are not harmful to humans, and many serve purposes that are beneficial to human health and activities. However, some microorganisms can cause human illnesses such as Salmonella and Escherichia coli, which are called pathogens. Bacterial pathogens are a part of our environment, and the potential always exists for them to contaminate fresh produce.

The importance of food safety has repeatedly been vigorously discussed after the occurrence of food scares, e.g., caused by the presence of salmonella in chicken or by cows infected with BSE. The increasing attention of the industry for food safety is partly since much legislation has been enforced on this matter [START_REF] Panozzo | Standards for transport of perishable goods are still adequate?: Connections between standards and technologies in perishable foodstuffs transport[END_REF]. It also has an economic motivation. Food safety (or related information) can be a competitive factor, and more importantly, the implications of a significant food safety failure can be commercially devastating, including product recalls damage to reputation, and punitive liability damages [START_REF] Berruto | Hybrid modelling for fruit quality prediction in supply chain networks[END_REF][START_REF] Hobbs | Liability and traceability in agri-food supply chains[END_REF]. Various systems and standards have been developed over the past decades to control food safety. The bestknown are the hazard analysis critical control point (HACCP) [START_REF] Francois | Traceability of fruits and vegetables[END_REF] system, the ISO 22000 standard (ISO 2005), and the British BRC standards (British Retail Consortium 2004). Systems like HACCP are developed to manage food safety, based on risk management principles and cover a range of biological, chemical, and physical hazards. The basic idea behind a HACCP system is to provide a structured way to identify food safety risks and reduce or eliminate them. Standards like ISO 22000 and BRC typically include HACCP aspects, but also offer a management system to incorporate food safety in an organisation. Governments are imposing legislation that enforces the traceability of food products during all stages of production, processing, and distribution . The key to prevention is education where specific bacteria and practical training followed by implementation of the lessons learned, verification of the implementation of Good agricultural produce (GAP) and good manufacturing practices (GMP), and periodic reinforcement of training.

Traceability system has become a vital issue in both technical and marketing terms in FDM. It is a risk-management tool which allows food business operators or authorities to withdraw or recall products which have been identified as unsafe. Governments imposed legislation that enforces traceability of food products during all stages of production, processing and distribution. While the firm needs a mechanism, which ensures information of fruit quality and safety can be followed over the entirety of the provider's setups, from producers (farmers) to consumers [START_REF] Francois | Traceability of fruits and vegetables[END_REF].

Fruit sustainability

Sustainability commonly refers to how the needs of the present human generation can be met without compromising the ability of future generations to meet their need [START_REF] Fleurbaey | On sustainability and social welfare[END_REF]. It includes environmental aspects as well as a social dimension [START_REF] Kleindorfer | Sustainable operations management[END_REF]. This entails, for instance, employees' health and safety, ethical trading in the procurement of raw materials, and animal welfare. For example, fair trade initiatives have been developed to improve the position of food producers in developing countries. The international fruit distribution in the current globalised economy, as well as in academic literature, is a major discussion point in the environment and society .The resulting transport intensification leads to environmental degradation by contributing to air pollution, global warming, ozone depletion, resource depletion, and congestion. At the same time, stakeholders in the fruit distribution also provide some of the challenges related to the responsibility of the social performance for enhancing the transparency of food supply chains [START_REF] Tsai | Studying the effect of ambient temperature exposure on refrigerated food quality and safety for sustainable food cold chains[END_REF] .Over the past years, sustainability has gained increasing importance in the fruit industry. It is increasingly evident that market and regulatory sustainability drivers shape the organization and operation of supply chains. People are gaining interest in more sustainable and responsible fruit, which relates to many aspects, such as working conditions, water use, and waste management, among other things. Furthermore, the awareness among consumers is growing thanks to more transparency. More integrated social and certification programs are introduced with increased sharing of information along the entire supply chain. Meanwhile, fruit innovations will improve the customer experience and taste. Sourcing sustainable fruits from the farm are a major impact on fruit exporter. The company needs to verify working conditions and environmental impact at the farm level to ensure that the fruits are produced under sustainable economic, social, and environmental conditions [START_REF] Baldwin | Principles of Sustainability for Food Products[END_REF]. At the same time, the temperature control throughout the fruit distribution supply chain also related to waste, energy used, and resultant in GHG emission [START_REF] Tsai | Studying the effect of ambient temperature exposure on refrigerated food quality and safety for sustainable food cold chains[END_REF] The environmental dimension of sustainability has likely gotten the most consideration. One of the best-known examples is the Life Cycle Assessment (LCA). This analytical approach helps in assessing a product's environmental impact from product development to consumption [START_REF] Parajuli | Environmental sustainability of fruit and vegetable production supply chains in the face of climate change: A review[END_REF]. Although these assessments can be and are used to decrease an environmental load of products, further standardization is still needed to improve comparative studies and to broaden practical applications in the food sector [START_REF] Roy | A review of life cycle assessment (LCA) on some food products[END_REF]. The social dimension has received less attention in the literature [START_REF] Lehtonen | The environmental-social interface of sustainable development: capabilities, social capital, institutions[END_REF]. Numerous companies have started to work on these issues under the label ' Corporate Social Responsibility' (CSR). In many cases, they also communicate their CSR performance to stakeholders like employees or customers. For instance, all ten major retailers in the UK have stated that they see CSR as an integral element of theirs. Supporting for social and environmental awareness can also be useful for corporate image [START_REF] Colinas | The socio-environmental impacts of public urban fruit trees: A Montreal case-study[END_REF]. On some occasions, it might lead to cost savings at the same time, for instance, while reducing fruit waste.

Interdependence between quality, safety, and sustainability

The fruit quality, safety, and sustainability are currently dominating the public debate concerning the fruit sector. It is essential to realize that there are strong relationships between these topics. The fact that fruit distribution deals with products that are eventually meant for human consumption results in a strong focus on fruit quality and fruit safety. It is especially true for products that do not undergo extensive shelf-life-extending treatments and remain 'fresh products' with short shelf lives. Both quality and safety are based on changes in the fruit. The main difference being that food quality is based on a more continuous process of degradation, whereas safety is modelled as a binary; a product fulfils safety requirements, or it does not. However, underlying it is often a continuous process related to, e.g., the growth of a certain bacteria.

Quality loss is a prime criterion considered to be strongly interdependent of quality, safety, and sustainability in FDM. To minimise the adverse effects on fruit quality by influencing the level of fruit quality degradation and fruit safety, influencing the growth of potentially harmful bacteria, cold chain systems, and various quality standards is an essential factor. Using optimal temperature can preserve fruit quality and prevent risks [START_REF] James | Advances in the cold chain to improve food safety, food quality and the food supply chain[END_REF]. Additionally, a significant amount of energy is necessary for the area of sustainability. On the other hand, producing greenhouse gases (GHG) can negatively affect the environment in which products grow and are stored.

Quality standards were initially designed to control food safety as well as increase product quality throughout the supply chain [START_REF] Panozzo | Standards for transport of perishable goods are still adequate?: Connections between standards and technologies in perishable foodstuffs transport[END_REF]. It also concerns the traceability system, in which fruit quality must be traceable. Further, the information must be declared to customers as a sustainability requirement. Furthermore, extending these quality and safety control systems provides transparency in the food chains in order to enable the supply of affordable food with high quality and diversity, which is a challenge related to the sustainability of the food industry [START_REF] Akkerman | Quality, safety and sustainability in food distribution: a review of quantitative operations management approaches and challenges[END_REF]

Loss in fruit distribution

General structure of global fruit distributions stretch from farmer to consumer and usually involve a manufacturing stage in the packaging house, as well as fruit service or retail activities. Distribution management typically refers to the physical flows and storage of fruit from the final production point to the customer or end-user [START_REF] Akkerman | Quality, safety and sustainability in food distribution: a review of quantitative operations management approaches and challenges[END_REF][START_REF] Rushton | The handbook of logistics and distribution management: Understanding the supply chain[END_REF], as shown in Figure2.

Fruit losses occur at all stages of the supply chain. The reasons for fruit losses are diverse. They comprise losses due to mechanical damage, sorting, degradation, storing, processing, and transportation ( [START_REF] Rezaei | Food loss and waste in the food supply chain[END_REF]. In addition to this, the market system and legal and private quality standards are also important reasons for food losses [START_REF] Frieling | The beauty and the beast-how quality management criteria at supermarkets create food waste[END_REF][START_REF] Willersinn | Quantity and quality of food losses along the Swiss potato supply chain: Stepwise investigation and the influence of quality standards on losses[END_REF]. FAO reported that 40-50 % of horticultural crops produced are lost before they can be expended in a developing country, for the most part, due to high rates of bruising, water loss, and consequent decay during postharvest handling [START_REF] Roy | A review of life cycle assessment (LCA) on some food products[END_REF]. Murthy et al., 2009, reported that a vast amount of food is wasted in various stages of the fresh food supply chain. An estimated 30% of the food produced for human consumption globally is lost or wasted somewhere along the food supply chain [START_REF] Rezaei | Food loss and waste in the food supply chain[END_REF].It is important to distinguish between food loss and food waste and the circumstances of their occurrence, especially when identifying causes and developing solutions and interventions to address this issue.

Food loss is defined as the decline in the quantity or quality of the food, which results from decisions and actions made by food suppliers in the chain, excluding retailers, food service providers, and consumers (FAO, 2015). In a technical context, food loss is mostly caused by the malfunctioning of the food manufacture and distribution system or its institutional and policy framework. It could be due to managerial and technical limitations, such as an absence of appropriate storage facilities, cold chain, proper food handling practices, infrastructure, packaging, or an efficient marketing system.

Consumer value and quality loss in fruit

Consumer perception of fruit quality is a crucial issue for an operational research tool to optimise FDM. Understanding fruit quality attributes that are important to the consumer is also useful in the assessment and control of fruit quality in the supply chain to be at the highest level of consumer satisfaction [START_REF] Wismer | Identifying flavour targets for fruit breeding: a kiwifruit example[END_REF]). The quality loss in fruit results from the concerted action of two leading causes: mechanical injury (MI) and natural decay (ND). The quality loss level is different depending on fruit owners' biological or physical product property [START_REF] Hertog | Shelf life modelling for first-expired-first-out warehouse management[END_REF]. In the remainder of this section, we present the consumer value in the fresh fruit quality in 1.4.1 and presents the characteristics of quality loss in fruit caused by MI in 1.4.2 and by ND in 1.4.3.

Consumer values in fresh fruit quality

Fruit quality is often defined separately from the product or consumer orientation. It is the combinations of fruit attribute and the consumer's perception, including the response of consumers in terms of acceptability. In an interpretative review of point of view and orientations of quality, the fruit quality is frequently characterized from fruit or consumer orientation, and that the combination of fruit attributes comprise quality while the consumer's perception and response to those attributes be referred to as acceptability [START_REF] Shewfelt | What is quality?[END_REF]. However, Abbot (1999) considered that the parts of quality attributes differ with the specific circumstance or existence in the supply chain, and contented that the concept of quality encompasses both perception and acceptability.

Consumers' perceptions of the quality of fresh product at the point of Contemporary research literature in food decision considers product attributes as one point of view to increase understanding of consumers. Consumers during a complex, cognitive process form beliefs and develop attitudes and intentions [START_REF] Kovacic | Behaviour of fruit and vegetable buyers on the city markets in Croatia[END_REF]. Food as goods can be classified into search(e.g., taste and odour), experience(e.g., taste and odour), and credence goods (e.g., freshness, nutrition, medicinal value) according to the level of quality that can be discovered by the consumers at different stages [START_REF] Kapoor | Fruit and vegetable consumers' behavior: Implications for organized retailers in emerging markets[END_REF].

Several researchers have concluded that credence characteristics positively affect on consumers' attitude toward a product and consequently influence consumers' buying intentions [START_REF] Dentoni | The direct and indirect effects of 'locally grown'on consumers' attitudes towards agri-food products[END_REF][START_REF] Gao | Consumer willingness to pay for cue attribute: The value beyond its own[END_REF][START_REF] Wirth | The relative importance of search versus credence product attributes: organic and locally grown[END_REF]. The component of smell, visual, and aroma were regularly first class among attributes recored, which is logical because they represent the basic components of eating pleasures [START_REF] Ernst | What matters in consumer berry preferences: price? Source? Quality?[END_REF][START_REF] Moser | Consumer preferences for fruit and vegetables with credence-based attributes: a review[END_REF] [START_REF] Kapoor | Fruit and vegetable consumers' behavior: Implications for organized retailers in emerging markets[END_REF] found that consumers attached more importance to credence attributes than to search and experience attributes while making their purchase decisions. At the same time family income and consumers' education were found to have significant influence on the consumers' willingness to pay for graded and packaged products.

Mechanical injury

The MI aspect of fruit distribution can be described in terms of the characteristics of fresh fruit products. Most fresh fruits contain a high level of water, about 65 to 95 per cent water. They can be easily bruised and damaged from mechanical forces such as shock, vibration, and compression during transportation, handling, and storage. The MI due to transportation is the main cause of downgrading and wastage of fresh fruit during distribution and represents a high cost for companies [START_REF] Rong | An optimization approach for managing fresh food quality throughout the supply chain[END_REF]. The fresh fruit might demonstrate physical injuries sustained during transportation. These physical injuries can contribute to 5 to 40% of total market loss which can also fluctuate by the relative susceptibility of the commodity to physical damage, the quality of the road, shipment distance, and the type of package in which they were packed. To prevent physical damage, fresh fruits and vegetables must be appropriately selected, packaged, handled, and kept at an optimal temperature at all stages of distribution and handling, including each step of transportation.

MI occurs because of mechanical forces (shock, vibration, and compression) during transportation, handling, and storage. Mechanical damage to fresh fruit represents a severe hazard to quality and has the potential to reduce the value of the product significantly. (Li and Thomas, 2014). Among different causes of damage to fruits, shock, and vibration generated by vehicles during road transport has a vital role in the damage process to the agricultural products, mainly fruit with sensitive skin. Inflicted damage on fruit is related to the available energy for bruising, which in turn is related to the suspension characteristics of the transporting vehicle, the energy input in the system as a function of road roughness, vehicle speed, and the properties of the packaging system [START_REF] Chonhenchob | Effect of truck vibration during transport on damage to fresh produce shipments in Thailand[END_REF]. These energy values can be estimated in terms of the root mean square acceleration value (Grm 2 ), which is measured in specific gravity units (g) within a bandwidth (BW) of frequencies or the average power density spectrum (PSD, G 2 /Hz) according to Equation :

Natural decay

Most fresh fruits are susceptible to physiological change due to the loss of freshness, the process of natural ripening and microorganism contamination. They are direct and indirect results of maintaining the physiological system and the metabolic processes of fruit after harvesting. Loss of freshness is a result of continuous loss of water in fruit after harvesting. Loss of water causes shrinkage and loss of weight. The rate at which water is lost fluctuates as indicated by the physical characteristics of fruit and environmental storage conditions. Fruit that has thin skin and many pores or a high ratio of the surface area of the fruit to its volume tend to lose water quickly. The rate of loss is identified with the contrast between the product water vapour pressure and the air-water vapour pressure. Fresh fruit must be kept in an optimally moist atmosphere (Kader, 2001).

Fruit ripening is the other factor dealing with physiological change in fruit.

Ripening happens when the fruit is mature. Ripeness is trailed by senescence and breakdown of the fruit. We can divide the fruit into two types according to ripeness: nonclimacteric fruit and climacteric fruit. Non-climacteric fruit only ripens while still appended to the parent plant. Their eating quality endures on the off chance that they are harvested before fully ripe as their sugar and acid content does not increment further.

Examples are citrus, grapes, and pineapple. Climacteric fruit is those that can be harvested when mature but before ripening has begun. These include banana, melon, papaya, and tomato. ( Kader, A. A. , 2005, andLopez-Camelo, 2004) Fruit ripening involves a significant number of complex changes, including colour changes, abscission from the parent plant, tissue softening, volatile production, wax development on skin changes in respiration rate, ethylene production, tissue permeability, carbohydrate composition, and organic acids and proteins [START_REF] Wills | Postharvest: an introduction to the physiology and handling of fruit and vegetables[END_REF]. Ethylene gas is delivered in most plant tissues and is essential in starting the ripening stage. It can be utilised commercially for the ripening of climacteric fruits. However, natural ethylene delivered by fruits can lead to in-storage losses. For instance, ethylene destroys the green colour of plants. Leafy vegetables will be lost whenever put away with ripening fruit. Ethylene generation is expanded when fruits are injured or decaying, and this can cause early ripening of climacteric fruit during transport. Reduction of these processes by technologies such as cooling, storage surface coating, packaging, atmospheric modification technology such as modified atmosphere packaging and controlled atmosphere packaging and active packaging ethylene scavenger, carbon dioxide emitter, and oxygen absorber enable the postharvest life of fresh produce to be prolonged.Infections brought about by fungi and bacteria cause losses, but viral diseases, prevalent in developing yields, are not a significant post-harvest problem. The profound entrance of rot makes infected produce unusable. It is regularly the aftereffect of contamination of the product in the field before harvesting. Quality loss happens when the infection influences just the surface. Skin imperfections may bring down the deal cost yet do not render fresh produce inedible. A fungal and bacterial infection is spread by microscopic spores, which disseminate noticeably all around the soil and through rotting plant material.

Contamination after harvest can occur at any time. It is usually the result of harvesting or handling injuries and reflects the dynamics of quality degradation, as this plays a vital role in modelling quality in food supply chains. In general, the quality degradation of food products in storage (or transport, for that matter) is dependent on storage time t, storage temperature T, and various constants (e.g., activation energy, gas constant). The following general equation can describe it:

[2]
where q is the quality of a product, k the rate of ND depending on environmental conditions like temperature, and n a power factor called the order of the reaction, determining whether the reaction rate is dependent on the amount of quality q left [START_REF] Rong | An optimization approach for managing fresh food quality throughout the supply chain[END_REF].

A power factor might have a value of either 0 or 1 based on a fruit's own biological or physical product properties. The amount of quality left as a function of time is either linear or non-linear, as illustrated in eq 2. Concerning the power factor, we can identify two types of ND related to different physiological change characteristics in each fruit: zero-order kinetics (n =0) is mostly associated with freshness loss (weight loss) and enzymatic degradation, while exponential decay (n = 1) generally concerns microbial growth and vitamin losses (Labuza T. P., 1982).

The rate of ND (k) is, therefore, often based on the Arrhenius equation, a formula for the temperature dependence of a chemical reaction. The general type of this condition can be communicated as:

[ 3]
Where: k0 is a constant, Ea the activation energy (an empirical parameter is characterising the exponential temperature dependence), R the gas constant, and T the absolute storage temperature [START_REF] Wang | A dynamic product quality evaluation based pricing model for perishable food supply chains[END_REF]. Considering the distribution of fruit in practice for prediction of quality levels in eq.3, the fruit must be stored and transported at an optimal temperature (the chilled chain at temperatures ranging from 0°C to 15°C) throughout the supply chain in order to preserve fruit quality as well as reduce potential hazards that could affect product safety. Furthermore, in the case of multi-fresh fruit exportation, all fruit cannot be stored in the same place and at the same temperature. Each fruit type must be stored separately in order to prevent the effects of temperature injury and ethylene production in fruit [START_REF] Thompson | Postharvest treatments. Postharvest technology of fruit and vegetables[END_REF]. In this case, we consider Ea and T, as constant values. Finally, we can estimate the quality level of fruit at a specified location in the production and distribution network, based on an initial quality (q0), and subsequent total holding period (ti) i = 1,.., m, and degradation rate (k) (depending on the temperature (T), leading to:

    m i i kt q q 1 0 [ 4] [A] [B]               m i i kt q q 1 0 exp [ 5]
For zero-order kinetic (ZO), and exponential decay(ED), respectively. However, quality loss appearance in fruit is caused by a combination of many factors. Assessment of quality loss by considering all factors is difficult. An evaluation must find quality loss indicators that are most important to the consumer's decision. The quality loss indicator considered as a parameter in the optimisation approach in the fruit distribution might be both intangible values (e.g., sugar content, vitamin losses, acid content and growth of potentially harmful bacteria, e.g., Salmonella and Escherichia coli), and tangible value (e.g. freshness, colour, texture, and bruising) by a consumer. These quality loss values may be a function or non-function of time under control and/ or without environmental conditions. The characteristics of quality loss indicator have a variety of formats depending on the type of fruit and the purpose of use in the production stage. For instance, Blackburn, J., and Scudder, G., 2009 developed a hybrid model for the design of a supply chain of perishable foods by using melons and sweet corn as examples based on optimising the value of marginal products over time.

The model considers the percentage of initial sucrose in fruit over time as the quality index that tends to decrease according to quality deterioration. [START_REF] Ferrer | An optimization approach for scheduling wine grape harvest operations[END_REF] presented mixed-integer linear programming for scheduling grape harvesting operations in wine production, which takes into account the costs of quality loss for the grapes to delay harvesting and processing. [START_REF] Amorim | Multi-objective integrated production and distribution planning of perishable products[END_REF] compared the effects of tangible and intangible value on quality indicator based on consumer perceptions of perishable products. They formulated a model for two cases of perishable food, including a fixed and a loose shelf-life through a multi-objective framework to study the economic benefits. However, no work has been done in terms of an in-depth study of the effects of quality loss function based on order reaction ( zero-order kinetics and exponential decay) of the effectiveness of problem-solving in operation research.

Fruit distribution management

Loss in the fruit distribution was driven by issues around awareness, supply chain infrastructure, supply chain efficiency, collaboration, and the policy environment.

Improving FDM efficiency would not only help to reduce food loss and waste but also it will also improve operational efficiency and potentially lessen costs for organizations.

In this section, we discuss the specificity of FDM, which consist of the fruit distribution system in 1.5.1, and the logistics cost structure of fruit distribution in 1.5.2.

Fruit distribution system

Fruit distribution system commonly refers to the physical flows and storage of fruit from the final production point to the customer or end-user [START_REF] Rushton | The handbook of logistics and distribution management: Understanding the supply chain[END_REF], as represented by the general structure of the distribution part of the fruit exportation supply chain in Figure2. An essential characteristic of fruit distribution systems is temperature control. For a wide variety of foods, temperature control is essential for controlling food quality and food safety. Temperature control affects food quality by influencing the level of quality degradation and affects product safety by influencing the growth of potentially harmful bacteria (such as Salmonella and Escherichia coli).

Furthermore, insufficient temperature control may even lead to chemical reactions that could change a product's appearance or texture. These undesirable changes in product characteristics determine the shelf life of the food product, which is hence often linked to a temperature requirement. In the food industry, we can identify three levels of temperature control: frozen, chilled, and ambient.

For the frozen and chilled chain, several different temperatures are used. The frozen chain mainly operates at -18C, although a product like ice cream requires a frozen chain with an even lower temperature of -25C. For the chilled chain, temperatures range from 0C for fresh fish to 15C for, e.g., potatoes and bananas [START_REF] Smith | Temperature controlled supply chains[END_REF]. Finally, ambient chain concerns products that do not require temperature control, such as canned goods.

Generally, most fresh fruit storage concerned chilled temperature, which must be kept at an optimal temperature at all stages of distribution and handling, including each step in transportation. Table 1 presents an example of optimal temperatures and the percentage of relative humidity (%RH) conditions for some common fruits and vegetables. Different kinds of fresh fruit have various capacities to endure and keep up their quality. Some types have a very short shelf life because of their high metabolic rates and high rates of water loss and must be held under cold, sticky conditions. Other types with low metabolic rates and low rates of water loss can be stored for long periods without the requirement for cold storage. However, fresh produce is a living organism;

this does not always mean that the lower the temperature, the longer the storage life.

Fruit quality can be irreversibly damaged by applying the wrong temperature. Knowing the characteristics of the living produce can assist with decisions about managing storage and minimising deterioration before consumption.

Logistics cost structure of FDM

Logistics costs can be calculated in many ways. Activity-based costing (ABC) systems have been developed to improve the costing system, and claim to be more accurate than traditional costing methods [START_REF] Zaini | Costing structure improvement using activity based costing in palm oil plantation of Malaysia[END_REF]. For instance, [START_REF] Ruben | Vegetables procurement by Asian supermarkets: a transaction cost approach[END_REF] studied the transaction cost of the vegetable procurement system in Asian supermarkets by using case studies in Bangkok, Thailand, and Nanjing, China. They compared two significant types of suppliers for TOPS supermarket in both countries: local wholesalers and preferred suppliers. [START_REF] Ongkunaruk | Logistics cost structure for mangosteen farmers in Thailand[END_REF] study the mangosteen supply chain in eastern Thailand and analyse the logistics cost structure for mangosteen farmers. The results show that most logistics cost dealing with material handling such as post-harvest, grading, and handling, followed by acquisition, client interchanges, customer communications, and inventory, respectively.

Zaini, S.N. A.M., and et al. (2020) apply the activity-based costing (ABC) as a method of cost evaluation for the palm oil plantation. The result showed that accurate profitability is the most important factor for the management to identify the money that process in order to keep up rapid but sustainable growth. ABC has doled out actual cost information and appropriate cost drivers for each of the activities being involved, and it makes the company's profitability more accurate.

Generally, activities in each type of logistics cost in fruit distribution consist of activity from the upstream stakeholders to the downstream stakeholders, as shown the detail in Table2. The logistics cost structure differs by the size of farms; also, the yield of fruit increases as the size of the farm increases. As mention above, the quality loss assessment and management to optimise structuring fruit supply chain network is complex. Each fruit has its specificity in terms of quality loss appearance and appropriate management for quality control, while decision-making process in the fruit supply chain must be optimised by analysing several factors, such as logistics cost, supply, demand, and price variability/uncertainty.

These challenges generate a need for management efficiency and the use of modern decision technology tools. Many operation research models have proposed to solve many problems in FDM.

The remainder of the research is organised as the following.

Chapter 2 is a literature review. Theory and all the revised research papers dealing with the optimisation modelling approaches are reviewed. First, we review the mathematical model approaches in FDM in 2.1. Second, the quality loss assessment for the optimisation model in FDM is discussed in 2.2. Third, we present a logistics network configuration for the optimisation model in FDM in 2.3. Fourth, the managerial decisionmaking in FDM, mainly relating to the time horizon is represented in 2.4. Fifth, the algorithms applied to solve problems in FDM are discussed in 2. 5. Sixth, Genetic algorithm (GA) is discussed in more detail in 2.6. Seventh, we discuss the multi-objective optimisation in FDM. Finally, the non-dominated sorting genetic algorithm (NSGA-II) is described in more detail.

Chapter 3 is material and methodology. We present the methodology to achieve the purpose of the research. First, we describe the estimated logistics costs in 3.1, the cost of MI in 3.2 and the cost of ND in 3.3, and GHG emission in 3.4. Second, the state problem of fruit exportation and model formulation in case of a quality loss with zero-order kinetics (DIP-ZO) and exponential decay (DIP-ED) are represented in 3.5.

Third, we present the numerical study, which consists of supply and demand simulation, and material and market price determination are described in 3.6. Finally, multi-objective solution methods based on genetic algorithm to solve the DIP model, adjusted weightsum approach with genetics algorithm (AWS-GA), and NSGA-II are presented in 3.7.

Chapter 4 presents the results and discussion. We present results from numerical analysis and propose a way to improve the value of fruit product and logistic efficiency. First, the optimal Pareto front of numerical result based on three scenarios of various fruit supply and demand are present to verify the DIP model in 4.1. Second, the evaluation of the performance algorithm by comparing the Pareto front of DIP-ZO and DIP-ED is represented in 4.2. Third, we present the effects of quality loss in fruit on the fruit distribution scheme in 4.3. Fourth, we discuss the interdependence between fruit quality, net profit, and total GHG emission. Finally, we discuss all results, and propose a way to improve the value chain of fruit exportation

CHAPTER II LITERATURE REVIEW

The objective of this research is to develop an integrated distribution and inventory planning (DIP) which considers the quality loss of fruit from MI and ND, as a multi-objective mixed-integer model to maximize net profit (NP) and the percentage of remaining quality of fruit (%RQ) in FDM. The aim is to analyse the value chain base on cost advantage and to propose a fruit exportation planning for logistics efficiency improvement. In this chapter, we discuss an overview of operations research modelling approaches applied in FDM in 2.1. We present a quality loss assessment for the optimisation model in FDM in 2.2. A logistics network configuration for the optimisation model in FDM is discussed in 2.3, and then algorithms applied to solve problems in FDM are detailed in 2.4. Lastly, we discuss the multi-objective optimization in 2.5.

Operational research models applied to FDM

Because of globalization, competitors, regulations and the increasing consumer demand for high fruit quality, value-added and customized products, the fresh fruit sector tends to be specialized and vertically integrated into FDM to become more competitive and dynamic. These challenges generate a need for management efficiency and the use of modern decision technology tools [START_REF] Akkerman | Quality, safety and sustainability in food distribution: a review of quantitative operations management approaches and challenges[END_REF]Lowe and Preckel, 2004). FDM comprises all the activities to produce, transport, and distribution fruits to the end customers, produce transport, and distribution planning needs to be integrated in order to be optimized simultaneously. An operational model is a tool that can help fruit exporters in FDM. In this section, we review the overview of operational research models applied to the fresh FDM in an attempt to gain a better understanding of the operation modelling methods used in FDM. A comprehensive search of related research papers from 1970 -2020 was applied to produce a synthesis of peer-reviewed literature. We searched articles published in international peer-reviewed journals from the following main electronic bibliographical sources (Scopus, Web of Science) by using the following keywords for the search: 1) Fresh fruit 2) Supply chain 3) Distribution 4) Optimisation 5) Operational research.

We summarized an overview of the all revised papers associated with operational research models applied to the fresh fruit supply chain in Table 3, including a brief description and the goals to achieve for each one. We focus the discussion of the overview of the operations research model on the following four issues: 1) analytical modelling approach, 2) functional area, 3) decision level, 4) optimization models and solution approaches.

Table 3: Summary of all the revised papers dealing with FDM.

Authors

Description of the research 1. [START_REF] Willis | Temporal Model for Long Run Orchard Decisions[END_REF] A mathematical model based on dynamic programming, which optimises the resources needed in the apple fields.

Furthermore, the model plans the kind of variety to plant on the farm 2. Starbird, S.A (1988) A powerful programming model on arranging the stacking of storerooms at an apple pressing plant 3. [START_REF] Maia | Selection of postharvest technology routes by mixed-integer linear programming[END_REF] A mixed-integer linear programming model to support fruit preservation planning 4. Broekmeulen, R.A.

(1998)

A mixed-integer linear programming model to improve the effectiveness of the operations of a distribution centre for fruits and vegetables. The model seeks the optimal production planning for allocation and storage at a tactical level.

5. [START_REF] Gigler | On optimisation of agri chains by dynamic programming[END_REF] Dynamic programming (DP) that deals with the appearance and quality of products are presented. Chain optimisation refers to the construction of optimal routes defining which actors in the chain should perform which actions at which process conditions at minimum integral costs.

Table 3: Summary of all the revised papers dealing with FDM.

Authors

Description of the research 6. [START_REF] Hester | Modelling apple orchard systems[END_REF] A dynamic simulation model represents the bio-economic characteristics of an orchard. The evaluation of different alternatives allows the user to identify the management strategy maximising the net present value for 15 years 7. [START_REF] Vitoriano | Two alternative models for farm management: discrete versus continuous time horizon[END_REF] Two mathematical formulations are presented to plan and organise the inputs necessary for crop production in a specific time horizon. Discrete-time and continuous-time hd 8. [START_REF] Blanco | Operations management of a packaging plant in the fruit industry[END_REF] A planning model to maximise the profit of an apple and pear packaging plant. The costs considered are raw material purchase, storage, and labour costs. Income is calculated from different selling prices according to the varieties of fruit 9. Caixeta-Filho, J.V.

(2006)

A linear programming model for managing orange orchards to maximise the total profit. A fractional decision variable represents the part of the orange grove to be harvested each period. Quality measures to determine the suitability for fresh consumption or to the juice industry is balanced 10. [START_REF] Ortmann | Modelling the South African fruit export infrastructure: A case study[END_REF] Two models (a theoretical graph model of a single product and a mathematical programming model with multiple products) to determine the maximum weekly flow or yield of fresh fruit through the national export infrastructure in South Africa are introduced. 11. [START_REF] Masini | Supply chain tactical optimization in the fruit industry[END_REF] An extension of the model presented by Masini, Petracci, and Bandoni (2003). It combines the optimal production of fresh fruit and juice concentrate introducing a penalty for unmet demand of customers Table 3: Summary of all the revised papers dealing with FDM. A DSS aimed at allowing winemakers to make decisions like when to pick grapes, allocates processing vats and wine presses, and manage operations within the warehouse.

Authors

The DSS was designed and validated with the assistance of winemakers through collaborative research 19. [START_REF] Ahumada | Operational model for planning the harvest and distribution of perishable agricultural products[END_REF] This paper presents a planting model for the fresh produce industry. The objective is to maximize revenues by making production and distribution decisions during the harvest season.

Rong, A., et al. (2011)

A mixed-integer linear programming model considering food quality degradation for integrated production and distribution planning was developed. The resulting model can be used to design and operate food distribution systems, using both food quality and cost criteria.

21. [START_REF] Amorim | Multi-objective integrated production and distribution planning of perishable products[END_REF] Production and distribution of perishable foods are integrated to optimise the freshness of fruit based on minimising stocks of stored raw material. Two cases are compared depending on whether life's products are fixed or variable 22. [START_REF] Yu | A vendor managed inventory supply chain with deteriorating raw materials and products[END_REF] This paper studies a food-industry vendor management inventory system where a typical replenishment policy is used to manage the inventories of a fast deteriorating raw material and a slow deteriorating product. An integrated model to obtain the total inventory and deterioration costs is given in a closed form and an exact algorithm 23.Banaeian, N. et al.

(2012)

A nonparametric method, data envelopment analysis (DEA) was used to study the technical efficiency of producers concerning effective resource allocation like energy utilisation on greenhouse strawberry yield Table 3: Summary of all the revised papers dealing with FDM.

Authors

Description of the research 24. Ampatzidis, Y.G., et .al. (2013) The fruit harvest and the bin collection process are modelled by using queuing theory to analyse the performance and find optimal resource allocation. The algorithm can be used as a part of a general simulation tool which utilises operational research techniques and optimisation algorithms in order to model and improve the total harvest process and minimise the probability that a worker or machine will be idle for a long period of time 25.Catalá, L.P., et al. An Expert System (ES) using Fuzzy Logic is proposed to discuss two cases of an exporting company. The results show an increase in production yield and fruit quality in the orchard and improved synchronization along the supply chain is observed.

28. Van der Vorst, J.G. and et al. (2014) The authors propose an integrated approach towards logistics, sustainability, and food quality analysis by introducing a new simulation environment, ALADINTM.

A case example of pineapple illustrates the benefits of its use in relation to speed and quality of integrated decision making

Table 3: Summary of all the revised papers dealing with FDM.

Authors

Description of the research 29. González-Araya,

M.C. and et al. (2015)

A mixed-integer linear programming model to support planning decisions in an orchard, aiming to minimise the number of resources used and ensuring the production of fruit with the highest quality 30. Nadal-Roig, E. and Plà, L.M.( 2015)

A linear programming model for planning daily transport of fruit from warehouses to processing plants is presented, aiming to minimise transport costs 31. Li P. and et al. (2016) A vehicle routing problem considering MI from different road classes based on improved genetic algorithm for fruits and vegetable distribution is proposed, aiming to minimise total logistics costs 32 Orjuela-Castro, J.A.

(2017)

A mixed linear programming model for the localization of collection centres and companies processing perishable foods in mountainous regions, based on a multi-product and multi-echelon transport system is proposed, aiming to optimize locating facilities which are linked to the perishability of the food and its quality at the moment of reaching the final consumer.

33 Musavi, M. and Bozorgi-Amiri, A.

(2017)

A multi-objective mixed-integer linear programming is proposed, aiming to optimize the total transportation costs, freshness and quality of foods at the time of delivery and the total carbon emissions of the vehicles to fulfil the sustainability desire of the environment. 34 Grillo, H., et al., 2017 A research paper proposed a mixed-integer mathematical programming model to support the multiple order promising process in fruit supply chains. The model aims to maximise two conflicting objectives: total profit and mean product freshness.

Table 3: Summary of all the revised papers dealing with FDM.

Authors

Description of the research 34. [START_REF] Li | An integrated location-inventory problem in a closed-loop supply chain with third-party logistics[END_REF] A model formulation is proposed to develop mixed-integer non-linear programming (MINLP) models for the locationinventory problem under study, aiming to reduce operating costs 35. Tordecilla-Madera, R.,et.al., (2018).

The model of vehicle allocation problems related to collection and distribution is proposed to determine the optimal allocation of vehicles for fruit collection minimising both total transportation costs and carbon dioxide (CO2) emissions. 36 Tiwari, S., et al. (2018) A two-echelon supply chain model for deteriorating items is proposed. The objective of a function is to optimize the inventory level by using a differential calculus method. It is proved that the optimal solution not only exists but also is unique.

37 Hua, J., Gu, S. and Zhang, L., 2019.

The research proposed the model of distribution optimization of logistics node and used the improved ant colony algorithm for optimizing node distribution of maritime in fresh fruit and vegetable. 38. [START_REF] Nguyen | Optimization Model for Fresh Fruit Supply Chains: Case-Study of Dragon Fruit in Vietnam[END_REF] An optimization model for fruit plantations is proposed.

The timing of cultivating and harvesting decisions are taken into account with the maximum average yield in the fourth year. 39. Sahebjamnia, N., et.al, 2020. A new multi-objective integer non-linear programming model is developed for designing citrus three-echelon supply chain network. The proposed model aims to minimize network costs, including waste cost, transportation cost, and inventory holding cost, and to maximize the network's profits.

Analytical modelling approach

The models and solution methods for fruit distribution planning are relatively abundant. The models can be classified as deterministic or stochastic, according to the certainty of the value of the parameters used (Min and [START_REF] Zhou | Supply chain modeling: past, present and future[END_REF].

Deterministic is a traditional modelling approach that can be used to solve the problem in many ways. For instance, integer linear programming/Linear programming mixedinteger ( ILP), non-linear programming ( NLP), multi-objective linear programming (MOLP) and dynamic programming (DP). In contrast, stochastic modelling approaches are used as a framework for modelling optimisation problems that involve uncertainty.

These include simulation models(SM), stochastic optimisation (SP), as shown in Figure 6 The problems common with most FDM most often deal with factors such as food quality, safety, sustainability and weather-related viability. Also, they may manage issues related to limited shelf life, which restricts the amount of time that most products can spend in storage and therefore, the capacity of holding inventory as a buffer for variability. Furthermore, compounded with issues of variability and perishability, we have very long lead times from the moment that planting is completed, until harvest (Mason et al., 2015;Lowe and Preckel, 2004;[START_REF] Salin | Information technology in agri-food supply chains[END_REF]. The models and solution methods for FDM problems are relatively abundant due to the non-deterministic polynomial-time hardness (NP-hardness) of supply chain problems (Bixby et al., 2000) and the large-sized data in the real world. When considering deterministic modelling approaches, ILP models have been widely used to solve FDM problems. Because the ILP model can solve the NPhardness of distribution network design problems and the large-sized problems in reallife instances. Furthermore, it is available for many solvers, for example, IBM Ilog Cplex, Gurobi, XPress, and Scip, etc.). This result is confirmed by the revised paper collection in Table 4, in which we found that most of the papers preferred linear programming as a modelling technique. From 39 papers, 24 are included in this category is the larger. Most papers employed just one method. Only five papers combined different methodologies either to compare them, to use as an alternative to an unsuitable first approach to the problem, or to refine and complement first approaches. [START_REF] Willis | Temporal Model for Long Run Orchard Decisions[END_REF] is the first group of researchers to start using ILP to solve problems in operational research models for the fresh fruit distribution. They formulated a temporal model utilizing dynamic linear programming to aid in selecting an optimum mix of varieties of apples for planting over time. The results found that the model treats alternative goals such as minimum acceptable family living expenses and maximum acceptable risk in lexicographic fashion is highly adaptable to other regional situations. However, we were not able to find a new development of ILP within the last five years (2015-2019). It is because most researchers tend to focus on the development of solution techniques rather than mathematical techniques.

Some papers applied dynamic programming to solve the problem in FDM

because it has the flexibility that allows the application to other types of mathematical programming problems. The process of breaking down a complex problem into a series of interrelated subproblems often provides insight into the nature of problems in FDM.

For example, Starbird, S.A (1988) presents a computer simulation model to arrange the stacking of storerooms at an apple pressing plant. The result illustrates the firm's ability to accurately coordinate orders and apple supplies to enhance the firm's ability to compete in this quality and oriented market. [START_REF] Gigler | On optimisation of agri chains by dynamic programming[END_REF] p r e s e n t a methodology for optimisation of agri-chains by dynamic programming (DP). They elaborate on their proposed concept of chain optimization by dynamic programming.

Chain optimisation refers to the construction of optimal routes defining which actors in the chain should perform which actions at which process conditions at minimum integral costs.

Some research papers address some advantages of nonlinear programming (NLP)-based methods for inequality path-constrained optimal control problems in FDM.

For example, [START_REF] Yu | A vendor managed inventory supply chain with deteriorating raw materials and products[END_REF] studied a Vendor Managed Inventory (VMI) type supply chain where the manufacturing vendor decides how to manage the system-wide inventories of its fast deteriorating raw material and its slowly deteriorating product.

They prove the convexity of the cost functions and formulated the NLP model based on

Functional area

The functional area of the operations research models for fresh fruit supply chain usually can be in the fields of planting production (i.e. decisions on production planning and scheduling), Harvesting (i.e. decisions on harvesting means and season), distribution (i.e. decisions on transport) and Inventory (i.e. decision associated with the inventories in different storing), according to the activity of the supply chain they target.

From the list of the operations research models presented in Table5, we can observe that distribution-related decisions are the most common of the models presented with 18 papers. At the same time, production, harvesting, and inventory are less common with 14, 13, and 12 papers, respectively. We found only five papers about an operations research model associated with the decision in planting. Furthermore, we found that 23 of the papers presented a combination of functional area and only 13 papers focused on optimizing a single production stage.

We observed that most operations research model of the past five years is related to distribution and inventory planning, as a result of the dramatic growth in global fruit trade and grocery retail market in recent years. Regarding the coverage of operations research paper in the distribution and inventory planning, there are two remarkable papers : Li P. et al. (2016) and [START_REF] Li | An integrated location-inventory problem in a closed-loop supply chain with third-party logistics[END_REF] The former developed a nonlinear mathematical model that considered not only the vehicle routing problem with time windows but also the effect of road irregularities on the mechanical injuries of fresh fruits and vegetables. The main objective of this work was to obtain the optimal distribution route for fresh fruits and vegetables, considering different road classes with the least amount of logistics costs. An improved genetic algorithm was used to solve the problem. The experimental results showed that the vehicle routing problem with time windows could significantly influence total delivery costs compared with traditional VRP models. Mechanical injury is an important cause of quality loss in fresh fruit.

However, there are quite a few studies that have applied mechanical injury to the operations research model for FDM. The latter studied location-inventory decisions jointly in a closed-loop system with 3PL. They proposed a model formulation to develop mixed-integer non-linear programming (MINLP) models for the locationinventory problem. A novel heuristic based on differential evolution and the genetic algorithm is designed to solve the MINLP models. The numerical study shows that the solution approach is very effective and efficient. This research represents the model of the logistics cost of third-party logistics (3PL) which plays a significant role in today's supply chain management. The result can be used to analyse the competitive advantages in fruit value chain analysis.

Regarding the integrated supply chain planning, many authors have shown the economic advantages of using an integrated decisions model over a decoupled approach. For example, the work by [START_REF] Amorim | Multi-objective integrated production and distribution planning of perishable products[END_REF] on multi-objective integrated production and distribution planning of perishable products shows that the Pareto front of the integrated approach strongly dominates the Pareto front of the decoupled one for perishable products. It reached around 42% of savings for the mean remaining shelf life of products. *Note: Planting (PL), Harvesting(H), Production(P), Distribution(D), and Inventory (I)

Decision level

Managerial decision-making in FDM is commonly divided into different levels of decisions, mainly relating to the time horizon for these decisions. It usually leads to the distinction between long-term (strategic), mid-term (tactical) and short-term (operational). In this hierarchical approach, we can distinguish three distinct planning levels in distribution management:

1. Distribution network design concern long-term decisions on the physical distribution structure. It includes, e.g., the number and sizes of warehouses and crossdocking points, as well as the related transportation links.

2. Distribution network planning concern mid-term distribution planning.

The decisions related to fulfilling demand (or forecasts) on an aggregate level. It includes, e.g., aggregate product flows and delivery frequencies.

3. Transportation planning concern short-term planning of the distribution of actual customer orders. It includes, e.g., the loading and routing of vehicles.

Planning decisions are typically made based on cost or profit evaluations Shapiro, 2007). The characteristics of distribution planning on different hierarchical levels are summarized in Table 6. Not only do the above planning levels relate to different planning decisions and their related planning horizon, but they are also ( i) strongly associated with hierarchical levels in the organization, and (ii) distinctly different in terms of the models that are developed and implemented in planning systems to support these decisions.

(
Obviously, some of these differences have to do with how detailed the time aspect is modelled, if included at all. Also, the time distribution managers spend on analysing the solution differs significantly; strategic and tactical decision-making often include extensive scenario analysis based on the modelling work, while operational decision making needs quick solutions and the possibility to replant on an ad-hoc basis T h e classification of the revised papers according to the decision level, is presented in Table 7. As it is shown, there are eight papers dealing with strategic decisions, 28 related to tactical decisions and also 22 at the operational level. At the same time, 15 papers are devoted to one specific decision level, 12 papers combine decisions at different levels like strategic-tactical or tactical-operational. Most of the strategic decisions in FDM consider the optimal mix of varieties to plant and how to replace them over time. These studies were presented as an analysis of the investment project in fruit production while the most recent research often involves distribution and transportation planning in which they have to make a decision on flows, delivery frequencies, vehicle route.

Among the operational decisions made by the fresh fruit producers, storage and harvesting are particularly crucial given the limited shelf life of fruit [START_REF] Ahumada | Application of planning models in the agrofood supply chain: A review[END_REF]. Since many agricultural activities remain labour intensive, another factor that needs to be considered in the operational planning of perishable crops is the use of labour (Ahumada, O. and Villalobos, J.R., 2011). The work by Ferrer et al. (2007) can be considered a good representative of the papers dealing with operational planning given by harvesting models, which include decisions such as the amount of product to harvest per period, the transportation of the harvested product to the packing site, and the scheduling of packing and processing plants. Other examples of operational models in the literature include those related to production-distribution, such as the work of [START_REF] Rong | An optimization approach for managing fresh food quality throughout the supply chain[END_REF] who present an integrated food quality in decision-making on production and distribution in a food supply chain. They provide a methodology to model food quality degradation in such a way that it can be integrated into a mixedinteger linear programming model used for production and distribution planning. The resulting model was applied in an illustrative case study and can be used to design and operate food distribution systems by using both food quality and cost criteria. From the existing literature consulted we conclude that although the food supply chain is an area that is attracting growing interest, there is a limited number of models addressing operational planning models which combine the shelf life of products.

Optimization models and solution approaches

Regarding the solution approach, fresh fruit is one of the hardest to manage ( Ahumada, O. and Villalobos, J. R. , 2019). The complexity of managing the fruit distribution is compounded by the highly perishable nature of the fruit, which can result in significant product waste and other inefficiencies, such as excess of energy consumption. Furthermore, the fresh produce industry has become very competitive and complex, with increasing variety and requirements for producers, based on consumer and retailer demands. Most decisions in FDM involve the NP-hardness of the problem in which they have several conflicting-objectives that must be optimized simultaneously.

Evolutionary multi-objective optimization is one effective method that has been widely used in recent operations research model for fresh fruit. For instance, [START_REF] Amorim | Multi-objective integrated production and distribution planning of perishable products[END_REF] propose a multi-objective model for integrated production and distribution planning which considers the percentage of remaining quality (%RQ) based on the case of fixed and a loose shelf-life (i.e. with and without a best-before-date).

Non-dominated sorting genetic algorithm-II (NSGA-II) was used to solve the problem in both cases. The results show that the economic benefits derived from using an integrated approach are much dependent on the freshness level of products delivered. [START_REF] Musavi | A multi-objective sustainable hub locationscheduling problem for perishable food supply chain[END_REF] present the model as a multi-objective mixed-integer linear program for optimizing the total transportation costs, freshness and quality of foods at the time of delivery and the total carbon emissions of the vehicles to fulfil the sustainability desire of the environment. An adopted NSGA-II is proposed to solve large instance problems. Numerical experiments are performed on CAB and AP datasets. The testing result represents that the proposed meta-heuristic is able to generate proper Pareto solutions considering all of the objectives for the decision-maker. Tordecilla-Madera, R., and et al. , ( 2018) proposed a multiple objectives model to determine the optimal allocation of vehicles for fruit collection while minimising both total transportation costs and CO2 emissions. The ε-constraint method with the GA algorithm has been used as a solution technique for the proposed mathematical models. The results show the efficiency of the proposed methodology in solving vehicle allocation problems related to collection and distribution.

As mentioned above, the evoluntary algorithm is an optimization approach that plays an important role in solving multi-objective problems in FDM. To gain a better understanding of its operations and related foundations, we review shelf life modelling and application in operation research model for FDM in 2.2, and then we discuss a logistics network configuration for the optimal model in FDM in 2. 3. We describe algorithms applied to solve problems in FDM in 2.4. Finally, we describe the theory of multi-objective optimisation and application in FDM in 2.5.

Shelf life modelling and application in operation research model for FDM

Among the specific issues of FDM problem, perishability, in particular, is very critical for horticultural products, whose shelf life is significantly lower than that of traditional crops, like grains, fruits and other vegetables. Fruit quality can be seen as resulting from the combined action of several quality attributes, each based on its own biological or physical product property. These fruit properties generally change over time, as part of the normal metabolism of the product [START_REF] Hertog | Shelf life modelling for first-expired-first-out warehouse management[END_REF].

A wide range of shelf life mathematical models have found their application in the operation research model, especially in inventory management. A considerable number of different approaches could be considered. Within the framework of developing shelf life models, three approaches of increasing complexity are considered:

1. Statistical process control ( SPC): the distribution conditions are monitored and controlled to stay within limits defined by statistical concepts.

2. Generic shelf life models: the shelf life of fruit is modelled as a function of the conditions in the logistic chain.

3. Specific quality attribute models: it describes a particular quality-related property of a specific fruit (e.g. avocado ripening, and strawberry spoilage) as a function of the measured logistic chain conditions.

The SPC approach forms the foundation for first-order logistics. At the same time, the generic shelf life model and the specific quality attribute model focus on second-order logistics, eventually enabling the development of third-order logistics strategies. Each approach has different applications in research for FDM depending on the operation level and the specific product knowledge. All details are discussed as follows.

Statistical process control

SPC is about monitoring process variables to make sure that the process stays constant within certain well-defined specifications. Applied to FDM, the process refers to controlling the environment and time in the fruit distribution while the variables are the environmental conditions realized. The dimensionality of the control problem is, by definition limited, as the number of variables often limited to the three main factors, temperature, humidity, and holding time.

SPC provides a simple generic approach focusing on the quality of climate control more than on controlling the quality of a specific food product. Therefore, SPC can add value to the supply chain management of perishable food products in situations where specific product knowledge is lacking, but where there is an urgent need to guarantee strict climate control.

The limited application to date to supply chain management might be due to the fact that the supply chain is owned by various players, hampering the data exchange essential to proper SPC. When applying SPC for operation model, batches of fruit products can be differentially handled based on their environmental history incurred to date relative to the targeted environmental conditions and the control limits.

In this approach, fruits having been exposed to more extreme conditions can be considered the first to expire.

Most operation researches model use SPC as a basis for controlling the time of transportation and storage, warehouse location selection, allocated inventory. These researches involve the use of statistical data in the past as a reference for developing models to solve problems in FDM. For example, [START_REF] Li | Vehicle routing problem with soft time windows based on improved genetic algorithm for fruits and vegetables distribution[END_REF] proposed a vehicle routing problem with soft time windows based on improved genetic algorithm for fresh produce distribution. The main objective of the research was to obtain the optimal distribution routes considering different road classes and transportation time with the least amount of logistics costs. [START_REF] Yu | A vendor managed inventory supply chain with deteriorating raw materials and products[END_REF] applied a vendor management inventory system for fruit, which considers the historical data of common replenishment policy and deteriorating rate of product (a fast-deteriorating and a slowdeteriorating product) to manage the inventory. They developed an integrated model to obtain the total inventory and deterioration costs, which is given in a closed form and an exact algorithm to find the optimal solution of the model. However, the application of the SPC in operational research model is an indirect control of the quality of the fruit. It results on the level of quality loss and the on the real cost can not be evaluated. The generic shelf life models and specific quality attribute models will provide better data for quality loss analysis.

The generic shelf life models

Shelf life models are models where the shelf life of a product is modelled as a function of the conditions in the logistic chain taking into account the overall acceptance by the end-users, focusing on the product's suitability for subsequent marketing. Model predictions give an appreciation of the quality of the incurred logistic handling chain by translating the impact of the logistic conditions on product quality in terms of the days of remaining shelf life.

The shelf life models of fruit are complex. It is an assessment of the relationship between the level of fruit quality and consumer acceptance. As described in 1.4.3, the level of fruit quality depends on the type of fruit and environmental condition such as temperature, oxygen (O2), CO2, and %RH which can be represented in the form of a linear function (zero-order kinetics) and non-linear function of holding time (exponential decay). The consumer acceptance in fruit quality depends on consumer lifestyle, eating habits, and culture. The colour, flavour, texture, and the nutritional value of fruit are factors critical to consumer acceptance and the success of these products.

Taking into account the evaluation of quality level in fruit, consumers evaluate the fruit quality by depending on visual assessment, which may differ from the broader general type of perishable food.

The classification of shelf life for fresh products has received attention from various research activities in this subject area. For instance, Nahmias (1982) classified deteriorating products into two types, as indicated by their lifetime and application in inventory models. Firstly, a fixed lifetime can be specified under the storage condition.

Secondly, random lifetime or lose shelf-life means there is no specified lifetime with random variables and probability distribution in various forms. [START_REF] Amorim | Multi-objective integrated production and distribution planning of perishable products[END_REF] described certain differences in consumer behaviour. On account of a fixed lifetime, customers tend to consider the intangible value of products based on the best-before date (BBD) or their perceptions or outer wellsprings of information to evaluate the rest of the shelf life of products. For loose shelf-life, the expiry date of a product cannot be predicted by the consumer because of the absence of implicitly introductory attributes that the fruit should have. In this case, shelf-life needs to be assessed by using models, for example, Davey equation, Arrhenius equation, and Square root equation, which consider the microbial growing rotting sustenance as indicated by various environmental conditions of food distribution.

Considering the operation research model applied the generic shelf life model to solve the problem in FDM, most research is in the field of inventory management. Deterioration based on a linear function of time was first accounted for by Whitin (1953). He considered fashion items deteriorating after a prescribed storage period. Ghare and Schrader first modelled quality loss in terms of non-linear function in inventory control. Almost 50 years later, many variations exist that differ in assumptions on not only the lifetime of an item but also on the type of demand. The presence of price discounts allowed shortages and back-ordering, single or multiple items, one or two warehouses, single or multi-echelon modelling, average cost or discounted cash flows, and whether a delay in payment is permissible.

The quality loss assessment of operations research in FSCM was presented for the first time by [START_REF] Ferguson | Note: An application of the EOQ model with nonlinear holding cost to inventory management of perishables[END_REF]. They proposed a way to estimate nonlinear holding cost causing yeast and mould growth in blueberry as a case study. They applied the cost to an economic order quantity (EOQ) model for the inventory management of perishables. After that, Caixeta-Filho, J.V. ( 2006) presented an LP model to operate orange orchards to maximise the total profit. A fractional decision variable was used to represent the quantity of harvested orange groves in each period. He applied total soluble solids (TSS), as quality index measures to determine the suitability for fresh consumption or the juice industry. [START_REF] Arnaout | Optimisation of quality and operational costs through improved scheduling of harvest operations[END_REF] presented two heuristics that were applied and compared to solve the vineyard harvesting problem. The objective was the optimisation of the quality of grapes using sugar and acidity as the quality index to minimise operational costs. [START_REF] Bohle | A robust optimization approach to wine grape harvesting scheduling[END_REF] The evidence that consumers of perishable goods search for visual and other cues of freshness, such as the printed expiry dates. These expiry dates are also known as BBD which are defined as the end of the period, under any stated storage conditions, during which the product will remain fully marketable and retain any specific qualities for which tacit or express claims have been made [START_REF] Busetti | A theory-based evaluation of food waste policy: Evidence from Italy[END_REF]. This cues of freshness have triggered the development of the shelf life model applied in many operation research model for the perishable product (Amorim, P. , and et al. , 2011).

However, using the relative cues of freshness to estimate the remaining quality cannot be used to assess the actual cost of quality loss because the fruit has a variety of quality loss forms, both linear and non-linear function with time.

In addition, the spoilage of fruits results in changes in profits from fruit sales.

Customers are usually sensitive to quality changes of the expiring products and, as a result, give them a lower valuation. Price discount is often used in practice when perishable products approach their expiration date. All major supermarkets employ price markdown policies, although they may differ across perishable foods and vary over time for each product. We start with a simple policy in which the retailer offers a lower price in a mark-down period to attract customers to purchase products approaching their expiration date [START_REF] Wang | A dynamic product quality evaluation based pricing model for perishable food supply chains[END_REF].As a result, two different prices are set in the selling period:

p t p 0 t T ; p * 1 θ T t T; [6]
Tm is the price markdown time (Tm) after which a price discount θ (0<θ<1)

is deployed for a given product. As a price markdown is always applied before a product reaches its expiration date, the selling period can be divided into two intervals: (0, Tm) and (Tm, T).

Regarding the application of the generic shelf-life model, Tm associated with kinetics parameter of product stability or lag time before fruit quality deterioration can be observed by the consumer, as shown in Figure7. After a lag time, an ageing fresh fruit may require markdowns in their prices or removal of the spoiled product until the end of shelf life or marketable period.

Lag time Quality loss appearance

End of shelf life

Marketable period

Understanding quality loss mechanism and consumer evaluation in marketable period can be applied to develop the operating model to solve the problem in FDM.

The application of the shelf life model in recent research mainly involves problem-solving for the multi-objective function to be optimized simultaneously, which they have to be optimized simultaneously. For instance, [START_REF] Amorim | Multi-objective integrated production and distribution planning of perishable products[END_REF] proposed multi-objective model to optimize to maximize the remaining shelf life of the perishable product and to minimize the total system cost. Ahumada, O. and Villalobos, J. R. ( 2011) develop a quality model based on production/ harvesting planning.

Maximizing the system profit and minimizing total system cost are optimized under the quality requirement of the products/ shelf life. [START_REF] Musavi | A multi-objective sustainable hub locationscheduling problem for perishable food supply chain[END_REF] considered the product quality function with time-based on the ratio of product quality and applied it to solve a multi-objective sustainable hub location-scheduling problem for perishable food supply chain

The relationship between loss of fruit quality and holding period can be modelled to assess the costs of quality loss that change according to the holding time. model. They proposed how the holding cost curve parameters can be estimated via a regression approach from the product usual holding cost (storage plus capital costs), lifetime, and markdown policy. The model can be used to estimate the cumulative holding cost for one unit that has been stored during t units of time in both case of a linear and non-linear function of holding time, as in:

[ 7]
where and  are constants; if  = 1 : linear function and  > 1 : non-linear function with being the cost to hold one unit for one time period.

However, the price of fruit changes day by day, depending on the supply and demand in each day. The cumulative holding cost of fruit should be determined by

 t h t H ) (  h h ~
considering the material price of fruit each day (PMi) to assess the cost of fruit quality loss that is consistent with the changes in raw material prices in each day. This will be described in 3. Understanding the characteristics of quality loss and assessment is an essential factor in the model development to solve the problem in FDM.

Specific quality attribute models

Specific quality attribute models describe the advancement of a particular quality attribute for a particular product as a function of the supply chain handling conditions which quality attributes are of interest depends on the product under study.

At the same time, the generic shelf life models do not intend to model the product's physiology. Still, only the time for which a perishable product will remain acceptable to a consumer, the specific quality attribute models do pretend to describe the processes going on inside the perishable product that bring about the observed change in quality.

By definition, such a model will be founded on an improvement of the food product and, therefore, will never be 'true' as the only true model is the product itself.

The objective of modelling food quality attributes is, in any case, not to develop true models but to develop valid models; that is, models that are reliable with the present knowledge level and that contain no known or detectable flaws of logic [START_REF] Hertog | Shelf life modelling for first-expired-first-out warehouse management[END_REF] Additionally, models ought to be detailed enough for the intended purpose and yet rearranged adequate to give robust manageable models. The fundamental strategy to build up an appropriate model is to apply a systematic process of problem decomposition, dissecting the problem into its basic building blocks and afterwards reassembling them, leaving out the unnecessary detail. What is essential and what is redundant depends mainly on the intended application of the model. At last, the models are to be utilized to give an appreciation of the quality of the logistic handling chain and to make an interpretation of this into the effect the logistic conditions have on product quality attributes.

Given the dynamic conditions influencing fruit quality traits, the models ought to be founded on differential equations that can manage dynamic data sources.

Kinetic models [START_REF] Van Boekel | Kinetic modeling of reactions in foods[END_REF] are most suitable to generically describe sophisticated quality attributes, such as fruit mealies [START_REF] De Smedt | A mathematical model for the development of mealiness in apples[END_REF], starting from the underlying (bio) chemical, physiological and physics mechanisms. Specific quality attribute models can give more detail to evaluate the cost of quality loss corresponding to the form of fruit quality deterioration ( zero order and exponential decay) , and consumer behavior than SPC and generic shelf life model. However, the application of specific quality attribute models for the operation research model of the FDM is still quite limited because it lack insights into the loss of quality in fruit. In past five years, we found only [START_REF] Aiello | A multi objective approach to short food supply chain management[END_REF] research that they presented the specific quality attribute models, which can be applied to operation production and distribution planning. The resulting model can be used to design and operate food distribution systems, using both food quality and cost criteria.

A logistics network configuration for the optimized model in FDM

Fruit distribution network design and planning is a complex process, mainly because of uncertainty in supply and demand, quality loss during distribution, and traceability system requirements. These factors that contribute to most of the problems in the fruit distribution are NP-hardness and have a high risk of local optimisation with large size problems in the real-world fruit trade. They have also included simplicity and flexibility to capture a large variety of decisions . Finally, because of increasing consumer concerns for food safety and dependence on climate conditions (Yared Lemma, D.K. and Gatew, G., 2014), the fruit modelling and optimisation approach must balance traceability with the ability to capture the essential elements of the fruit distribution realistically .They need to address environmental transport and storage conditions, the quantity of quality loss and volume and hold time in each node . In practice, the measurement unit of these factors is enormous, with many nodes and a long period. Thus, the problem with non-linear programming is that it tends to turn out to be an NP-hard problem and lead to local optimisation [START_REF] Ji | Logistics network configuration for fresh agricultural products[END_REF].

Algorithms applied to solve the problem in FDM

In this section, algorithms applied to operations research model in FDM are discussed in more detail. More specifically, we discuss the basics of the algorithm in 2. 4. 1, followed by the role of the algorithm in FDM in 2. 4. 2. Lastly, we focus on discussing GA's work processes and apply it to optimize the multi-objective problem in FDM.

Algorithms

The concept of an algorithm is basic to software engineering. Algorithms exist for some fundamental issues and designing efficient algorithms plays a crucial role in developing large-scale computer systems. Therefore, before we continue further, we have to examine this idea all the more completely. An algorithm is defined as a finite set of instructions that, if followed, accomplish a particular task. Besides, all algorithms must fulfil the accompanying criteria: (1) Input: there are at least zero amounts that are externally supplied. (2) Output: at least one quantity is created, (3) Definitions: each instruction is clear and unambiguous, (4) Finiteness: In the event that we follow the instructions of an algorithm, then for all cases, the algorithm terminates after a limited number of steps. (5) Effectiveness, every instruction must be sufficiently fundamental to be completed, in principle, by a person using only a pencil and paper. It is not enough that each operation is definite as in (3); it also must be feasible. Algorithms exist for some regular problems, and designing efficient algorithms plays a crucial role in developing large-scale computer systems. An optimisation tool can be partitioned into two sorts: traditional optimisation tools and non-traditional optimisation tools.

At the point when we state traditional optimisation methods, we are referring to three main types: calculus-based, exhaustive search, and random. Calculus-based optimisation methods come in two categories: direct and indirect. The direct method hops onto the objective function and follows the direction of the gradient towards a local maximum or minimum value [START_REF] Goldberg | Genetic algorithms and machine learning[END_REF]. It is otherwise called the hill-climbing or gradient ascent method. The indirect method takes the inclination of the objective function; sets its equivalent to zero, then solves the set of equations that result. Even though these calculus-based techniques have been considered broadly and improved, they still have insurmountable problems. First, they look for local optima, which renders them useless if we do not know the neighbourhood of the global optimum or if there are other local optima nearby (and we usually do not know). Second, these methods require the presence of derivatives, and this is virtually never the case in practical applications.

Exhaustive search algorithms require a finite search space or a discretised infinite search space" of possible values for the objective function. Then they test each value, one at a time, to find the maximum or minimum. While this technique is essential and subsequently alluring, it is the least efficient of all optimisation algorithms. In practical issues, the search spaces are too huge to test every possibility one at a time and still get an opportunity of utilising the resulting information to some practical end [START_REF] Goldberg | Genetic algorithms and machine learning[END_REF].

Random search algorithms turned out to be progressively prevalent as people realised the shortcomings of calculus-based and exhaustive search algorithms. This style of algorithm randomly picks some representative sampling from the search space and finds the optimal value in that sampling. While faster than an exhaustive search, this approach can be expected to do no better than an exhaustive search. Utilising Differential Evolution is another modified version of GA, which was proposed by [START_REF] Storn | Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces[END_REF] It is a population-based self-organising metaheuristic. The weighted difference between two population vectors (solutions) is added to the third one to update the population of solutions. Simulated Annealing, annealing is a process of slow cooling. Metal will be in its high-energy level during its molten state, and its energy content decreases, as it gets solidified. In simulated annealing, the cooling process of molten metal has been modelled mathematically, to minimise its energy level, in order to use it as a tool for minimisation. The algorithm starts by assuming a high initial temperature of molten metal and a randomly chosen initial solution. The temperature is decreased iteratively, and at each iteration, an appropriate neighborhood solution is obtained. This algorithm uses the concept of Boltzmann probability distribution. Iterations proceed until a predefined termination criterion is reached.

Tabu Search is similar to simulated annealing. Simulated annealing generates only one updated solution, whereas Tabu Search deals with many solutions at a time. Here, a Tabu list of partial and complete solutions is maintained.

Ant Colony Optimization is a probabilistic technique used to model the behaviour of ants searching an optimal path (in terms of travelled distance) between their colony and a source of food. It was proposed by Dorigo in 1992. It carries out metaheuristic optimisation to determine the optimal path through graphs.

The role of algorithms in FDM

Fruit distribution network design and planning is a complex process mainly because of uncertainty in supply and demand, quality loss during distribution, and traceability system requirement. These factors contribute to most of the problems in the fruit distribution, which are NP-hardness and the high risk of local optimisation with large size problems in the real-world fruit trade. Also, they have simplicity and flexibility to capture a large variety of decision. The optimisation problem in FDM involves a nonlinear function of either one or more than one independent variable. Most problems are NP-hardness, and they have the high risk of local optimisation with large size, simplicity and flexibility to capture a large variety of decision (Valadi, J. and Siarry, P., 2014). Meta-heuristics such as evolutionary algorithms have been widely used to solve such problems, as shown the detail in Table 8. We found that most evolutionary algorithms applied in the fruit optimisation model are genetics algorithm (GA), while branch and bound (BB), simulation annealing (SA), and ant colony (AC) can be found in some paper.

Genetic Algorithms

GA is a search heuristic that is inspired by Charles Darwin' s theory of natural evolution. It is one branch of the field of study called evolutionary computation and represents a type of optimisation algorithm. Meaning GA is used to find the optimal solution( s) to a given computational issue that maximises or minimises a particular function in that they mimic the biological processes of multiplication and natural selection to solve for the fitness solutions [START_REF] Goldberg | Genetic algorithms and machine learning[END_REF]. These algorithms are more dominant and effective than random search and exhaustive search algorithms because they allow the identification of solutions to problems that other optimisation methods cannot handle due to a lack of progression, derivatives, linearity, or different highlights. [START_REF] Kinnear | A perspective on the work in this book[END_REF] since the genetic algorithm is based on the theory of evolution, it has the following specific terminology.

1) Population: it is a subset of all the possible (encoded) solutions to the given problem. The population for a GA is practically equivalent to the population for human beings except that instead of human beings, we have candidate solutions representing human beings.

2) Chromosomes: a chromosome is one such solution to the given problem.

3) Gene: a gene is one element position of a chromosome.

4) Allele: it is the value a gene takes for a particular chromosome.

5) Genotype: genotype is the population in the computation space. In the computation space, the solutions are represented in a way that can be easily understood and manipulated using a computing system. 6) Phenotype: phenotype is the set of the population in the actual real-world solution space in which solutions are represented in a way that they are represented in real-world situations.

7) Decoding and Encoding: for simple problems, the phenotype and genotype spaces are the same. However, in most cases, the phenotype and genotype spaces are different. Decoding is a process of transforming a solution from the genotype to the phenotype space, while encoding is a process of transforming from the phenotype to genotype space. Decoding should be fast as it is carried out repeatedly in a GA during the fitness value calculation.

The basic structure of a GA has six phases that are considered in an algorithm: 1) chromosome encoding, 2) initial population, 3) fitness function, 3) parent selection, 4) crossover and mutation, 5) survivor selection and 6) termination condition, as shown in Figure 9.

Multi-objective optimisation

Most real problems in FDM have multiple objectives that need to be satisfied. Usually, these objectives conflict with each other, i.e. one must accept decreases in one objective to achieve increases in another objective which involves many decision variables and constraints. The process of optimising systematically and simultaneously, or a collection of objective functions, is called multi-objective optimisation (MOO). In this part, we discuss the multi-objective optimisation analysis and different types of analysis methods in 2.5.1. More specifically, we describe the generating methods and preference-based methods in 2.5.2 and 2.5.3 respectively, followed by a summary of multi-objective analysis for fresh FSCM in 2.5.4. Finally, we present the NSGA-II.

Multi-objective optimisation is an area of multiple criteria decision making that is concerned with mathematical optimisation problems involving at least two objective functions to be optimised all the while. The objective functions may be conflicting with one another. Additional objective functions are usually handled as constraints in order to simplify the solution process. In terms of mathematics, a multiobjective optimisation problem can be formulated as

[8]
Where the integer (k>=2) is the number of objectives, and the set is the feasible set of decision vectors. Some constraint functions regularly characterise the feasible set. Besides, the vector-valued objective function is often defined as

[9]
If some objective function is to be maximised, it is equivalent to minimise its negative. The image of  is denoted by R k . An element x*X is called a feasible solution or a feasible decision. A vector z*:=f(x*)R k for a feasible solution. x* is an objective vector or an outcome. In multi-objective optimisation, there does not typically exist a feasible solution that minimises all objective functions simultaneously.

Therefore, Pareto optimal solutions pay attention to solutions that cannot be improved in any of the objectives without corrupting at least one of the other objectives. In mathematical terms, a feasible solution x 1 X is said to ( Pareto) dominate another

solution x 2  X, if   ) ( ),...., ( ), ( min 2 1 x f x f x f k  X t s    . . X T k k x f x f x f R X f )) ( ),..., ( ( ) ( , 1   
1.

[10]

2.

[11]

In other words, there is Pareto improvement which is a movement from one feasible solution to another that can make anyone objective function return to better In theory, there exist many methods to solve a multi-objective problem, and a considerable lot of them include changing over the MOO problem into one or a series of single-objective optimisation (SOO) problems, as shown in Figure 10. Each of these problems includes the optimisation of a scalarising function, which is a function of original objectives, by an appropriate method for SOO (Rangaiah, G.P., 2009). A set of non-dominated solutions or Pareto front, being chosen as optimal, if no objective can be enhanced without sacrificing at least one other objective. In contrast, a solution x* is referred to as dominated by another solution x if, and only if, x is correspondingly good or better than x* concerning all objectives. (Reddy, M.J. and Kumar, D.N., 2015.)

There are many ways of defining a scalarising function, and therefore many MOO methods exist. Although the scalarisation approach is conceptually simple, the resulting SOO problems may not be easy to solve. Available methods for MOO can be characterised into two principle gatherings generating methods and preference-based methods, based on whether many Pareto-optimal solutions are generated or not, and the role of the decision-maker (DM) in solving the MOO problem, as shown in Figure 10. Miettinen ( 1999) and Diwekar ( 2003) , as the names suggest, the previous methods generate one or more Pareto-optimal solutions without any inputs from the DM. The solutions obtained are then given to the DM to choose. On the other hand, preference-

  k i indices all for x f x f i i ,...., 2 , 1 ) ( ) ( 2 1     k j indices all for x f x f j j ,...., 2 , 1 ) ( ) (

The generating methods

The generating methods are further divided into three sub-groups, namely, no-preference methods, a posteriori method using the scalarisation approach, and a posteriori method using the multi-objective approach.

No-preference methods

N o -preference methods are used when a decision-maker does not explicitly articulate any preference information. The multi-objective optimisation method can be classified as the no-preference method (Ching-Lai, H., and Abu Syed, M.M., 1979). As the name shows, no-preference methods do not require the relative priority of objectives whatsoever. Although a specific method gives just one Pareto-optimal solution, a few Pareto optimal solutions can be obtained by utilising different no-preference methods ( and so different metrics). Methods in this sub-group include the method of global criterion and multi-objective proximal bundle method in which a scalarised problem of the form eq.8 is solved.

Multi-Objective Optimization Methods

Preference-Based Methods Generating Methods

A Posteriori Methods

[12]

In the above problem, can be any Lp norm, with typical choices including L1L2, and L  [START_REF] Miettinen | Nonlinear multi-objective optimization[END_REF]. The method of the global criterion is sensitive to the scaling of the objective functions, and thus, it is prescribed that the objectives are normalised into a uniform, dimensionless scale.

Posteriori methods using the scalarisation approach

The methods (also known as multi-objective programming) aim at producing all the Pareto optimal solutions or an agent subset of the Pareto optimal solutions where an algorithm is rehashed, and each run of the algorithm produces one Pareto optimal solution. The methods convert a MOO problem into an SOO problem, which can then be solved by an appropriate technique to discover one Pareto-optimal solution. In addition, it is regularly necessitated that each Pareto optimal solution can be reached with some parameters of the scalarisation (Ching-Lai, H., and Abu Syed, M.M., 1979).

With various parameters for the scalarisation, different Pareto optimal solutions are produced. A general formulation for a scalarisation of multiobjective optimisation is thus

ideal z x f  ) ( min X x t s   . .

 [13]

W h e r e :  is a vector parameter, the set X   X is a set depending on the parameter  and g: R k+1  R is a function.

Very well-known examples are the so-called a) weighting methods or linear scalarisation [14] Where: the weights of the objectives (wi >0) are the parameters of the scalarisation.

b) -constraint method [15] Where upper bounds j are parameters as above, and fj is the objective to be minimised. However, the multi-objective programming method fails to find Pareto optimal solutions in the non-convex region, although modified weighting methods can do so. It is hard to choose appropriate estimations of weights and . The solution of the resulting SOO problem may be ambiguous or non-existent. (Kaisa M.,1999).

A posteriori methods using the multi-objective approach

A posteriori methods using the multi-objective approach, also known as evolutionary algorithms rank trial solutions based on objective values (fitness value) and lastly find many Pareto-optimal solutions. These methods are popular approaches to ) ), ( ),...., ( ( min

1  x f x f g k X x t s  . .    k i i i x f w X x 1 ), ( min ) ( min x f i X x t s  . .    , \ ,...., 2 , 1 ) ( j k i for x f j i   
generating Pareto optimal solutions to a multi-objective optimisation problem. 12. Benson's algorithm designed for multiple objective linear programs and multiple objective convex programs 13. Multi-objective particle swarm optimisation

Subpopulation Algorithm based on Novelty

The main benefit of evolutionary algorithms, when applied to solve multiobjective optimisation problems, is the fact that they usually produce sets of solutions, allowing computation of an approximation of the entire Pareto front. The main weakness of evolutionary algorithms is their lower speed, and the Pareto optimality of the solutions cannot be guaranteed. It is just realised that none of the produced solutions dominates others.

Preference-based methods

Preference-based methods have been divided into two sub-groups: a priori methods and interactive methods.

A priori methods

It requires that adequate preference information is stated before the solution process. They will afford one Pareto-optimal solution consistent with the given preferences, and so maybe considered as efficient. Well-known examples of a priori methods consist of the utility function method, lexicographic method, and goal programming.

a) The utility function technique

It is assumed that the decision maker's utility function is available. A mapping u: YR is a utility function if for all y 1 , y 2  Y if it holds that u(y 1 )>u(y 2 ) if the decision-maker prefers y 1 to y 2 , and u( y 1 )=u( y 2 ) if the decision-maker is indifferent between y 1 and y 2 . The utility function requires ordering of the decision vectors (recall that vectors can be ordered in many different ways). Once u is obtained, it suffices to solve [START_REF] Van Boekel | Kinetic modeling of reactions in foods[END_REF] However, in practice, it is complicated to construct a utility function that would accurately represent the decision maker's preferences, mainly since the Pareto front is unknown before the optimisation begins.

b) The lexicographic technique

The lexicographic technique assumes that the objectives can be ranked in order of importance. We can adopt, without loss of generality, that the objective functions are in order of importance so that f1 is the most important and fk the least important to the decision-maker. The lexicographic technique consists of solving a sequence of single-objective optimisation problems of the form:

[17]
Where y * j is the optimal value of the above problem with l= j, thus, and each new problem of the form in the above problem in the sequence adds one new constraint as l goes from 1 to k. Note that a target value is not indicated for any objective here, which makes it different from the Lexicographic Goal Programming method.

Interactive methods

The solution process is iterative, and the decision-maker continuously interacts with the method when searching for the most preferred solution. In other words, the decision-maker is expected to express preferences at each iteration in order to get Pareto optimal solutions that are of attention to the decision-maker and learn what kind of solutions are attainable. Examples of these methods are intuitive surrogate worth exchange method and the NIMBUS method, which have been applied to several chemical engineering applications. The following steps usually exist in interactive methods of optimisation:

1) Initialise (e.g., calculate ideal and approximated objective vectors and show them to the decision-maker)

) ( min 1 x f , 1 ,..., 1 , ) ( . . *    i j y x f t s j j X x    X x x f y   ) ( min :
2) Enerate a Pareto optimal initial point (by using, e.g., some no-preference method or solution given by the decision-maker)

3) Ask for preference information from the decision-maker (e.g., aspiration levels or number of new solutions to be generated) 4) Generate new Pareto optimal solution along with the preferences and show it/them and possibly some other information about the problem to the decisionmaker 5) If several solutions were generated, ask the decision-maker to select the best solution so far 6) Stop (if the decision-maker wants to; otherwise, go to step 3).

The above aspiration levels imply required objective function values forming a reference point. Instead of mathematical convergence that is frequently used as a stopping criterion in mathematical optimisation methods, a psychological convergence is regularly stressed in interactive methods. Generally speaking, a method is terminated when the decision-maker is confident that he/ she has found the most preferred solution available.

Multi-objective analysis for FDM

Multi-objective analysis has been used for modelling fresh fruit supply chain management. The approaches have been used as research tools or teaching aids by advisory and extension services to improve decisions in agricultural resource management. The decisions in fresh fruit distribution have increased in complexity because of the increasing demand of customers concerned with requirements of quality, safety, and sustainability. Therefore, the multi-objective analysis will be an essential approach to fresh produce supply chain and management planning and policy modelling.

Regarding the characteristics of quality and safety for fresh fruit supply chain management, fresh produce generally has a short lifecycle. The value or quality of fresh produce rapidly decreases once harvested, and will continue to decay while being delivered. The high perishability of fresh produce results in immense food loss, further stressing PFSCMs and the associated quality, safety, profitability, and food sustainability (Yared Lemma, D. K. and Gatew, G. , 2014). It also generates more complications for the suppliers to manage the inventory due to the substitution.

The suppliers have to keep the inventory level at a balanced point to meet the highly fluctuating demand due to substitution and avoid the wastage of perishable products [START_REF] Duong | A multi-criteria inventory management system for ESCIP Consortium[END_REF]. When considering rapidly deteriorating fresh produce, we have to take into account the perishability phenomenon even at the operational level of production, distribution, inventory planning, which has a period ranging from 1 week to 1 month. The life of fresh fruit and vegetable depends on time.

Thus, timely delivery and holding perishable food not only significantly affects the delivery operator's cost, but also the satisfaction of customers. Furthermore, with fresh e-commerce developing rapidly in recent years such as Alibaba, JD, Amazon, Local harvest, and so on, the characteristics of the order tend to be smaller lot-size and higher frequency, which increase the complexity of the distribution (Wang, X., and et al., 2016).

Aside from transportation costs and responsiveness in optimising a logistic system, sustainable characteristics of the network are also considerable. In the classification of drivers of sustainable supply chain management, environment conservation is one of the noteworthy points of sustainability, which consists of controlling worldwide carbon emission.

Most authors have proposed multi-objective analyses on perishable food products by considering the factors that indirectly affect the loss of fruit quality, most of which relate to the relationship of the holding time (distribution time and storage time) and economic point view. For instance, [START_REF] Khalili-Damghani | A new bi-objective location-routing problem for distribution of perishable products: Evolutionary computation approach[END_REF] developed a new bi-objective mixed integer mathematical programming that proposed to reduce the total cost of the supply chain and to balance the workload of distribution centres while the due dates of delivery of the perishable product were met to keep quality of the product. [START_REF] Esmaeili | A multi-objective Two-Echelon Capacitated Vehicle Routing Problem for perishable products[END_REF] proposed a general tri-objective twoechelon capacitated vehicle routing problem (2E-CVRP) to minimise the total transportation cost, customer waiting for times and carbon dioxide emissions simultaneously in distributing perishable products by using NSGA-II algorithm to solve the presented mathematical model.

The multi-objective approach, considering the direct loss of quality, has increased in the present because the test results reflect the fact that it is more beneficial to make decisions in the problem. An example of this research is Wang, X.P. [START_REF] Aiello | A multi objective approach to short food supply chain management[END_REF] represented a multi-objective approach for optimal inventory management, with the purpose to preserve the shelf-life of the products in a serial two-echelon system to ensure supply chain efficiency.

Summaries of the multi-objective optimisation analyses in all the revised papers dealing with the application in the perishable product in the field of economical, quality, and safety, and sustainability are represented in Table 9. We found that most multi-objective optimisation research focused on studies in the field of economics, which is closely associated with product quality and safety in the fresh produce supply chain. For example, [START_REF] Gong | ABC-ACO for perishable food vehicle routing problem with time windows[END_REF] developed a multi-objective model for vehicle routing problems with a time window in order to reduce the increased distribution cost via meeting the time window. [START_REF] Rabbani | Vehicle routing with time windows and customer selection for perishable goods[END_REF] introduce a vehicle routing problem model with multiple middle depots and recommend the freshness of perishable foods to maximise the profit of delivering the product and level of delivered product perishability.

Most of the research poses an enormous problem or NP-hard problem, which offers a comparison of multi-objective analysis between a posteriori methods using a scalarisation approach and a posteriori methods using a multi-objective approach to balance two conflicting objectives. Many research papers indicate that NSGAII is more effective for multi-objective analysis compared to other techniques. These are because the main advantage of evolutionary algorithms, when applied to solve multi-objective optimisation problems, is the fact that they characteristically generate sets of solutions, allowing for computation of an approximation of the entire Pareto front, which can solve real-life problems in the perishable product supply chain.

Non-dominated sorting genetic algorithm (NSGA-II)

The NSGA-II, Non-dominated sorting genetic algorithm is an improved version of the algorithm NSGA proposed by Srinivas and Deb [START_REF] Deb | A fast and elitist multiobjective genetic algorithm: NSGA-II[END_REF].

It is a scheme for solving multi-objective optimisation problems using the concept of non-dominance introduced by Goldberg [START_REF] Goldberg | Genetic algorithms in search[END_REF] and a genetic algorithm to produce new solutions. N S G A -II is one of the most popular multi-objective optimisation algorithms with three unique characteristics: a fast non-dominated sorting approach, fast crowded distance estimation procedure and simple crowded comparison operator. [START_REF] Deb | A fast and elitist multiobjective genetic algorithm: NSGA-II[END_REF] simulated several test problems from the previous study using the NSGA-II optimisation technique and found that this is asserted system outflanked PAES and SPEA in terms of finding a diverse set of solutions.

The schematics of this algorithm is shown in Figure 11. 10.

The fast non-dominated sorting procedure separates the population into different fronts according to their level of dominance suggested the following algorithm:

Dominated sorting

Crowding distance

Table 10: The pseudocode for the non-dominated sorting.

The non-dominated sorting pseudocode

Rt = Pt  Qt F = fast-non-dominated -sort(Rt) While l Pt l < N do
Crowdingdistanceassignment (Fi)

Pt + 1 = Pt + 1  Fi end while Qt + 1 = make -new -pop(pt + 1) t = t+1
First, for each solution, two entities are calculated, which is the number of solutions that dominate the solution i, and ii) Si which is the set of solutions that i dominates. It identifies all the points that have ni = 0 and puts them on the list F1. It is named to the list F1 current front. For each solution (i) of the current front visit, each member ( j) for a whole ( Si) and is reduced by one, or the number of individuals dominating nj. By doing this, if some member of j the counter becomes zero (nj = 0), is put on a new list H. When all members of the current front have been revised, declare the members of the front F1 as the first front and the front H becomes our current front.

This algorithm maintains the diversity of the population in each nondominated frontier by using a density estimator for each individual (Crowding Distance), which is the average separation between two contiguous individuals. Individuals who are at the ends are assigned infinite distance. The pseudocode for this procedure is shown in Table 11.

Table 11: Pseudocode for the crowding distance procedure.

The crowding distance pseudocode

l = l F l for all i  F do di = 0 for all objective m do l = Sort(l,m) d m 1= d m 1=
for j2,(l-1) do

d m j= d m j+F m j + 1-F m j + 1
end for end for end for

Application of operation models in FDM

As mention above, quality loss control is a way to achieve a competitive advantage in VCA for FDM under three specific-challenge of fruit quality safety, and sustainability. Enormous value can be added by optimizing FDM, taking into account the estimated remaining shelf life of the fruit, and matching it to the profits earned from exporting fruits. This contribution focuses on how model approaches estimating quality changes and remaining shelf life can be combined in optimizing FDM strategies for fresh fruit. The quantification of the amount of quality loss and its cost in the FDM is complicated. The quality loss assessment needs to use reliable data and methods, which involve the quality loss appearance in each type of fruit and consumer acceptance of fruit quality through visual assessment. Furthermore, FDM is described by significant distance transportation combined with significant the uncertainty of supply, demand, and fruit price, including sustainability. These difficulties produce a requirement for the use of modern decision technology.

Many operation models focusing on quality losses assessment in FDM have been widely used to optimise and to support the decision-making process in FDM. Most operation research models involve solving complex problems through a multi-objective framework, where optimal decisions should be taken within sight of trade-offs of at least two or more conflicting objectives. They also must balance traceability with the ability to capture the essential elements of fruit distributions realistically.

Multi-objective optimisation methods based on both a posteriori method by using a scalarisation approach ( Non-Pareto technique) and multi-objective approach MI is a major cause of quality losses in fruit distribution. It may be a great impact on the level of fruit damage at about 5%-60% of total trade volume, especially in global fruit exportation. (Li, Z., and Thomas, C., 2014). We found that most operation research models involve solving short-distance transportation problems, of which the MI due to transportation is not the main factor to consider. The MI evaluation can help exporter to analyse actual total cost in long-distance transport of fruit exportation. The cost is also helpful in choosing the optimal transportation route, including the development of a packaging system for transportation.

(
Regarding the sustainability indicators in FDM model, most of the research papers focused more on the study of environmental impacts in the form of greenhouse gas emission (GHG) than on social impacts since the environment can be quantified easily. While the assessment of GHG emission in operation research model usually specifies the scope of activities that need to be studied. They do not consider comprehensive in all the activities of distribution management.

To meet these limits in operation research modelling, we designed a multi- Order Quantity (EOQ) models [START_REF] Ferguson | Note: An application of the EOQ model with nonlinear holding cost to inventory management of perishables[END_REF].

We proposed the different scenario of fruit exportation based on the data history of fruit supply, demand, and selling price. While the balance of supply and demand in the form of excess supply function will be applied to determine the price of fruit material. Solution spaces of models are analysed through the different scenario of fruit exportation with restrictions in terms of two cases of ND: DIP-ZO and DIP-ED, variability in raw material prices, selling prices, supply and demand, including CO2-e emission factors produced for each activity in the fruit distribution.

A fast and elitist multi-objective genetic algorithm: NSGA-II is developed to solve the problems with various constraints and variables. The results of NSGA-II in both cases of ND with ZO and ED will be compared with results of posterior methods using adjusted weight-sum approach with a genetic algorithm (AWS-GA) (Liu and Reynolds, 2014) to evaluate the performance of the algorithm. Finally, we analyse the cost advantage of value chain analysis through the relationship between NP and %RQ on the optimal Pareto front in both cases of ND. The obtained results can be extended to study the optimal decision variable, transportation time, storage time, and total CO2 emission, which they also prove significant for making decisions in FDM.

The experimental result expected that the NSGA-II algorithm would be able to capture the non-convexities in both cases of optimal Pareto fronts of DIP-ZO and DIP-ED. It can provide the optimal Pareto front that leads to effective multi-objective function solutions for FDM. Finally, the optimal Pareto front of NSGA-II will provide important information for making decisions concerning fruit export planning, choosing the most appropriate distribution scheme, setting inventory management, and environmental policy under the variability associated with fruit demand, supply rate, and price.

5) Analysis step and statement: we describe the statistical analysis in 3.8. The results of such states will be analysed along with the value chain of fresh fruit exportation to discuss the way to increase the value chain and to improve logistic efficiency in section 3.9.

The following figure provides a clear view of this methodology. We verify the DIP model by comparing NSGA-II result of DIP-ZO in three scenarios (SC1, SC2, and SC3). We evaluate the performance of the algorithm by comparing the NSGA-II results and ASW-GA result in both cases of quality loss with ZO and ED. We use the optimal Pareto front of NSGA-II in both cases of quality loss to analyse the cost and different advantages in value chain analysis through the relationship between %RQ and NP. These results can be extended to study the optimal decision variable, transportation time, storage time, and the effects of total CO2 emissions, which prove significant for making decisions in fruit supply chain management. Finally, we propose guidelines to reduce the logistics costs, and increase the value chain to help ensure the profitability and sustainable development of the exporter and stakeholders in the fruit exportation supply chain.

3.7

Value chain analysis (3.9)

The logistics costs

In FDM, the logistic cost consists of two main parts: common logistics cost and the cost of quality loss due to MI and ND.

For our use case, we establish some assumptions, indices, parameters and decision variables that apply to the multi-objective model, as described in Table 12 by the following. Assumptions 1. The company has a policy for a total holding time of fruit transportation and storage, which is not more than ten days after the export of fruit in order to guarantee a final product with sufficient residual life.

2. Shortage or reverse logistics is not allowed.

3. First -In-First-Out (FIFO) issuing policy is used.

4. Container (ctn) is used as a unit of the quantity of fruit exported and sold each day. quantity of fruit exported from packaging house on day i , with route j, with storage planning for k days s ij quantity of fruit transported by route j and sold immediately at DC on day i w ij quantity of fruit in inventory at DC transported by route j and sold on day i

Table 12: Abbreviation of indices, parameters and decision variables

Abbreviation

The total logistics costs in FDM

We estimate the logistics cost per ctn for each activity based on Activity-Based Costing systems [START_REF] Ongkunaruk | Logistics cost structure for mangosteen farmers in Thailand[END_REF]. We consider the cost of each activity of the fruit exporter from production to consumer. The total costs are composed of expenses incurred from purchasing raw materials (ci), material handling ( mi) , transportation( di) , storage( hi) , logistics communications and other costs (bi) , including the total cost of quality loss ( TQL). The total logistics cost function is formulated as in eq 18.

[18]

We specify to estimate the TLC in one season (n=40 day) of fruit. We set 1 unit of cost equal to Full Container Load (FCL) of 1 refrigerated cube container (ctn),

with the following internal dimensions: 11.58m x 2.29m x 2.40m (LWH), volume 67.3 M 3 , and 55,000 kg of capacity, as shown in Figure 13 The logistics cost functions for each activity of fruit exportation is composed of:

Material cost

Material cost, ci is the cost of buying material fruit from the orchards of the exporter each day. ci depends on the material price (PMi) which concerns the quantity of demand and supply of fruit from orchard each a day (PMi is described in more detail in 3.6.2). ci can be estimated by multiplying the total quantity of fruit exported each day

with PMi, as it can be expressed in eq19. We estimate the total number of exported fruits by considering the sum of the quantity of fruit exported without storage (xij) and with storage planning ( yij k ) each day. We set two routes of fruit transportation (m= 2) :

refrigerated truck (1), and cargo ship (2) where k is the number of days planned for fruit storage in inventory before it is sold. We decided that the total holding time of fruit (THT)

must not be more than ten days since the date the fruit is exported because the fruit quality is not acceptable to consumers. So, the maximum number of days of fruit storage

(msj) is THT-Lj, where THT =10. [19] TQL b h d m c TLC n i i n i i n i n i i n i i i               1 1 11 1 i m j ms k k ij m j ij i PM y x c j * 11 1            

Material handling cost

Material handling, mi is the cost arising from exporters contracting with the collector in the procurement, gathering materials, sorting, cleaning, packing and loading into containers. Same as ci, mi can be estimated by multiplying the total quantity of fruit exported each day with the fixed costs per ctn of material handling cost in fruit exportation (MH), which can be shown in the formula:

[20]

Transportation cost

Transportation costs di depend on the mode of transportation. Each transportation mode is different in cost (TCj) and distribution time. In practice, Fruit exporters will hire companies to carry out fruit transportation, and so the depreciation costs and maintenance costs do not need to be considered in transportation cost estimation. di can be shown in the formula:

[21]

. Storage cost

We consider the storage cost from advance storage planning for k day, hi, which arises from energy consumption from electricity-related to temperature-controlled storage. The hi depends on the storage time of fruit ( k) and hi can be estimated by multiplying the number of fruits exported that have been stored in the inventory for different times with the storage cost of reefer container per ctn per day at an optimal temperature (SC), as shown below:

[22] MH y x m m j k ij ms k m j ij i j * 11 1                   m j ms k j k j i m j ij i j TC y x d 11 , 1 * ) (     m j ms k k ij i j SC k y h 11 *

Logistics communication and other costs

The logistics communication and other costs, bi arising from the ordering of the fruit in advance of the exporter with the collector or the group of farmers and cost of requesting a certificate about pesticide safety is estimated as shown in the formula of eq 23. We set the communications and other costs of fruit exportation per ctn(CO) as the fixed cost which can be estimated by multiplying the sum of the quantity of fruit exported by without storage (xij) and with storage planning (yij k ) each day.

[ 23]

The total cost of quality loss

We estimate the total cost of quality loss (TQL) due to MI (gi) and ND (qi) in the fruit supply chain each day, as represented in eq24. The qi may be in the form of zero-order kinetics (q0i) or exponential decay (qei) depending on the type of fruit. We describe how to assess the cost of quality loss in the fruit supply chain in 3.2 and 3.3.

TQL = gi + qi [24]

Estimating the cost of MI

The loss of quality in the transportation of fresh fruit due to mechanical force is a significant cost for companies, which influences network designs. We present how to estimate the degree of MI and its cost, which depends on the vibration level of each route of transportation. We applied data from laboratory testing results in mangosteen exportation, as a case study in both cases of DIP -ZO and DIP -ED. The MI and cost assessment consists of three parts: 1) vibration level assessment of each route of fruit transportation, 2) a study of the effects of vibration level on the percentage of fruit damage, and3) the estimation of the percentage of fruit damage and its cost on each route of transportation. Vibration data was recorded in real-time for three seconds for every one minute of road travel. The total recording time was 43,200 s for about five days driving.

The fruit was transported to the distribution centre. We calculate the average Power Density Spectrum (PSD, G 2 /Hz) within a narrow band of frequencies of the spectrum (BW) at various frequencies, and plotted against the frequency of the bandwidth to develop the PSD-BW curve.

The transportation vibration level for each route of transportation in terms of the root means square acceleration value or Grm level (Gj 2 ) measured in specific gravity unit (g) can be determined by the integration area under the PSD-frequency curve in the frequency range 1-5 Hz. Gj 2 , as represented in eq 25. The results of the vibration level measurements for both transport mode (Gj 2 ) are shown in Table 13. The results will be used to estimate %MI and its cost in the next part.

N BW PSD G n i j * ) ( 1 2          [25]
Where:

Gj 2
root mean square acceleration value for each route of transportation measured in specific gravity unit (g) within a BW of frequencies, BW a narrow band of frequencies on the spectrum N number of instants sampled

In the second part, to study the relationship between vibration level and the % MI, the packed fruit were placed under simulated transportation conditions by the vibrator with different vibration levels: 0.5, 1.0, 1.5, 2.0, 2.5 and 3.0 of G 2 .

We set 0 of G 2 as the control treatment and tested vibrations for eight replications. After the vibration testing, all treatments were stored at room temperature for three days, and then, the fruit was monitored for the percentage of MI in each treatment by visual inspection at more than 0.5 centimetres of the bruising diameter. The bruising diameter (BD) was determined as the following in Figure 14 and eq 26. The percentage of fruit damage was determined as the following in eq 27. The relationship between G 2 and % MI were plotted as of G 2 -%fruit damage graph and formulated in terms of the linear equation to determine the % MI for each transportation route.

 

2 mn mx BD   [26] 100 %         NF ND damage Fruit [27]
Where:

BD

bruising diameter (cm.) Figure 15 shows % MI per ctn in mangosteen related to the vibration level in terms of G 2 . In the first period [ 0-A1] , the fruit is bruised due to mechanical force.

However, there are no discernible changes, and the apparent quality shows stability. In the second period [A1-A2] (G 2 .>1.0), the bruising of the fruit is noticeable, and fruit quality is deemed unacceptable by the consumer.

In the final part, we can estimate the MI for each route of transportation. We found that the % MI of fruit per ctn expresses a linear relationship with the vibration level of route transportation (R-squared value (R 2 ) =.0.9755), according to: -12.82 [28] mx mn

%MI = 13.698 G 2 .
We substitute the transportation vibration level for each route of transportation (Gj 2 ) with G1 2 =1.5 and G2 2 =1.2 into G 2 in eq 28 to estimate the MI of fruit for each route of transportation (%MIj), as shown the results in Table 13. Then, we can estimate the cost of MI per ctn for each a route of transportation (ij), as expressed in eq 29.

[29]

Lastly, we can determine the total cost of MI in fruits exported without storage and with storage planning each day:

[ 30]

Estimating the cost of Natural decay (ND)

There are two general types of ND for fresh fruit-based on kinetics model: zero-order kinetics and exponential decay. Most ND in fruit with zero-order kinetics concerns freshness loss and enzymatic degradation. In exponential decay, ND concerns microbial growth and vitamin losses. The change of these quality losses as a function of holding time (t) is either linear or non-linear. According to Ferguson model (2007):

[31]

Where is the constant value, and  =1 in the case of a linear function and  >1 in the case of a non-linear function, we develop two example models in which the cumulative holding cost is a linear function of time (zero-order kinetics), and the cumulative holding cost is a non-linear function of time (exponential decay).

 t h t H ) (  h ~

ND with Zero-order kinetics

To determine the cost of ND with Zero-order kinetics function, we consider the following steps:

 We consider the characteristics of ND with the linear function of time in mangosteen as a case study.

 We apply quality loss in terms of freshness loss measured in a unit of percentage weight loss (%WL) at various holding times as an indicator.

 We focus on the relationship between %WL and holding time by using laboratory testing,  We determined the cost of ND in fresh fruit at the various material price each day.

The packed fruits in packaging system (non-returnable polypropylene box with internal dimension (33x44.5x16 cm) supported both at the bottom and top with the sponge (polyurethane), as a cushioning system) were kept in a cooling room at 13 C and 75% RH which simulate the conditions of fruit export. The weight of mangosteen was monitored at various storage times: 0, 1, 3, 5, 7, 9 and 11 days to estimate the percentage of weight loss each day of fruit with the equation:

  100 * %           i f i W W W WL [32]
Where %WL is percentage weight loss, Wi = initial fruit weight in gram, and Wf = final fruit weight in gram at the indicated period.

We plot the relationship graph between %WL and holding time to determine the rate of weight loss in the form of a linear equation. The cumulative holding cost at various holding times will be determined.

Figure 17 represents the characteristics of ND with the linear function of time in mangosteen in terms of freshness loss measured in a unit of %WL at various holding times. At the first period from t0 to the date of fruit, deterioration begins to appear (DFD), the quality appearance of the fruit is stable, and freshness loss of the fruit is unnoticeable by consumers. Subsequently, fruit deterioration begins to appear until it is unacceptable by consumers in the period DFD to end of holding time (EOH). It is evident that fruit may require a markdown in price or the removal of decayed product to meet customer satisfaction and constant demand over this period. Furthermore, the cumulative holding cost resulting from freshness loss needs to be considered to optimise net profit The accumulative %WL per ctn in fresh fruit %WLjk (t) is given as a linear function withholding time with R 2 =0.9898 which can be formulated in eq33, where Lj + k is total holding time for transportation time (Lj) and storage time (k):

2.2571 + k) + 3.2542(L = (t) %WL j jk [33]

DFD EOH

Apparent stability Quality loss appearance E q .33 can be applied to estimate the cumulative holding cost per ctn each day for zero-order (Hoij k (t)) by multiplying it by the price of material fruit in the date of the fruit exported. (PMi), according to:

[34]

The relationship between PMi and Ho(t) at various holding time is presented in Figure 18. Considering all graphs are a straight line with the difference of slope (i)

and the intercept (i) depending on PMi each a day. So, we can estimate the cumulative holding cost per ctn of fruit each day that changes with the time of holding (transportation time (Lj) and storage time (k)), according to:

[35]
)) ( % * (( ) ( t WL PM t Ho jk i k ij    i j i k ij k L t Ho       ) (
Finally, the total cumulative holding cost ( qoi) of fruit exported without storage planning (qoxi) and with storage planning (qoyi) based on zero-order kinetics can be estimated by as expressed in eq 36.

[36]

We modify dynamic pricing model based on single price markdown to estimate the cost of quality loss corresponding of consumer evaluation in fruit quality and the price markdown time (Tm) [START_REF] Wang | A dynamic product quality evaluation based pricing model for perishable food supply chains[END_REF]. We consider that the customer begins sensitive to quality changes of fruit; as a result, gives a lower valuation on the date of fruit deterioration begins to appear (DFD). So qoxi and qoyi will be estimated if we hold fruit for more than DFD (Lj or Lj +k >DFD):

[37]

[38]

ND with exponential decay

We consider the cost of the quality loss estimation approach for fruit in the form of a non-linear function withholding time. We modified an example of blueberry spoilage in terms of the percentage of microorganism growth (%MO) at various times as a case study [START_REF] Ferguson | Note: An application of the EOQ model with nonlinear holding cost to inventory management of perishables[END_REF]. The experiment has three parts, as described by the following.

In part I, based on [START_REF] Ferguson | Note: An application of the EOQ model with nonlinear holding cost to inventory management of perishables[END_REF], we study the relationship between the %MO and holding time of fruit. We consider the average spoilage of

i i i qoy qox qo   ,                DFD L x DFD L qox j i m j ij j i : L * * : 0 i j 1 ,                     DFD k L y DFD k L qoy j i m j ms k k ij j i j : , k) (L * * : 0 i j 11 ,  
blueberry with a holding time of 10 days based on the historical observations in Figure 19, the quality of fruit is stable due to the lag time of microbial growth and goes unnoticeable by consumers in the f irst stage (period 0-DFD). The exponential or logarithmic phase occurs due to the increase of yeast and mould growth in blueberries.

After that, the loss of quality will appear until it is unacceptable to the consumer or the end of shelf life is reached (period DFD-EOH).

The %MO curve is given as a non-linear function of time. To estimate %MO function with time, we transform the exponential function into a linear relationship taking its logarithm in both side yields of %MO and holding time, as shown in Figure20.

So, the linear equation can be estimated, according to:

LN(%MO) = 2.7831LN(t) -2.8103 [39]
Figure 19: %MO of blueberry stored at 5C/85%RH at various holding times (day). We use a linear regression technique to estimate %MOj,k which depends on the holding time of transportation (Lj) and storage (k) according to eq40 , where is exp(intercept), and  is the slope.

Quality loss appearance

EOH DFD

Fruit stability

[40]

In part 2, the cumulative holding cost per ctn of ND with ED in fresh fruit at the various PMi is estimated, according to:

[41]
The linear regression technique estimates the cumulative holding cost per ctn of fruit (Heij k ) function at various holding times and various PMi each day by taking a logarithm of both of Heij k and holding time ( t) , as shown in Figure 21. The linear equation can be estimated:

h    k L h t MO j k j   ) ( % , 100 )) ( % * (( ) ( t MO PM t He jk i k ij  [42]
We consider all graphs as a straight line with the difference of slope (i) and the intercept (i) depending on PMi of each day. We can run a linear regression of log Heij k (t) vs log(t), to estimate the cumulative holding cost per ctn of fruit with ED for each day that changes with the holding time (transportation time (Lj) and storage time (k)), according to:

[43]
In part 3, similar to ND with zero order, we summarize the cumulative ND-ED cost of fruit exported without storage planning (qex i ) and with storage planning (qey i ) to estimate the total cumulative holding cost of fruit for each day (qei) based on exponential decay, as shown in eq 44.

We set that the qei will be estimated if total holding time of fruit for more than DFD (Lj or Lj +k>DFD). The qei is equal to zero if Lj or Lj+k=<DFD because the loss of fruit quality cannot be observed.

[44]

[45]

[46]

t h t He k ij log log ) ( log    i k L h t He j i k ij  ) ( ) (   i i i qey qex qe   ,              DFD L k L h x DFD L qex j j i m j ij j i i : ) ( ~ * : 0 1 ,                 DFD k L k L h y DFD k L

Total GHG emissions in fruit exportation

Land fruit transport has a higher rate of GHG emission per ctn and waste generated by transport compared to shipping. While the release of GHG from storage in refrigeration systems varies, it depends on the source of energy and the storage period.

Cooling during transportation will have a greater amount of GHG emission than cooling in the warehouse because it requires oil as a source of energy use rather than electricity.

In terms of environmental impact in FDM, although maintaining the quality will have a beneficial effect, fruit quality preservation typically requires a significant amount of energy, thereby negatively affecting the environmental impact of the products.

In order to analyse the impact of the quality loss in fruit exportation, we use the modifies standard method of Publicly Available Specification 2050:2008(BSI, 2008) to assess GHG in terms of total Carbon footprint (Cf) emissions. We consider the activity in the fruit exportation supply chain concerning CO2 emissions, as shown the formula in eq. 47.

[47]

The Cf provides the total carbon dioxide equivalent (CO2e) emissions in the fruit exportation supply chain, which is calculated by multiplying the total quantity of fruit exported with CO2e emission factors for each activity causing greenhouse emissions. These activities include transportation activity (CTj), storage activity (CSk) and waste material generation (CW). We consider one ctn equal to FCL of one refrigerated cube container (ctn),40ft 2 which consist of net weight of fruit = 5,000 kg, and overall weight of fruit (tare weight+gross weight) = 5,500 kg . We set the total quantity of fruit exported in a season at 200 ctn.

CO2e emission is a term for describing different GHG in a common unit. For any quantity and type of GHG, CO2e signifies the amount of CO2 which would have the equivalent global warming impact. We use data from both primary and secondary sources to determine CO2 e emission factors for each activity in the fruit supply chain, as shown in the details of Table14. [48]

[49]

In the first objective, NP is maximized. It is composed of two parts, which include total revenue (ri), and total logistics cost. (TLC). The ri generated from the sale of fruits is exported by without storage (sij) and without storage (wij) at DC. It depends on sale price of fruit each day (SPi), as shown in eq 37. This objective function aggregates the measurable economic importance throughout the considered fruit distribution. The

         n i i i i i i b h d m c CTL 1 [50] [51]
In the second objective, the percentage of mean remaining quality of fruit exportation (%RQ) considering the average percentage of MI each route and % WL throughout the fruit supply chain is maximized. The total revenue can be formulated as:

[52] Exporters need to decide to sell fruit as soon as the fruit is transported to the destination centre if the SPi of the fruit at that time is high, or to store fruit in a reefer container to wait for the SPi to increase if the SPi of fruit at that time is low. Nevertheless, exporters also need to consider the appropriateness of storage costs in terms of quality loss and energy.

To make a decision in terms of export and inventory planning, choosing the appropriate distribution scheme, and marketing plan, the decision variable constraints function is represented in the following.

a) The quantity of fruit exported and sold

Fruit exporters want to know the optimal quantity of fruit exported and sold each day. They also need to plan the proper transportation route and storage time for the highest profit. We specify two kinds of decision variables to determine the quantity of

      n i i n i i q g TQL 1 1 0 i m j ij m j ij i SP w s r * 1 1              
fruit exported and sold each day: without storage planning (x ij and s ij ) and with storage planning,( y ij k , and w ij ).

In the first part, we consider the quantity of fruit exported without storage planning. We set xij and sij as the quantity of fruit exported from the packaging house (PH) each day, transported by route j without storage planning, and the quantity of fruit transported by route j and sold immediately at the distribution centre (DC) each day, respectively. We consider that xij is an integer with xij>= 0 except on the last period before the end of the season for fruit exports (EOS) due to an inability to deliver fruit in advance for Lj day of the end of EOS, according to:

[53]
In case of sij, all fruit with x ij is transported on the day i and they will arrive in DC on day Lj +1. After that, all fruit with x ij is sold immediately at DC in an amount of sij. However, fruit cannot be sold if i < Lj because the fruit is being transported, as shown in the details of Table 15. So, we can formulate s ij in eq.54 [54] To ensure that all exported fruit in a season of fruit will be sold, we formulate the constraint as the following: In the second part, we set yij k as the quantity of fruit exported from the packaging house each day, with route j, with storage planning for k days and wij as the quantity of fruit in inventory that was transported by route j and sold each day, respectively. In the case of yij k , all fruit is transported on day i, and arrive in inventory on day i+ Lj to store in the cooling room for k day and sold on day i+ Lj + k, as shown in the details of Table 16.

[55]            j j ij L EOS i L EOS i x : 0 : 0          j j L i j ij L i x L i
We consider that yij k is an integer with yij k = 0 except on the last period before the end of the season for fruit exports (EOS) due to an inability to deliver fruit in advance for Lj day of the end of EOS, according to:

[56]

In the case of wij, the total fruit from inventory sold each day can be estimated by the sum of the fruit planned for sale that day in the inventory, as shown in the details of Table16. We consider three cases of fruit transportation from the packaging house to inventory. In the first case, if Lj =< Lj +1, fruit cannot be sold because there are

           j j k ij L EOS i L EOS i y : 0 : 0
no fruit in inventory due to being in transport, so wij = 0. In the second case, if i > Li and i < the maximum holding time of fruit (MHT= Lj +msj ), some fruit exported with a storage plan (from k=1 day to k = msj -1 day) arrived in inventory, and the total fruit in the inventory sold each day (wij) can be estimated by summarizing the number of fruit exported from the packaging house on day i-(Lj+ k ) by route j with a storage plan for k=1 day to k = i-(Lj+1) day, according to . 1), (

       ) 1 (
Lj i k k j k L i ij j y w 117
+ y1,1 2 y3,1 1 + y2,1 2 + y1,1 3 y4,1 1 + y3,1 2 + y2,1 3 + y1,1 4 y 5,1 1 + y4,1 2 + y3,1 3 + y2,1 4 + y1,1 5 y6,1 1 + y6,1 2 + y6,1 3 + y6,1 4 + y6,1 5 + y6,1 6 y7,1 1 + y7,1 2 + y7,1 3 + y7,1 4 + y7,1 5 + y7,1 6 + y7,1 7 y8,1 1 + y8,1 2 + y8,1 3 + y8,1 4 + y8,1 5 + y8,1 6 + y8,1 7 .. .. .. . y ( EOS -Lj ) ,1 1 + y ( EOS -Lj ) ,1 2 + .. y ( EOS -Lj ) ,1 msj if i Lj+1 L j +1< i MHT i > MHT
*We suppose route j =1, Lj= 2 days, the maximum holding time (MHT) =10 days, the end of the season for fruit exports (EOS)=40 day

Day

In the final case, if i > MHT, all fruit with a storage plan from k= 1 to k= msj are sold. So wij is the total number of fruits with storage plans from k=1 to k= msj each day. The condition of wij estimation is represented:

[57]

To ensure that all exported fruit in the inventory will be sold, we formulated the constraint as the following:

[58]

b) Supply and demand

Fruit is a seasonal product. The supply and demand of fruit can fluctuate from day to day over a season. To ensure that the total quantity of fruit exported and sold is not greater than the total fruit supply (TSi) and demand (DMi) each day, we formulated the following constraints in eq 59 and 60.

[59]

[60] 1), ( In the case of DIP -ED, we define the same main objectives function and constraint function as the DIP -ZO, as shown in the detail of eq 48 and 49. We substitute the cost of zero-order kinetics (q0i) with the cost of exponential decay (qei) in the TQL function of eq 51 to estimate the total cost of quality loss, according to:

                         MHT i y MHT i L y L i w j j j j ms k k j k L i j L i k k j k L i j ij : : 1 : 0 1 , ) 1 (
[61]
We instead %WLjk(t) with %MOjk(t) in eq.48 to estimate %RQ of fruit in the supply chain, according to:

[62]

Numerical study

The uncertainty of fruit supply, demand and price are the important factors affecting the FDM chain. In this section, we present numerical studies part of a simulation for fruit supply and demand in 3.6.1, and fruit price determination in 3.6.2 which will be applied in the DIP model to solve problems in FDM.

The Simulation

We give three simulations based on historical data of the quantity of fruit supply and demand of Mangosteen exportation from Thai to Chinese fruit markets, as a case study, (ITCC, 2019) in order to obtain accurate and consistent results of the study.

We choose the normal pattern of demand rate (SC1) to be compared with two different patterns of demand rates: SC2 and SC3, as shown in Figure 23, Figure 24, and Figure 25, respectively. To compare all cases of scenarios in the same situation, we set the total quantity of fruit supply at 800 ctn and total fruit demand at 200 ctn. We fix two parameters for the exportation route in our analysis, including delivery time (2 and 4 In SC1, We give the high demand rate at two periods of seasonal time.

      n i i n i i qe g TQL 1 1             
During the first period, the demand rate is high because the total quantity of mangosteen and the other seasonal fruits of China released on the market at that time is low. During the second period, fruit consumption increases again due to the effect of a Chinese festival which stimulates higher customer demand. In SC2 and SC3, we consider a high demand rate of the consumer at the beginning season and at the end of the season, respectively.

Fruit price determination

The price of fruit is mainly determined by supply and demand. Basically, a balance is achieved between what consumers are prepared to supply at a price and what consumers are willing to pay for the fruit. As the price rises, the quantity that will be supplied also rises, and the quantity demanded falls and vice versa. In this section, we describe how to determinate fruit price based on the Walrasian stability condition. We review the fruit price determination in two parts: the price of fruit material (PMi) and selling price of fruit (SPi), which will be discussed in the following.

Price of fruit material determination

Fruit material prices are important in determining the logistics cost and net profit in the fresh fruit supply chain. Unlike the prices of staple foods such as maize or rice, fruit prices fluctuate enormously. They can fluctuate from day to day and hour to hour during the day depending on supply and demand. The main causes of short-term price changes of fresh fruit are:

 The amount of fruit on sale in the market on a particular day and the quantities sold the previous few days.

 Short-term demand changes (e.g. holidays and festivals).

 The effect on demand for prices of competing products.

The PMi determination concern three-parameter assessments: 1) supply and demand function with PMI, 2) price equilibrium (PE), and 3) excess supply function.

a) Supply and demand function with PMi

We applied the history data of the number of supply (SPi), demand(DMi), and material price of Mangosteen exportation (PMi) from Thai (Chantaburee province) to Chinese fruit markets each day from April to May to determine a supply and demand function with PMi, as shown in Figure 26 (ITCC, 2019). The total quantity of fruit supply and demand in a season are 13,582 ctn, and 13,118 ctn respectively.

We found that the relationship between TSi and DMi, is a linear function with PMi which is confirmed by R 2 =0.9781, and 0.9359 respectively. We can formulate the demand and supply function with PMi, according to [63] [64] However, fruit suppliers can procure the fruit materials for no more than 800 ctn/ a seasonal fruit or equivalent to 4.38 per cent of the total quantity of fruit supply.

We need to reduce the scale of the data to be able to evaluate the supply and demand function, including price equilibrium, and excess supply function with 800 ctn of the total quantity of fruit supply in the next step, as shown in Figure 27. So, the demand and supply functions with PMi can be formulated as:

[65]

[66]

b) The price equilibrium

In this section, we use the demand and supply functions from eq 65 and 66

to estimate the price equilibrium of fruit. The equilibrium price of fruit is the market fruit price where the quantity of fruit supplied is equal to the number of fruits demanded. This is the point at which the demand and supply curves in the market intersect. To determine the price equilibrium, we have to figure out at what price the demand and supply curves intersect. We consider the relationship between the quantities of fruit supply and demand in Figure 27. The supply and demand curves intersect at the equilibrium point (EP), and this point represents the price equilibrium (PE) and the quantity equilibrium (QE). To find these equilibrium points at the equilibrium intersection, we set SPi = DMi, according to

[67]

W e can estimate the PE = 1,243,460 baht /ctn, and then we can estimate the quality equilibrium (QE) by substituting the PE in eq.62 and 63. Finally, we obtain that QE = 14 ctn.

c) Excess supply function.

T h e excess supply is the situation where the material price is below its equilibrium price, as shown in the example in the area under the curve of Figure27. We consider how the excess supply will arise when the number of fruits supplied (SPi)

increases more than the equilibrium level (QE), while the number of fruit demanded by the consumers (DMi) decreases less than QE. The situations market forces will also interact to drive the prices to lower its equilibrium level (PE). In other words, when we have lower prices and excess demand, there will be a shortage of goods, putting upward pressure on the price as there will be more buyers chasing the available goods. As price increases, the suppliers will start producing more but the demand from buyers will decrease. This will drive the price and quantity to its equilibrium level. (Marwala, T.and Hurwitz, E. 2017).

In Figure 28, we estimate the excess supply of each price level (ES(P)) by using the difference between the quantity fruit supplied and demanded at the same price level, according to ES(P) = SPi(P) -DMi(P) [68] After that, we plot a graph between ES(P) and PMi to find the excess supply function with PMi, as shown in Figure 28. We found that the relationship of the E(P) and the PMi is linear, so, we can formulate the PMi function with time, according to eq 69.

The result of

Multi-objective solution method

In this section, we present two multi-objective solution methods based on generating methods to solve the DIP model. We propose an adjusted weight-sum approach with a genetics algorithm (AWS-GA), and a non-dominated sorting genetic algorithm (NSGA-II) for optimizing multi-objective problems, as shown in the details of the following.

ASW-GA

Weighted sum method (WS) is a simple method for forming a combined objective function. The purpose of the WS method is to minimise deviations of the existing objective functions from an ideal solution. Therefore the overall objective function will be as in eq 72, where the weights of the objectives (1>wl >0) are the parameters of the scalarisation, M is the number of the objective function, and X is a set R. (Mahmoodjanloo, Esmaili and Hajiaghaei-Keshteli, 2016).

[72]

We developed the weighted-sum additive (SW) with an adjusted weighted-sum approach (AWS), as shown in the details of Figure 33. Firstly, we exchange the multi-objective problem with the single-objective problem to vary the relative importance of the weight vector of multi-objective with m objective function (wm) and solve the resulting single objective model. We consider that the NP concern with two-parts of the total logistics cost ( TLC): total common logistics cost ( CLC) and total cost of quality loss ( TQL) according to:

[73]    M l i l x f w X x 1 ), ( min      n i i TQL CLC r NP Maximize 1 ) (
So, we can add wm in NP function to analyse the multi-objective function base on the maximization of NP and %RQ in the form of a single objective function, according to eq. 74, where w1 and w2 are the relative importance weight vector of objective functions 1 and 2, w1+ w2=1, and 1> wm > 0.

[74]

Secondly, the GA method was used to solve the models with constraints for functions. The algorithm was coded in MATLAB 2017b and run on a PC (Intel® Core™i5, 1.7GHz, 8 GB memory). We set 4 decision variables including xij, yij k , sij, and wij as integers, to determine the quantity of fruit exported, sold, and stored each a day.

All four decisions are combined into 1 chromosome or string with the length of chromosome = 880 genes, upper bound = 0, and lower bound = 30. The string shows all days of fruit exported and sold (i), route(j), and the number of days stored (k). The fitness value of the individual is calculated by using root mean square error (RMSE) which is formulated as in eq 75, where is a predicted value for times t, yt is a regression's dependent variable observed over T times.

[75]

We set the best fitness function at < 5, and the best 0.5 individuals (Ps) were selected to reproduce while the rest were thrown away using a roulette-wheel technique.

The probability (PC) used in this crossover process was 0.90., while the mutation probability is 0.001. If the continuous generation of 100 is not improved, then the operation will be terminated.

Thirdly, each run of the model can find a Pareto solution. So to find a Pareto front, the problem must be run several times. To overcome the difficulties of the weighted sum method which we are not able to obtain any solution on the concave part

     n i i TQL w CLC r w NP Maximize 1 2 1 ) ( i y ˆ     r i t t y y T RMSE f 1 2 ) ( 1 1 1
of the Pareto front, we applied an adjusted weighted sum method for the mutations () , by considering the fitness value of each objective function on each optimal solution point on the optimal Pareto front (i), according to eq 76 (Liu and Reynolds, 2014).

[76]

Where: J1(ui) = Fitness value of objective 1, so maximising at optimal solution i of weight w1, J1(ui + 1) = Fitness value of object 1 so maximising at optimal solution i+1 of weight w1 J2(ui) = Fitness value of objective 2 so maximising at optimal solution i of weight w1 J2(ui + 1) = Fitness value of object 2 so maximising at optimal solution i+1 of weight w1 Finally, we then replace w 1 and w 2 in eq. 75 to maximize NP as in the normal weighted sum procedure. Step7: Replace the best solutions based on its rank and crowding distance to the parent population.

End while

We propose the ranking and crowding degree method based on Pareto dominance. fit1( x) is the population selection of fitness. Use rank( x) to denote the relationship of Pareto dominance, rank(x) < rank(y) indicates that x dominates y. The crowding distance is Crowdingdistance(x). The first keyword ascends in a particular order, and the other key sort descends according to the crowding distance.

Fit1(x) = (rank (x), Crowdingdistance(x))

[77]

Statistical analysis

The answers from GA and NSGA-II are not exact values because it is a population of randomly generated solutions. To make the results reliable and easy to analyze, the completely randomized design was used with all points on the Pareto front.

We analyzed by Pearson's correlation (r). An analysis was performed using the SPSS package (SPSS 11.0 for windows, SPSS Inc., Chicago, IL, USA). The statistical significance was considered to be p<0.05.

Value chain analysis

The result from the numerical study under the variability associated with fruit demand and supply rate will be used to analyze the value chain based on a cost advantage approach. We identify primary, support activities and logistics operations from production to delivery to the consumers, and analyze the logistics costs of exporters from these activities based on the results from numerical study to reduce costs during each activity. The possible guidelines to reduce these logistics costs to help ensure the profitability and sustainable development of the stakeholders in the supply chain of fruit exportation management take place at three decision levels: strategic network design, tactical network planning, and operational transportation planning will be proposed.

Firstly, to study the effects of quality loss on NP, we consider the behaviour of the optimal Pareto front from 3 different scenarios: SC1, SC2, and SC3 in Figure 35, Figure 36, and Figure 37. This intermediate conclusion illustrates that just a small increase in the NP fosters significant %RQ of fruit for lower values of quality loss for all three scenarios. We studied the behaviour of the algorithm in reacting to different dynamic scenarios. We considered that all scenarios had the same trade-off between NP and %RQ at 84%-88% of %RQ. They represent the behaviour of the algorithm and how the dramatic increase of %RQ had little effect on the rise of NP, as shown in the details of Figure 35, We found that there are significant differences in each scenario (p<0.05). SC2 had the highest net profit, whereas the net profit of SC3 is the lowest. These results demonstrate how as the demand rate at the end of the season gets higher and the supply rate for SC3 gets lower, the fruit needs to be stored up to meet such demand under limited supplies, as shown in Table17. It affects not only the increase of the total transport (TT) and storage time (ST) but also the decrease in total NP when we compare to SC1 and SC2. To maximize the net profit of fruit exportation under the demand rate change, choosing shorter transit routes in both x1 and y1 is the way to achieve the desired results. These results can be confirmed in that all scenarios have a total value of x1 more than the other decision variable (p < 0.05). This result can be described by how the DIP model tries to find the maximum profit and the minimum cost of storage by choosing to transport fruit by the shortest route and to sell the fruit as soon as it arrives at the market destination, rather than to store it in a reefer container. Furthermore, we observed that there is a statistically significant interaction between the values of x1 and NP. At the same time, the main effects of the other decision variables (x2, y1, and y2) on NP were not significant. It can be indicated that choosing shorter transit routes affects the increment of net profit.

As mentioned above, we can conclude that the higher demand at the end of the season in SC3 can be affected by the decrease of total NP and % RQ of fruit exportation. The exporter should have long-term cropping plans with the farmer by carrying over the effects of demand and supply in the yearly decisions. The different results of each scenario show that the Pareto front can take many forms in the solution space, even nonconvex. It confirms the DIP model that was taken regarding a solution method is able to cope with such complexities.

The DIP model can help the exporter prevent unnecessary quality losses of fruit and improve net profits and the cost of fruit exportation throughout the supply chain. This model modification is even more significant because the logistics exporter can make a decision regarding export planning and choose the appropriate distribution scheme under uncertainty of supply and demand rate.

The effect of quality loss on net profit

In this section, we consider the Pareto front of the DIP-ZO and DIP-ED model in which they have solved the multi-objective problem by using the AWS-GA and NSGA-II approach. We focus on presentation in two main parts. Firstly, we evaluate the performance of each algorithm by comparing the fitness value of each multi-objective approach. Secondly, we analyze the effect of ND in the case of zero-order kinetics and exponential decay on the overall planning of fruit exports.

To evaluate the performance of the algorithm, we consider the Pareto front of the DIP-ZO and DIP-ED model solved by the multi-objective problem using AWS-GA and NSGA-II, as represented in Figure 39 and Figure40, respectively. We observed that both the optimal front curves of AWS-GA and NSGA-II tend to have similar behaviours, in that they have more NP and more %RQ. However, it is rather clear from the comparison of the Pareto fronts that NSGA-II is much more dominant than AWS-GA in both DIP-ZO and DIP-ED. NSGA-II is significantly more capable of finding a better f than AWS (P<0.05), and it also is able to capture the non-convexities in both cases of DIP-ZO and DIP-ED problems as shown in Table 18. To analyse the effects of ND on the overall planning of fruit exports, we 18. The result from Pareto-optimal solutions represents that the developed DIP model can be applied to solve the problem in both the zero-order reaction and exponential decay by the non-dominated solution.

The effects of appropriate holding time of fruit on FDM

It is interesting to note that the quality loss of fruit is a function of total holding time. For global fresh fruit exportation, most holding times are concern with transportation time (TT) and storage time ( ST) in fruit distribution. These times are important for making decisions in FDM to achieve maximum NP and %RQ under highly uncertain factors. In this section, we bring the results of the optimal Pareto front from Secondly, we look at the correlation value between the TT, ST, NP, and %RQ, as in Table 19. The result reveals that lower levels of ST correspond to higher levels of NP and %RQ in both DIP-ZO and DIP ED with negative correlation values of r ( NP -ST ) = -0.9502 and r (% RQ -ST ) = -0.9965 for DIP-ZO, and at r ( NP -ST ) = -0.9593 and r (% RQ -ST ) = -0.9893 for DIP-ED. Furthermore, the lower level of TT has less correspondence to a higher level of NP and %RQ in both of DIP-ZO and DIP ED which can be confirmed by the negative correlation values of r ( NP -TT ) = -0.5543 and r (% RQ -TT ) = -0.5377 for DIP-ZO, and at r ( NP -TT ) = -0.6242 and r (% RQ -TT ) = -0.5294 for DIP-ED. All results indicated that reducing fruit holding time by choosing the shortest route and taking the least time to storage fruits are the best way to maximize NP and %RQ in FDM. The total logistics costs and total revenue depend on material price and selling price, which fluctuate day by day throughout a seasonal fruit period, while the cost of quality loss depends on the material price each day and total holding time.

In this section, we want to know how appropriate transportation and inventory planning to maximize NP and %RQ in FDM. We consider the effects of the four fruit distribution schemes: Xi, Y i, Si, Wi, on NP and %RQ in DIP-ZO and DIP-ED, as they are presented in Figure 43 and Figure 44, respectively.

We analyse the impact of the distribution scheme on the changing of NP and %RQ in two parts. In the first part, we discuss the trend behaviour of the fruit distribution scheme to maximize NP and %RQ in both cases of DIP-ZO and DIP-ED. The second part concerns the discussion of optimal transportation and inventory planning to maximize NP and %RQ. Secondly, we consider the appropriate distribution scheme to maximize NP and %RQ, as shown in Table 21. We found that the distribution scheme in both the cases We consider the appropriate plan for storing the exported fruit to maximize net profit, while the %RQ of fresh fruit are met in both cases of the DIP-ZO and DIP-ED model, as shown in Table21. We found that both cases have similar behaviour in which they are found that storing fruit in the shortest time (k=1 day) is the best way to achieve the desired results. The result is consistent with the studying effects of appropriate holding time of fruit on FDM in 4.1.3. It found that the reduction of fruit holding time can lead to maximum net profits and %RQ in FDM.

In addition, we found that algorithm tries to control the total holding time of fruits (THT) not to exceed the lag time for the quality loss appearing or THT <= DFD by using the short route (Lj =2 days) and a short time to storage fruit (k<=2 days) to prevent the costs of ND from holding time in FDM, as shown in Figure 45. Understanding the relationship between the characteristics of the continued decline in fruit quality and consumer evaluation in fruit quality can be applied to set up the inventory management policy in terms of just in time (JIT) and first-in, first-out (FIFO) policy. We found that employing JIT with two days in both cases of DIP-ZO, and

Value chain analysis

In this part, we analyze the numerical results from 4.2.1 to 4.2.3 to propose a way to achieve the cost advantage with the highest profits of fruit exports under sustainable conditions. We discuss the solution at three decision levels: strategic level, tactic level, and operation level, according to Shapiro, 2007. The strategic level is concerned with long-term decisions, such as the selection of farming technology, cropping plans, and design of supply chain networks. The tactical decision level is concerned with mid-term distribution planning decisions related to fulfilling demands (or forecasts) on an aggregate level, which includes, e.g., aggregate product flows and delivery frequencies. Lastly, the operational decision level dealing with short-term planning of the distribution of actual customer orders, which includes the loading and routing of vehicles.

Strategic planning

Considering the different scenario results in NP and %RQ at the same range of horizon time in a seasonal fruit base on fruit inventory level in Figure 48, we found that the increase of inventory level in SC1 and SC3 affects the decrease of total NP and % RQ in FDM by significantly ( p>0.05) when compared with SC2. The results can be interpreted as the fruit supply shortage resulting in fruit exporter need to store fruit in inventory to fulfil demand, as represent in Table 24. This fruit storing in inventory contributes to the increase in cost due to ND and storage. It must use the energy to preserve fruit quality and also affects the increase of GHG emissions. Planning fruit exportation for each seasonal fruit in order to keep inventory levels as low as possible is a key factor that can lead to achieving the cost advantage in FDM. As mentioned above, understanding the mechanism of quality loss in each type of fruit is a key parameter to improving logistics efficiency, which is concerned with setting up the inventory policy to maximize NP and %RQ in FDM. We can assess the way to achieve cost advantage in FDM that uses a short route by truck with JIT policy 2 days and stores fruit for the shortest period while waiting for the market price to increase with FIFO policy < 1.6 days, and < 0.195 days in the cases of DIP-ZO and DIP-ED can help to increase %RQ and NP in FDM. In contrast, choosing a cargo ship instead of a truck to reduce MI may be an inappropriate approach because transportation by cargo ship spends more time than transportation by truck, which affects the increase of %ND. However, to achieve the highest profit and quality of fruits for export from the author's perspective, the exporter should develop appropriate post-harvest technology to extend the shelf life of fruit and improve the packaging system to reduce quality loss due to mechanical injury.

Operational planning

The developed DIP model can be applied to make decisions at the According to tactics analysis results in 4.2.2, fruit sales without storage is the most effective method for increasing %RQ and NP since there is no cost of quality loss and storage. However, to achieve the desired result, fruit transportation must be done within the time window to keep up with the demand and avoid the appearance of quality loss. JIT is therefore used to control the amount of time in shipping to avoid such problems.

Thirdly, Yi is the quantity of fruit exported from a packaging house with storage planning each day, as shown in the example of point (a) in Figure 53[A] and

Figure 54 [A]. The exporters need to consider the number of exported fruit that must be stored in reefer containers after they arrive at the distribution centre each day. This decision variable involves choosing an optimal transportation time and determining the number of days that the fruit is stored which using a total daily fruit ordering plan from an orchard has to order fruit under the limit of total fruit supply each day. while the output inventory level depends on the demand rate of fruit at the distribution centre each day (wij k ). In practice, the exporter needs to consider the inventory level each day to enable optimal space utilization, while the maximum number of fruits stored in inventory each day must not exceed the storage capacity of inventory, as shown in Finally, wij, is the quantity of fruit in inventory that will be sold each day.

The exporter needs to store fruit to fulfil consumer demand when there is a supply shortage. However, fruit storage must be processed based on the total holding time (THT: First, most operation research models assess the quality loss of fruit since the first day the fruit arrived in the inventory. Actual, the quality loss in fruit will be noticeable by the consumer after the fruit has been held for a lag time of quality loss occurrence. We consider that the cost of quality loss will occur when consumers feel sensitive to quality changes of the expiring products and, as a result, give them a lower valuation [START_REF] Wang | A dynamic product quality evaluation based pricing model for perishable food supply chains[END_REF].To assess the quality loss consistent with reality, we developed the DIP model to evaluate the ND based on lag time of quality loss occurrence. The ND will be estimated on the day that consumers began to notice the loss of quality (>=DFD).

Second, the other operation research papers applied only the assessment of ND in the form of liner function with time (zero-order kinetics). It is not cover the quality loss mechanism in some fruit, especially in fruit that has a quality loss in the form of exponential decay. So, we propose a kinetic model considering both cases of zero-order kinetics and exponential decay.

Finally, we found that most operation research models involve solving shortdistance transportation problems, which the MI due to transportation is not the main factor to consider. Nonetheless, for global fruit exports, MI is one of the main causes of quality loss in exported fruits, which needs to be evaluated. We develop the quality loss models to assess MI based on the different levels of vibration in each transportation route. The MI evaluation helps to reflect the actual loss and cost of fruit quality from long-distance transportation, as well as choosing the optimal route for fruit export.

Conclusion

The developed multi-objective model of integrated distribution and inventory planning for fruit exportation allows for a comprehensive and realistic understanding of these intertwined planning problems. Furthermore, it provides a significant improvement upon the profits and cost of fruit exportation concerning quality, safety, and environmental impact. This improvement is more significant in value chain analysis for logistics exporters who make decisions on export planning, concerning the choice of an appropriate distribution scheme and inventory policy under uncertainty of demand, supply rate, and price.

N S G A -II is more suitable for solving multi-objective functions than AWS-GA. It is capable of finding near-optimal solutions, and it can even find a better fitness value than an adjusted weight sum approach. The Pareto front of NSGA-II more strongly dominates than the Pareto front of the weight sum approach. It can also capture the nonconvexities of both Pareto fronts of zero kinetics and exponential decay.

Computational results for the illustrative example show that fruit quality is strongly influenced by two interrelated stages of distribution and inventory. Both Pareto front curves of zero-order and exponential decay trend show similar behaviour with the relationship between RQ and net profit being quite strong as they have more NP and more %RQ. We found the negative correlation between %RQ and CO2 e emission in both cases of ND, which mean that the reduction of % RQ is related to the increase of CO2 e emission by significantly.

The decision variable can be applied to analyse the value chain base on three decision levels in exportation planning: strategy, tactic, and operation planning. To achieve the cost advantage, the export fruit planning for each seasonal fruit should keep inventory levels as low as possible and is a key factor in the long-term decision, while the selection of short transport routes and appropriate storage time with THT < DFD strongly dominate other distribution schemes in the mid-term decision. Finally, the operation planning based on four decision variables provides the exporter with the ability to achieve maximum NP and %RQ in FDM.

CHAPTER V GENERAL CONCLUSION

Quality control is an important factor in achieving the cost advantage in FDM under the specifications and requirements of consumers for fruit quality, safety and sustainability. However, the fruit distribution for global fruit trade is characterised by long-distance transportation, continuous decline in fruit quality combined with significant supply, demand, and price uncertainties, and relatively thin margins. These challenges generate a need for management efficiency and the use of modern decision technology tools. There are implemented operation models to solve many quality management problems in FDM. Most operation research models for FDM involve solving complex problems through a multi-objective framework, which they have to optimise between fruit quality level and the logistics cost or profit in FDM. At the same time, NSGA-II has been identified as one of the most effective solutions for such complex problems.

The majority of the operation research models uses quality loss assessments that are conflicting with the mechanism of quality deterioration and consumer evaluation in fruit quality. They propose the relative cues of freshness based on zero-order kinetics to estimate the remaining quality, which it does not cover the characteristic of quality loss in some type fruit, especially in fruit that has a quality loss in the form of exponential decay. While the cost of quality loss corresponding of consumer evaluation in fruit quality which it is shown that the customers begin sensitive to quality changes of fruit and, as a result, give them a lower valuation on the date of fruit deterioration begins to appear (DFD). Most research has an attention on the application of shelf-life model to estimate the quality loss without considering the fruit stability or lag time before consumers can observe fruit quality deterioration. Overlooking lag time may prompt to an underestimation of shelf life with significant economic losses for fruit exportation, as well as lacking sufficient information for reducing fruit prices, which is necessary to stimulate consumer demand.

MI is one of the main causes of quality loss in exported fruits, which it needs to be evaluated. However, we found that most operation research models involve solving All numerical result can conclude that the DIP model for fruit exportation allows for a comprehensive and realistic understanding of these intertwined planning problems. Further, it provides an important improvement in the profit and cost of fruit exportation concerning quality loss and environmental impact. This improvement is more significant in value chain analysis for logistics exporters who make decisions export planning, concerning choosing the appropriate distribution scheme, and inventory policy under uncertainty of demand, supply rate, and price.

The DIP model is a tool that helps balance the profits and the fruit quality in FDM. However, management in order to achieve maximum efficiency, the fruit exporters need to set fruit quality standards and specification, as well as applying fruit quality inspection system, post-harvest technology and packaging system. Furthermore, they must work together with the other stakeholders, including the integration of farmers and collaboration among farmers and collectors should be encouraged to make understanding about the importance of fruit quality preservation Looking at the differences between the developed DIP model and the other operational research model, the DIP model can provide solutions that correspond to the kinetic of quality loss in fruits covering in both MI and ND and consumer evaluation in fruit quality. While, the other operation research model focuses on studying only ND, which they do not reflect the reality, especially global fruit trade that requires longdistance transportation. Finally, this paper considered only a single product in the fruit distribution network. Future work could, therefore, include the regard of multiple products and interactions between the different products.

  ............................................................................................................................................ 4.4 Conclusion .................................................................................................................... GENERAL CONCLUSION .................................................................................................. REFERENCE ......................................................................................................................... vii

  The optimal temperatures and moisture conditions for some common fruits and vegetables. ....................................................................................................Table 2 : Activities in each type of logistics cost. .......................................................... Table 3: Summary of all the revised papers dealing with FDM. .................................. Table 4: Modeling approaches used by the analyzed papers. ........................................ Table 5: Functional area used by the analyzed papers. ................................................. Table 6: Characteristics of distribution planning on different hierarchical levels. ..... Table 7: Decision level used by the analyzed papers. .................................................... Table 8: Evolutionary algorithm dealing with the fresh fruit supply chain. ................. Table 9: Summaries of the multi-objective optimisation analyses of all the revised papers dealing with the application of perishable products. ....................................... Table 10: The pseudocode for the non-dominated sorting. ........................................... Table 11: Pseudocode for the crowding distance procedure. ....................................... Table 12: Abbreviation of indices, parameters and decision variables .......................

Figure 2 :

 2 Figure 2: General structure of the distribution part of the fruit exportation supply chain. ............................................................................................................................

Figure 3 :

 3 Figure 3: Scope of food loss (FL), food waste (FW), and quality loss (QL) in the food supply chain. .................................................................................................................

Figure 4 :

 4 Figure 4: the relationship between Grm 2 level and %MI (Kamhangwong 2016a). ........

Figure 5 :

 5 Figure 5: The percentage of remaining quality of food product caused by ND at various times: linear function [A] and non-linear function [B]. .....................................

Figure 6 :

 6 Figure 6: Analytical modelling approach in FDM. ......................................................

Figure 7 :

 7 Figure 7: The example of lag time in fresh fruit caused by ND with zero-order kinetics. .........................................................................................................................

Figure 8 :

 8 Figure 8: Supply and price changes (--) over a season. .................................................

Figure 9 :

 9 Figure 9: Flow chart of simple GA. ..............................................................................

Figure 10 :

 10 Figure 10: Classification of multi-objective methods.. ..................................................

Figure 11 :

 11 Figure 11: Illustration of the NSGA-II process. ............................................................

Figure 12 :

 12 Figure 12: The overview of methodology and way to analyse results for this research. .......................................................................................................................

Figure 13 :

 13 Figure 13: The position of Tri-axial accelerometers on a refrigerated container to monitor the vibration level of transportation for each route. .......................................

Figure 14 :

 14 Figure 14: The mangosteen bruising and the bruising diameter of mangosteen, ........

Figure 15 :

 15 Figure 15: The relation of the average vibration level and % MI of mangosteen. ........

Figure 16 :Figure 17 :

 1617 Figure 16: The relationship between Grm 2 and the cost of MI per ctn in mangosteen at various PMi . ..........................................................................................

Figure 18 :

 18 Figure 18: The convex approximation for cumulative holding cost of mangosteen stored at 13C/75%RH at various storage times and different PMi. ............................

Figure 19 :

 19 Figure 19: %MO of blueberry stored at 5C/85%RH at various holding times (day). ..

Figure 20 :

 20 Figure 20: The convex approximation for %MO of blueberry stored at 5C/85%RH at various holding times. ............................................................................................

Figure 21 :

 21 Figure 21: The convex approximation for cumulative holding cost of blueberry stored at 5C/85%RH at various holding time and various PMi. ................................

Figure 22 :

 22 Figure 22: Behavior of the model in a season of fruit exportation supply chain. .......

Figure 23 :

 23 Figure 23: Simulations of SC1 with normal demand rate. ..........................................

Figure 24 :

 24 Figure 24: Simulations of SC2 with high demand rate at an early season. ................

Figure 25 :

 25 Figure 25: Simulations of SC3 with high demand rate at the end of the season. .......

Figure 26 :

 26 Figure 26: Material price, total fruit supply, and demand. ........................................

Figure 27 :

 27 Figure 27: The relation of fruit material price, total fruit supply, and demand for fruit from the orchard with 800 ctn of the total quantity of fruit supply. ....................

Figure 28 :

 28 Figure 28: The relationship of the ES(P) and the PMi of fruit export. .........................

Figure 29 :

 29 Figure 29: The selling price of fruit from data history and prediction at various times. ...........................................................................................................................

Figure 30 :

 30 Figure 30: Simulations with various raw PMi and SPi of SC1 ....................................

Figure 31 :

 31 Figure 31: Simulation with various raw PMi and SPi of SC2. .....................................

Figure 32 :

 32 Figure 32: Simulations with various raw PMi and SPi of SC3. ...................................

Figure 33 :

 33 Figure 33: Adjusted weighted-sum approach. (Liu and Reynolds, 2014). ...................

Figure 34 :

 34 Figure 34: Flow chart of NSGA-II algorithm. .............................................................

Figure 35 :

 35 Figure 35: Pareto-optimal front of the illustrative example for SC1 ..........................

Figure 37 :

 37 Figure 37: Pareto-optimal in front of the illustrative example for SC3 ......................

Figure 38 :

 38 Figure 38: The distribution scheme of Trade-off between NP and %RQ for SC1 [A], SC2[B], and SC3[C], ...................................................................................................

Figure 39 :

 39 Figure 39: The Pareto front of the DIP-ZO model solving the multi-objective problem by using AWS-GA and NSGA-II. ...................................................................

Figure 40 :

 40 Figure 40: The Pareto front of the DIP-ED model solving the multi-objective problem by using AWS-GA and NSGA-II. ...................................................................

Figure 41 :

 41 Figure 41: Relative importance regarding average holding time and net profit of the illustrative example in the case of DIP-ZO. ..........................................................

Figure 42 :

 42 Figure 42: Relative importance regarding average holding time and net profit of the illustrative example in the case of DIP-ED. ..........................................................

Figure 43 :

 43 Figure 43: Relative importance regarding the average distribution scheme and net profit of the illustrative example in the case of DIP-ZO. ............................................

Figure 44 :

 44 Figure 44: Relative importance regarding the average distribution scheme and net profit of the illustrative example in the case of DIP-ED. ............................................

Figure 45 :

 45 Figure 45: The amount of cumulative quality loss in fruit with zero-order kinetics and exponential decay. ...............................................................................................

Figure 46 :

 46 Figure 46: The relative importance regarding the average of total CO2 e emissions and net profit of the illustrative example in the case of DIP-ZO. ...............................

Figure 47 :

 47 Figure 47: Relative importance regarding the average of total CO2 e emissions and net profit of the illustrative example in the case of DIP-ED ...............................

Figure 48 :

 48 Figure 48: The optimal inventory level in each scenario: SC1 [A], SC2 [B], and SC3[C]. ........................................................................................................................

Figure 49 :

 49 Figure 49: Relative importance regarding the percentage of quality loss due to MI and ND and net profit of the illustrative example in the case of DIP-ZO ..................

Figure 50 :Figure 51 :

 5051 Figure 50: Relative importance regarding the percentage of quality loss due to MI and ND and net profit of the illustrative example in the case of DIP-ED. .................

Figure 52 :

 52 Figure 52: The operational planning of fruit exported without a storage plan based on Xi [A] and Si [B] in the case of DIP-ZO. .......................................................

Figure 53 :

 53 Figure 53: The operational planning of fruit exported with a storage plan base on Yi [A], IVi [B], and Wi [C] in the case of DIP-ZO. ........................................................

Figure 54 :

 54 Figure 54: The operational planning of fruit exported with a storage plan base on Yi [A], IVi [B], and Wi [C] in the case of DIP-ED. .......................................................

Figure 55 :

 55 Figure 55: Behavior of quality loss in fruit distribution regarding the DIP-ZO [A] and DIP-ED [B] model ................................................................................................

Figure 56 :

 56 Figure 56: Behavior of quality loss in fruit distribution regarding the other operational research model: Note: TR: transportation ...............................................

  The non-deterministic polynomial-time hardness NSGA-II Non dominated sorting genetic algorithm II PBH A priority-based heuristic PGEN Pareto surface generation for convex multi-objective instances PMi Price of material per ctn each day Q The quality of a product q0 An initial quality q0i Cost of natural decay with zero-order kinetics qei Cost of ND with exponential decay qoi The total cumulative holding cost of fruit export based on zero qoxi: The total cumulative holding cost of fruit exported without storage planning Qoyi The total cumulative holding cost of fruit exported with storage R: The gas constant ri: Revenue derived from the sale of exported fruit RMSE Root mean square error SA Simulation annealing SC Storage cost of reefer container per ctn per day at an optimal SCM The supply chain management s ij : Quantity of fruit transported by route j and sold immediately Quantity of fruit in inventory transported by route j and sold ondayi WS: Weighted sum method x ij : Quantity of fruit exported from packaging house on day i with route j y ij k Quantity of fruit exported from packaging house on day i , by route j ZO Zero-order kinetic

Figure 1 :

 1 Figure 1: Total import value of fruit and vegetable in Europe, United States, and Rest world in[START_REF] Velychko | Integrated modeling of solutions in the system of distributing logistics of a fruit and vegetable cooperative[END_REF]-2018. Source: (Segovia et al., 2019)

Figure 2 :

 2 Figure 2: General structure of the distribution part of the fruit exportation supply chain.Food waste refers to the decrease in the amount or quality of food, caused by decisions and actions made by vendors, food service providers, and consumers. In other words, it concerns the removal of the food supply chain, which is still proper for human consumption. It is done either by choice or after the food is spoiled or expired due to poor stock management or neglect.Quality loss refers to negative attributes such as spoilage, contamination with filth, discolouration, off-odours, and positive characteristics such as the origin,

Figure 3 :

 3 Figure 3: Scope of food loss (FL), food waste (FW), and quality loss (QL) in the food supply chain.

[ 1 ]

 1 Figure 4: the relationship between Grm 2 level and %MI (Kamhangwong 2016a).

Figure 5 :

 5 Figure 5: The percentage of remaining quality of food product caused by ND at various times: linear function [A] and non-linear function [B].

  Description of the research 12. Ferrer, A. et al. (2007) A m i x e d -Integer linear program for scheduling grape harvesting operations to wine production. The model takes into account the costs of harvest and loss of quality in the grapes to delay the harvesting and processing stages 13. Cittadini, E.D. et al. (2008) A multi-objective model for planning the production of fruit. The model optimises human resource utilisation and maximises fruit production. The model explores the robustness of solutions against price variations focusing on cherries 14. Bai, R. et al. (2008) A practical fresh produce inventory control and shelf space allocation model was built and presented upon the situation as described by a UK retailer 15. Blackburn, J. and Scudder (2009) A hybrid model to design a supply chain of perishable foods, based on optimising the value of the marginal product over time was developed. The model considers the changing value of perishable foods over time that tends to decline according to quality deterioration 16. Arnaout J.P.M. and Maatouk, M. (2010) This research presents mixed-integer linear programming for scheduling grape harvesting operations to wine production. Two heuristics are applied and compared to reduce computational time. The model is based on that of Ferreretal. (2007) but adapted to be applicable in Europe 17. Bohle, C.et al. (2010) Extension of a mixed-integer linear programming model to a stochastic one in which the productivity of labour is an uncertain parameter. The study analyses how labour affects the quality and quantity of fruit to harvest

  model to analyse investment decisions in the fruit industry. The decision variables are variety and density of fruit to plant and different scenarios related to types of financing plans over time 26.Velychko, O. (2014) The development of integrated methods and a model of preparing decisions in the logistics of the fruit and vegetable servicing cooperative is presented. Possible alternatives and existing limitations in separate technological, logistical and marketing businsse processes are explored 27.Lambert, G.F.and et al. (2014)

Figure 6 :

 6 Figure 6: Analytical modelling approach in FDM.

  a golden search algorithm to find the optimal solution of the model.[START_REF] Hester | Modelling apple orchard systems[END_REF] present a dynamic simulation model based on the interactions of the complex biological and economic relationships in an apple orchard system. The bioeconomic model is used to maximise the net present value of one orchard system by selecting optimal thinning strategies over 15 years.Considering stochastic modelling approaches, we found that there are a few research papers which apply stochastic modelling to solve problems in FDM. For instance, Broekmeulen, R.A. (1998) presents simulation models to determine an assignment plan based on historical data. He applied the local search techniques to find an assignment plan and analyse the effect of the assignment plan on several storage policies.Van der Vorst, J.G. and et al. (2014) propose an integrated approach towards logistics, sustainability, and food quality analysis by introducing a new simulation environment. A case example of pineapple illustrates the benefits of its use concerning speed and quality of integrated decision making.[START_REF] Morande | Design and validation of a decision support system for oenologists[END_REF] studied the periodical flowering-harvesting model to maximize demand and level satisfied. They formulated a mathematical form by introducing a plant maturation curve and a loss function to express the growing process and the decaying process of the fresh products, respectively. The simulation results show that the supply chain management (SCM) model can help to derive an optimal solution to a complicated model in future research.

  extended a mixed-integer linear programming model to a stochastic variable in which the productivity of labour is an uncertain parameter. The study analysis showed that labour affected the quality and quantity of the harvest.[START_REF] Ahumada | Operational model for planning the harvest and distribution of perishable agricultural products[END_REF] proposed an operational model for planning the harvest and distribution of bell peppers and tomatoes that considered the colour stage of maturity to maximise revenue.[START_REF] Lambert | An expert system for predicting orchard yield and fruit quality and its impact on the Persian lime supply chain[END_REF] studied the impact of the Persian lime supply chain on orchard yield and fruit quality predictions in order to improve fruit production yield by using Fuzzy Logic, which involves an inference engine with IF-THEN type rules. González-Araya and et al.(2015) considered a mixed-integer linear programming model that incorporated fruit ripeness to support planning decisions in an apple orchard. The objectives were to minimise the number of resources used while ensuring the production of fruit with the best possible quality.

Figure 7 :

 7 Figure 7: The example of lag time in fresh fruit caused by ND with zero-order kinetics.

  [START_REF] Ferguson | Note: An application of the EOQ model with nonlinear holding cost to inventory management of perishables[END_REF] developed the classical economic order quantity (EOQ)

  3. The operation planning models dealing with perishable products very often fail to incorporate shelf life and stochastic features in the different functional areas of the food supply chain (Lemma, Y., and et al., (2014) and Ahumada, O. and Villalobos, J. R. , (2009)). Most operation research model use quality loss assessments that are inconsistent with quality loss assessment, and consumer evaluation in fruit quality, and comprehensive with the cost of actual quality loss both from fruit distribution.

Firstly

  , most fruit is a seasonal product in which prices can fluctuate enormously from day to day and hour to hour, contingent upon supply and demand in each season. In countries with articulated seasons, supplies are low at the start of the harvest season, so prices are high. After that, prices are at their lowest when the crop reaches maturity in the main production areas. Toward the finish of the season, prices usually increase again as supply diminishes. Prices are commonly most elevated during the off-season when only a small percentage of farmers can grow the crop. These considerations are illustrated in Figure8 (FAO, 2018).

Figure 8 :

 8 Figure 8: Supply and price changes (--) over a season.

Figure 9 :

 9 Figure 9: Flow chart of simple GA.

  value with no other objective function becoming worse off. A solution x*X and the corresponding outcome f(x*) is called Pareto optimal or Pareto efficient if there does not represent another solution that dominates it. The set of Pareto optimal results is regularly called the Pareto front, Pareto frontier, or Pareto boundary.

  the inclinations indicated by the DM at some stage(s) in solving the MOO problem.

Figure 10 :

 10 Figure 10: Classification of multi-objective methods. (Rangaiah, G.P., 2009).

  Currently, most evolutionary multi-objective optimisation (EMO) algorithms relate to Pareto-based ranking schemes. Evolutionary algorithms, for example, the NSGA-II and Strength Pareto Evolutionary Algorithm 2 (SPEA-2) have become standard approaches, although some schemes based on particle swarm optimisation and simulated annealing are significant. (S. Motta and et al., 2012). Those commonly known a posteriori methods are recorded underneath: 1. NSGA-II 2. Normal Boundary Intersection (NBI) 3. Modified Normal Boundary Intersection (NBIm) 4. Normal Constraint (NC) 5. Successive Pareto Optimization (SPO) 6. Directed Search Domain (DSD) 7. Pareto surface generation for convex multi-objective instances (PGEN) 8. Indirect Optimization based on Self-Organization (IOSO) 9. S-metric selection evolutionary multi-objective algorithm (SMS-EMOA) 10. Approximation-Guided Evolution 11. Reactive Search Optimization implemented in LION solver by using machine learning for adapting strategies and objectives.

  , and et al.'s research in 2016. They proposed two multi-objective approaches in 2016 and 2017. The previous paper represents a multi-objective vehicle routing problem with time windows dealing with Perishability (MO-VRPTW-P) and a two-phase heuristic algorithm based on Pareto variable neighborhood search-genetic algorithm considering temporal-spatial distance (STVNS-GA) to solve the problem. The later paper in 2018 represents a multiobjective VRP optimisation model with mixed time windows and perishability (MO-VRPMTWP) to minimise the distribution costs and maximise the freshness of perishable products. They use a heuristic algorithm ( STVNSGA) composed of a variable neighbourhood search ( VNS) method and a genetic algorithm ( GA) considering the spatiotemporal distance (ST) to solve the complex multi-objective problem. In the other papers,

  : multi-objective particle swarm optimisation, non-dominated sorting genetic algorithm (NSGA-II), non-dominated ranked genetic algorithm (NRGA), multi-objective genetic algorithm (MOGA) ABC Ant Colony Optimization, SA: simulated annealing algorithm, A priority-based heuristic (PBH)

Figure 11 :

 11 Figure 11: Illustration of the NSGA-II process. The first randomly generates a population Pt with N individuals and from them creates an Rt set of offspring solutions based on the problem range and constraint by using the genetic operators of crossover and mutation Parents and generated offspring are added to a new set called Rt, where nondominated sorting with obtains different non-dominated fronts, and after, each solution is assigned a crowding distance. A new parent population is formed from the fronts with a better range of non-dominance and the last frontier by choosing solutions with the best crowding distance. The pseudocode for the non-dominated sorting is given in Table10.

  Pareto technique) are used in solving problems in FDM. Most research papers indicated that the NSGA-II had been demonstrated as one of the most efficient algorithms for multi-objective optimisation in FDM. In contrast, the non-Pareto technique takes quite a lot of running time because it must be run several times to solve the problem. The approach usually is not appropriate for large-sized problems.The ILP model is presented in most operation researches model because of the ability of ILP to solve the NP-hardness problem and the large-sized problems in reallife instances. Decision variables used in FDM can be in the fields of production scheduling, harvest operation, distribution of product, and inventory control, which the researcher might be focused on studying just one field or several fields simultaneously.However, the recent researcher tried to develop an integrated operational modelling instead of a decoupled operational model to take advantage of integrating these two intertwined planning problems.The majority of the operation research models evaluate the quality loss in fruit, which does not correspond to the quality loss assessment of the fruit customer in reality. They have a focus on the application of shelf-life model to estimate the quality loss without taking into account the product stability or lag time before consumers can observe fruit quality deterioration. Ignoring lag time may lead to an underestimation of shelf life with significant economic losses for fruit exportation.

  objective mixed-integer programming model of an integrated distribution and inventory planning (DIP), which considers the quality loss of fruit from MI and ND.The developed DIP model focused on a bi-objective function, aim to maximise the net profit (NP) and to preserve the percentage of remaining quality of fruit (%RQ) in fruit distribution. NP is concerned with the difference between total revenue and logistics cost, which depend on supply, demand, and fruit price each day. The logistics cost per unit (ctn) in each activity of the fruit distribution are estimated based on activity-based costing ( ABC) systems. These costs cover expenses incurred from purchasing raw materials, handling, transportation, storage, logistics communication, order processing, and other costs, and the cost of quality loss.%RQ is evaluated covering both MI and ND in FDM so that the results obtained from the evaluation are consistent with the actual costs of quality loss from long-distance transportation and storage in fruit exportation. We estimated the degree of MI by considering the vibration level of two routes of transportation (the refrigerated truck (short route) and cargo ship (long route)). While the cost of MI is different depending on the fluctuation of fruit material price every day. The degree of ND is estimated through the shelf life model, taking into account the product stability based on two cases of kinetics model: zero-order kinetics (ZO) and exponential decay (ED). While the cost of ND is quantified in the form of the cumulative holding cost by modifying Economic

Figure 12 :

 12 Figure 12: The overview of methodology and way to analyse results for this research.

  AbbreviationDefinition Indices i the date fruit is exported from the packaging house j transportation route number k the number of days of fruit storage at the distribution centre Parameters CO communications and other costs of fruit exportation per ctn DMi total consumer demand each day Lj lead time for each route j MH cost of material handling per ctn msj maximum number of storage day of fruit for each a route of transportation PMi price of material per ctn each day SC storage cost of reefer container per ctn per day at an optimal temperature SPi selling price of fruit each day TCj transportation cost per ctn for route j TSi total fruit supply each day

Figure 13 :

 13 Figure 13: The position of Tri-axial accelerometers on a refrigerated container to monitor the vibration level of transportation for each route.

  Figure 14: The mangosteen bruising and the bruising diameter of mangosteen, mx: the maximum fruit diameter, mn: the minimum fruit diameter.

Figure 15 :Figure 16 :

 1516 Figure 15: The relation of the average vibration level and % MI of mangosteen.

Figure 17 :

 17 Figure 17: The cumulative %WL of mangosteen stored at 13C/75%RH at various holding times (day).

Figure 18 :

 18 Figure 18: The convex approximation for cumulative holding cost of mangosteen stored at 13C/75%RH at various storage times and different PMi.

  100

Figure 20 :

 20 Figure 20: The convex approximation for %MO of blueberry stored at 5C/85%RH at various holding times.

Figure 21 :

 21 Figure 21: The convex approximation for cumulative holding cost of blueberry stored at 5C/85%RH at various holding time and various PMi.

  Figure 22: Behavior of the model in a season of fruit exportation supply chain. 3 .5.2 Model formulations 1. Case1: DIP -ZO

  common total logistics cost (CTL) and the total cost of quality loss (TQL), which can be formulated by :

Figure 25 :

 25 Figure 25: Simulations of SC3 with high demand rate at the end of the season.

Figure 26 :Figure 27 :

 2627 Figure 26: Material price, total fruit supply, and demand.

  Figure 28: The relationship of the ES(P) and the PMi of fruit export.

Figure 33 :

 33 Figure 33: Adjusted weighted-sum approach. (Liu and Reynolds, 2014).

Figure 34 :

 34 Figure 34: Flow chart of NSGA-II algorithm.

Step5

  test each point on the Pareto front with three replications and present the standard deviation (SD) of each point in the form of error bars. Furthermore, to analyze the scope NSGAGenetic operator (crossover and mutation) Step6 Non-dominated sorting Step7 Replace chromosome of the optimal point on Pareto front that does not dominate each main objective, each treatment was subjected to an analysis of variance (ANOVA) and mean comparisons were carried out by Duncan's multiple range testing to group the different average of each point on Pareto front. The correlation coefficient between the two factors was

Figure 35 :Figure 37 :

 3537 Figure 35: Pareto-optimal front of the illustrative example for SC1

Figure 36 Figure 38 :

 3638 Figure 36 36, and Figure37.

Figure 39 :

 39 Figure 39: The Pareto front of the DIP-ZO model solving the multi-objective problem by using AWS-GA and NSGA-II.

  found that both the Pareto front curves of DIP-ZO and DIP-ED tend to have similar behaviours. The increase in %RQ can contribute more NP in fruit exportation in both cases. However, we found differences from the Pareto front comparison between DIP-ZO and DIP-ED. The Pareto fronts of the DIP-ZO have more strength of the relationship between the relative movements of net profit and %RQ than The Pareto front of DIP-ED with positive correlation coefficient (r) = 0.9524 and 0.9267, respectively. To r=0.9267 maximize NP of fruit exportation, preserving %RQ> 91.81 in the case of DIP-ZO and %RQ> 91.92 in the case of DIP-ED can achieve the desired results of fruit exportation, as they are represented in Table

4. 1 Figure 42 .

 142 Figure 42. All results are analysed in terms of the trend behaviour and the correlation between factors that are represented by the following.Firstly, we discern that there is the same solution space for the DIP-ZO and DIP-ED on the appropriate transportation and storage schedule. The decrease in transportation and storage time markedly affected the increase of %RQ and NP in FDM.To gain maximisation of NP and %RQ in both cases of DIP-ZO and DIP-ED, the average transportation time (Lj) should be 2 days, while the average storage time of fruit (k) should be 1.6 days and 0.195 days for the case of DIP-ZO, and DIP-ED respectively. The effects of holding time on NP and %RQ correspond with the characteristic of changing quality loss in fruit. The quality loss of fruit can be observed by the consumer after DFD. To avoid the increase of cost due to quality loss, we should hold fruit to sell with total holding time < DFD

Figure 42 :

 42 Figure 42: Relative importance regarding average holding time and net profit of the illustrative example in the case of DIP-ED.

Figure 43 :

 43 Figure 43: Relative importance regarding the average distribution scheme and net profit of the illustrative example in the case of DIP-ZO.

Figure 44 :

 44 Figure 44: Relative importance regarding the average distribution scheme and net profit of the illustrative example in the case of DIP-ED. Firstly, we observed that the behaviour over the distribution scheme is quite similar in both cases of DIP-ZO and DIP-ED. Choosing x1 together with y1 has the most influence on changing both NP and %RQ on FDM, while the effects of choosing x2 and y2 are not as apparent on NP and %RQ maximization as shown in Figure 43 and Figure 44. These scatterplots represent a spectrum of different correlation coefficient values for the relationship between two continuous variables, as shown in the details of Table 20. We found that there is a fairly strong positive relationship between x1 and the strong negative relationship of y1 with NP and %RQ in both cases of DIP-ZO and DIP-ED. They present the correlation values at r ( NP -x1 ) = 0.9905, and r ( NP -y1 ) = -0.9713 for DIP-ZO, and at r ( NP -x1 ) = 0.9817, and r ( NP -y1 ) = -0.9629 for DIP-ED. However, we cannot find a relationship between x2 and y2 with NP and %RQ. This result corresponds with the studied effect of the appropriate holding time of fruit on FDM in 4.1.3. This finding demonstrates how choosing a shorter route to transport fruit can help to increase the NP and %RQ in FDM.

  of DIP-ZO and DIP-ED is similar. They require the distribution scheme with the maximum x1 at 180 ctn and 173 ctn for the case of the DIP-ZO, and the case of DIP-ED, respectively, while, y1 needs inferior with 20 ctn and 27 ctn for the case of the DIP-ZO and the case of DIP-ED. No selection was found for the use of the long route without storage (x2) and with storage planning (y2) for exportation in both cases of DIP-ZO and DIP-ED.

Figure 45 :

 45 Figure 45: The amount of cumulative quality loss in fruit with zero-order kinetics and exponential decay.

*

  and FIFO with 1.4 days of storage time in the case of DIP-ZO and 1.6 days of storage time in the case of DIP-ED can decrease fruit waste and inventory costs, as shown in Table22. Table 22: Summary of inventory planning at the maximum point of NP and %RQ in the cases of DIP-ZO and DIP-ED. For all fitness values, a, b different letters within a row indicate significantly different (P < 0.05)4.1.5 Total GHG emission in fruit exportationIn this section, we study the indirect effects of the fruit distribution schedule based on quality loss and NP in FDM. We estimate the total GHG emission in terms of the CO2 equivalent (CO2 e) in transportation and storage of fruit exportation. The total CO2 e emissions under different types of ND: DIP-ZO and DIP-ED will be obtained by decoding the optimal solution in the last iteration cycle. The experimental results of the relative importance between CO2 e emissions, NP and %RQ in both cases of DIP-ZO and DIP-ED are shown in Figure46and Figure47Based on the data analysis, we found that both graphs of DIP-ZO and DIP-ED have the same trend behaviour. Total CO2 e emissions in FDM decrease with the rise of both %RQ and NP, which are represented by the negative correlation, r < -0.9000, as shown in the details of Table23.

Figure 46 :

 46 Figure 46: The relative importance regarding the average of total CO2 e emissions and net profit of the illustrative example in the case of DIP-ZO.

Figure 47 :

 47 Figure 47: Relative importance regarding the average of total CO2 e emissions and net profit of the illustrative example in the case of DIP-ED

  NP and %RQ in the long-term decisions of FDM, especially in regards to the occurrence of supply shortages because of a climate unsuitable for production. To solve the problem of sustainability in the author's perspective, the exporter needs to look for another supplier to provide material in the expected year of supply shortages, or they should have long-term cropping plans together with the farmer by carrying over the effects of demand and supply in the yearly decisions. The horticultural technology should be used to control fruit supply and reduce the effects of demand in the event of an increase at the end of the season.

Figure 48 :

 48 Figure 48: The optimal inventory level in each scenario: SC1 [A], SC2 [B], and SC3[C].

Figure 49 :

 49 Figure 49: Relative importance regarding the percentage of quality loss due to MI and ND and net profit of the illustrative example in the case of DIP-ZO

  operational level dealing with fruit exportation planning each day. Considering the solution space in both cases of DIP-ZO and DIP-ED, two operational plans are dealing with the decision of the fruit exporter. The first operational plan considers the fruit exported without a storage plan. It concerns two decision variables: the total number of fruit exported in each day (Xi) and the total number of fruit exported without storage planning and sold each day (Si). The second operational plan regards fruit exported by a storage plan. It concerns two decision variables: the total number of fruit exported with storage planning each day (Yi) and the total number of fruit in inventory sold each day ( Wi). All decision variables of fruit exportation planning each day are based on the following decision variables: Xi, Yi, Si, Wi, and the inventory level of each day (IVi), can be represented in from Figure 51 to 54. Firstly, Xi is the quantity of fruit exported without a storage plan from a packaging house each day. It concerns a daily fruit ordering plan from the orchard in which the exporter has to order fruit under the limit of total fruit supply each day, as shown an example in point (a). At the same time, the fruit exporter also has to choose the shortest transportation time (Lj=2 days) to export fruit to the distribution centre, as shown in Figure 51[A] and Figure52 [A]. Secondly, Si is the total quantity of fruit exported without a storage plan that arrives at the distribution centre and sold at the distribution centre each day, as shown an example in point (b) in Figure 51[B] and Figure52 [B].

Figure 51 :Figure 52 :

 5152 Figure 51: The operational planning of fruit exported without a storage plan based on Xi [A] and Si [B] in the case of DIP-ZO

Figure

  Figure 53[B] and Figure 54[B].

Figure 53 :Figure 54 :

 5354 Figure 53: The operational planning of fruit exported with a storage plan base on Yi [A], IVi [B], and Wi [C] in the case of DIP-ZO.

  (a) (c)) to avoid quality loss in fresh fruit before reaching the consumer. The THT differs depending on the nature of the loss of quality and lag time of quality loss occurrence in each fruit, in which the studied amount of the cumulative quality loss in fruit in both cases of zero-order kinetics and exponential decay shows that THT should be less than the date that fruit deterioration begins to appear (DFD >4days), as shown in Figure53[C] and Figure 54[C].

Figure 55 :

 55 Figure 55: Behavior of quality loss in fruit distribution regarding the DIP-ZO [A] and DIP-ED [B] model

Table 13 :

 13 The vibration level (Gj 2 ) and %MIj each transportation mode. .....................

Table 14 :

 14 CO2e emission factors used for each activity in the fruit distribution. .......

Table 15 :

 15 The example of x ij and s ij planning for fruit exportation. ............................

Table 16 :

 16 The example of y ij k and w ij planning for fruit exportation. .........................

Table 17 :

 17 Summary of statistics for the quantity of fruit exported, net profit, and holding time in each scenario ....................................................................................

Table 18 :

 18 Summary of the statistics for the fitness value of the main objective

function in each type of quality loss. .......................................................................... viii

Table 19 :

 19 Summary of the correlation values for the relationship of the holding time with NP and %RQ in both cases of DIP-ZO and DIP-ED models. ......................

Table 20 :

 20 Summary of the correlation values for the relationship between the decision variable and NP and %RQ. ...........................................................................

Table 21 :

 21 Summary of the distribution scheme at the maximum points of NP and %RQ in case DIP-ZO and DIP-ED. .............................................................................

Table 22 :

 22 Summary of inventory planning at the maximum point of NP and %RQ in the cases of DIP-ZO and DIP-ED. ..............................................................................

Table 23 :

 23 Summary of the correlation values for the relationship between CO2 eFigure 1: Total import value of fruit and vegetable in Europe, United States, and Rest world in 2014-2018. ................................................................................................

emissions and NP and %RQ in FDM. ..........................................................................

Table 24: Summary of statistics for the quantity of fruit exported, net profit, and holding time in each scenario. .................................................................................... Table 25: Summary of correlation values for the relationship of the holding time with NP and %RQ in both cases of DIP-ZO and DIP-ED model ................................ ix LIST OF FIGURES

Table 1 :

 1 The optimal temperatures and moisture conditions for some common fruits and vegetables.

	Product	Optimal	Chill	Optimal
		Storage	Point	Humidity
		Temperature	(C)	(% RH
		(C)

) Top Ice Accepted Ethylene Production Sensitive to Ethylene Approximate Storage Life

	Apples	-1-4	-	9 0 -95 No	High	Yes	1-12 months
	Apricots	-1-0	-	9 0 -95 No	High	Yes	1-3 weeks
	Bananas,	13-16	12	85-95 No	Medium	No	-
	ripe
	Blackberries	0-1		90-95 No	Very Low No	2-3 days
	Asparagus	-	-	9 5 -100 No	No	Yes	2-3 weeks
	Avocados,	3-7	2	85-95 No	High	Yes
	ripe

Table 2 :

 2 Activities in each type of logistics cost.

	Logistics Cost Procurement	Steak holder Farmers	Detail Transportation cost of purchasing supplies
		Groups of farmers	such as fertiliser, pesticides, and
		Government	equipment; communication cost between
		Collectors	suppliers and farmers
		Exporters
	Material	Farmers	Harvesting cost, handling cost, grading
	handling	Groups of farmers	and depreciation cost of materials and
		Collectors	handling equipment, packing and package
		Exporters	cost and loss of harvesting
	Transportation	Exporters	Gas, depreciation of vehicles, maintenance
			of vehicles, driver salaries, and losses
			during delivery
	Inventory	Exporters	The opportunity cost of inventory of
		Wholesalers and	supplies, energy consumption related to
		Retailers	the temperature-controlled distribution
	Customer	Farmers	Communications cost between farmers
	communications	Groups of farmers	and customers, traceability system and
		Exporters	labelling
		Wholesalers and
		retailers
		Consumer
	Source: Ongkunaruk, P. and Piyakarn, C., 2011

Table 3 :

 3 Summary of all the revised papers dealing with FDM.

	Authors	Description of the research
	18. Morande, H. and
	Maturana, S. (2010)

Table 4 :

 4 Modeling approaches used by the analyzed papers.

	Authors 1. Willis, C. and Hanlon, W. (1976) 2. Starbird, S.A (1988) 3. Maia, L.O.A. et al. (1997) 4. Broekmeulen, R.A. (1998) 5. Gigler, J.K., et al. (2002) 6. Hester, S.M. and Cacho, O., (2003) 7.Vitoriano, B. et al. (2003) 8.Blanco, A.M. et al. (2005) 9.Caixeta-Filho, J.V. (2006) 10. Ortmann, F.G. et al. (2006) 11. Masini, G.L. et al. (2007) 12. Ferrer, A. et al. (2007) 13. Cittadini, E.D. et al. (2008) 14. Bai, R. et al. (2008) 15. Blackburn, J. and Scudder (2009) 16. Arnaout J.P.M. and Maatouk, M. * Modelling approach of the reviewed papers Deterministic Stochastic ILP NLP MOLP SM HEU HYB SP DP * * * * * * * * * * * * * * * * * * * * 17. Bohle, C. et al. (2010) * 18. Morande, H. and Maturana, S. 19. Ahumada, O. et al. (2011) *
	* * * * * 30. Nadal-Roig, E. and Plà, L.M.(2015) * 20. Rong, A., et al. (2011) 21. Amorim, P. et al. (2012) 22. Yu, Y. et al. (2012) 23.Banaeian, N. et al. (2012) 24. Ampatzidis, Y.G. et al. (2013) 25.Catalá, L.P. et al. (2013) 26.Ve l ychko, O. (2014) 27.Lambert, G.F. et al. (2014) 28. Van der Vorst, J.G. et al. (2014) 29. González-Araya, M.C. et al. (2015) * 31.Orjuela-Castro, J.A. (2017) 32 Musavi, M. and Bozorgi, A.(2017) 33 Grillo, H., et al. (2017) * 34. Li, Y., Guo, H. and Zhang, Y., 35. Tordecilla-Madera, R.,and et.al., * 36. Tiwari, S., et al. (2018) * 37. Hua, J., Gu, S. and Zhang, L., * 38. Nguyen, T.D., et al. (2020) 39. Sahebjamnia, N., et.al, (2020) 24	* 2	* * * * 5	* * * 5	2	* 4	0	2
	Note: HEU Heuristics algorithm and metaheuristics, HYB Hybrid models

Table 5 :

 5 Functional area used by the analyzed papers.

	Authors 1. Willis, C. and Hanlon, W. (1976)	PL *	H *	Functional area P	D	I
	2. Starbird, S.A (1988) 3. Maia, L.O.A. et al. (1997) 4. Broekmeulen, R.A. (1998) 5. Gigler, J.K., et al. (2002) 6. Hester, S.M. and Cacho, O., 2003 7. Vitoriano, B. et al. (2003) 8. Blanco, A.M. et al. (2005) 9.Caixeta-Filho, J.V. (2006) 10. Ortmann, F.G. et al. (2006) 11. Masini, G.L. et al. (2007) 12. Ferrer, A. and et al. (2007) 13. Cittadini, E.D. et al. (2008) 14. Bai, R. et al. (2008) 15. Blackburn, J. and Scudder (2009) 16. Arnaout J.P.M. and et.al. (2010)	* * *	* * * * * *	* * * * * * *	* * * * * *	* *

Table 5 :

 5 Functional area used by the analyzed papers.

	Authors 17. Bohle, C. et al. (2010) 18. Morande, H. and Maturana, S. (2010) 19. Ahumada, O. et al. (2011) 20. Rong, A., et al. (2011) 21. Amorim, P. et al. (2012) 22. Yu, Y. et al. (2012) 23.Banaeian, N. et al. (2012) 24. Ampatzidis, Y.G. et al. (2013) 24.Catalá, L.P. et al. (2013) 25.Velychko, O. (2014) 26.Lambert, G.F. et al. (2014) 27. Van der Vorst, J.G. et al. (2014) 28. González-Araya, M.C. et al. (2015) 29. Nadal-Roig, E. and Plà, L.M.(2015) 30. Li P. et al. (2016) 31.Orjuela-Castro, J.A. (2017) 32 Musavi, M. and Bozorgi, A., (2017) 33 Grillo, H. et al., 2017 34. Li, Y., Guo, H. and Zhang, Y., (2018) 35. Tordecilla-Madera, R., et.al., (2018). 36. Tiwari, S., et al. (2018) 37. Hua, J., Gu, S. and Zhang, L., 2019. 38. Nguyen, T.D. et al., 2020 39. Sahebjamnia, N.,and et.al, 2020.	PL * * 5	Functional area P * * * * * * * 13 H * * * * * * 14	D * * * * * * * * * * * * * * 18	I * * * * * * * * * * * * * 12

Table 6 :

 6 Characteristics of distribution planning on different hierarchical levels.

	Decision level Planning horizon Distribution network design 1-5 years None, or years Maximize net Time representation Objective function revenue or return on assets	Frequency of analysis Major studies once a year special studies if needed
	Distribution network planning	1-12 months	Days, weeks, months	Minimize total product mix varying revenue by maximize net demand or forecasted meeting costs of	Once a month
	Transportation planning	1-30 days Minutes, hours, days	Minimize myopic distribution costs	Once a day and event-driven rescheduling during the day
	Source: Shapiro, 2007

Table 7 :

 7 Decision level used by the analyzed papers.

	Authors 1. Willis, C. and Hanlon, W. (1976) 2. Starbird, S.A (1988) 3. Maia, L.O.A. et al. (1997) 4. Broekmeulen, R.A. (1998) 5. Gigler, J.K., et al. (2002) 6. Hester, S.M. and Cacho, O., 2003 7.Vitoriano, B. et al. (2003) 8.Blanco, A.M. et al. (2005) 9.Caixeta-Filho, J.V. (2006) 10. Ortmann, F.G. et al. (2006) 11. Masini, G.L. et al. (2007) 12. Ferrer, A. et al. (2007) 13. Cittadini, E.D. et al. (2008) 14. Bai, R. et al. (2008) 15. Blackburn, J. and Scudder (2009) 16. Arnaout J.P.M. and Maatouk, M. (2010) 17. Bohle, C. et al. (2010) 18. Morande, H. and Maturana, S. (2010) 19. Ahumada, O. and Villalobos, J.R., (2011) 20. Rong, A., et al. (2011) 21. Amorim, P. et al. (2012) 22. Yu, Y. et al. (2012) 23.Banaeian, N. et al. (2012) 24. Ampatzidis, Y.G. et al. (2013) 24.Catalá, L.P. et al. (2013) 25.Ve l ychko, O. (2014) 26.Lambert, G.F. et al. (2014) 27. Van der Vorst, J.G. et al. (2014) 28. González-Araya, M.C. et al. (2015) 29. Nadal-Roig, E. and Plà, L.M.(2015)	Decisions level ST * * * * * * * * * * * * * * * * * * * * * * * * * *	O * * * * * * * * * * * * * * *

Table 7 :

 7 Decision level used by the analyzed papers.

	Authors 31.Orjuela-Castro, J.A. (2017) 32 Musavi, M. and Bozorgi, A., (2017) 33 Grillo, H., et al., 2017 34. Li, Y., Guo, H. and Zhang, Y., (2018) 35. Tordecilla-Madera, R., et.al., (2018). 36. Tiwari, S., et al. (2018) 37. Hua, J., Gu, S. and Zhang, L., 2019. 38. Nguyen, T.D., et al., 2020 39. Sahebjamnia, N.,et.al, 2020. Note: Strategical(S), Tactical (T), and Operational (O)	Decisions level ST * * * * * * * * * 8 28	O * * * * * * * 22

Table 8 :

 8 Evolutionary algorithm dealing with the fresh fruit supply chain. to account for different classes of constraints and to fine-tune the parameters of the algorithm can be rather delicate. SA is very slow to optimise the problem in the fruit supply chain, especially if the cost function is expensive to compute.

	Authors 1.Hester, S. and Cacho, O. (2003)	GA X	Evolutionary algorithms BB SA	AC
	2.Ferrer, J.C. et al. (2007)		X
	3.Cittadini, E.D. et al. (2008)		X
	4.Bai et al. (2008)		X
	5.Arnaout , J. and Maatouk, M. (2010)	X
	6. Amorim, P. et al. (2012)	X
	7. Li, P. et al. (2016)	X
	8. Musavi, M. and Bozorgi-Amiri, A.,	X
	9 Li, Y., Guo, H. and Zhang, Y., (2018)	X
	10 Hua, J., Gu, S. and Zhang, L., 2019.			X
	11. Sahebjamnia, N., et.al, 2020.	X
	Among the evolutionary algorithms applied to solve FDM problem, GA is
	an efficient optimisation algorithm to solve the problem in the FDM. It is faster than the
	other algorithms and can be applied for NP -problem under non-linear constraint, and
	various conditions in fruit supply chain management. In the case of BB, this algorithm
	use rounded relaxation and branch and bound methods such as classical mathematics

methods to solve them. However, when exiting too many network nodes, this problem turns out to be an NP-hard problem . Regarding simulation annealing (SA), the tailoring work required

Using Multi- Objective Approach

	No-Preference Methods (e.g., Global Criterion and Neutral Compromise Solution)

(e.g., Nondominated Sorting Genetic Algorithm and Multi-Objective Simulated Annealing) A Priori Methods (e.g., Value Function Method and Goal Programming) Interactive Methods (e.g. Interactive Surrogate Worth Tradeoff and NIMBUS method) A Posteriori Methods Using Scalarization Approach (e.g., Weighting Method and -Constraint Method)

Table 9 :

 9 Summaries of the multi-objective optimisation analyses of all the revised papers dealing with the application of perishable products.Table9: Summaries of the multi-objective optimisation analyses of all the revised papers dealing with the application of perishable products. Summaries of the multi-objective optimisation analyses of all the revised papers dealing with the application of perishable products.

	Authors Gong, W. and Fu, Z., (2010)	Economic To minimise distribution cost	The objective function Quality and Sustainability safety To minimise shelf life loss -	Multi-Objective Optimization analysis ABC customer classification
	Amorim and et al. (2011)	To minimise lot sizing		To maximise scheduling	-	A hybrid genetic algorithm based on NSGA-II
	Amorim and et al. (2012)	To minimise the total costs	To maximise the remaining shelf life	-	A hybrid genetic algorithm based on NSGA-II
	Govindan, K., and et al. (2014).	To optimise the number of products delivered to lower stages and routes at each level.	To determine the number and location of facilities	To reduce costs affected by carbon footprint and greenhouse gas emissions	Comparing MOPSO with conventional GA based on metaheuristics: MOGA, NRGA, and NSGA-II.)

Table 12

 12

	Abbreviation of indices, parameters and decision variables
	Abbreviation Decision variables bi ci di gi hi mi q0i qei ri %RQ	Definition communications and other costs of fruit the material cost of export fruit transportation cost of export fruit cost of MI due to handling and transportation storage cost of fruit material handling cost of export fruit cost of natural decay(ND) with zero-order kinetics (ZO) cost of ND with exponential decay(ED) revenue derived from the sale of exported fruit the percentage of remaining quality for total fruit exported at DC in a season
	TQL	the total cost of quality loss
	x ij	quantity of fruit exported from packaging house on day i with route j without storage planning
	y ij	k

Table 13 :

 13 The vibration level (Gj 2 ) and %MIj each transportation mode.

	Transportation mode	m	G j 2	%MI j
	Refrigerated truck Cargo ship	1 2	1.57 .73 1.2 3.62

Table 14 :

 14 CO2e emission factors used for each activity in the fruit distribution.

	Activity Transportation,	CO 2 -e emission factor estimation Route 1: Refrigerator Truck
	CTj		 Overall weight of fruit = 5,500 kg/ctn
			 Emission = 1.8 tkm/kg of total product
			 %100 Empty trucks on return = 0.0446 kg CO2e/tkm
		So,	CT1 = 1.8 tkm/kg *0.0446 CO2e/tkm* 5,500 kg/ctn
			= 441.5 Kg CO2e/ctn
		Route 2: Cargo ship
			 Overall weight of fruit = 5,500 kg/ctn
			 Emission = 4.3 tkm/kg of product
			 %100 Empty cargo ship on return = 0.0100 kg CO2e/tkm
		So,	CT2 = 4.3 tkm/kg *0.0100 CO2e/tkm* 5,500 kg/ctn
			= 236.5 Kg CO2e/ctn

Table 15 :

 15 The example of x ij and s ij planning for fruit exportation. We suppose route j =1, L j = 2 days, the end of the season for fruit exports (EOS)=40 days

							Day in a season for fruit export
				1	2	3	4	5	6		… EOS-Lj …	EOS
	xjj			x1,1 x 2,1	x 3,1	x 4,1	..	..	..	..	0	0
		Packing house
	sij	Distributio	n center	s1,1 =0	s2,1= 0	s3,1 = x1,1	s4,1= x2,1	s5,1= x3,1	s6,1= x4,1	..	..	..	sEOS, 1= xEOS -Lj,1

*

Table 16 :

 16 The example of y ij k and w ij planning for fruit exportation.

	y ij k w ij	Packaging house Inventory	1 y1,1 1 y2,1 1 y3,1 1 y4,1 1 2 3 4 y1,1 2 y2,1 2 y3,1 2 .. y1,1 3 y2,1 3 . .. y1,1 4 . . .. y1,1 5 . . .. y1,1 6 . . .. y1,1 7 . . .. y1,1 8 y2,1 8 y3,1 8 .. 00 0 y 1,1 1 y2,1 1 5 .. .. .. .. .. .. .. .. 00 0 y1,1 2 00 0 00 0 00 0 00 0 00 0 00 0 0 0 0 y1,1 1 y 2,1 1	6 .. .. .. .. .. .. .. .. y3,1 1 y2,1 2 y1,1 3	7 .. .. .. .. .. .. .. .. y4,1 1 y3,1 2 y2,1 3 y 1,1 4	8 .. y1,1 5 .. .. .. .. .. .. .. .. .. .. ..	9 .. .. .. .. .. .. .. .. .. .. .. .. .. y1,1 6	MHT .. .. .. .. .. .. .. .. .. .. .. .. .. .. y 1,1 7	11 .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. y1,1 8	.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..	.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..	E O S -Lj .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..	.	… 00 EOS 00 00 00 00 00 00 0 y EOS,1 8 =0 . y ( EOS -Lj ) ,1 1 y ( EOS -Lj ) ,1 2 . .. . .. . .. . .. . .. . y ( EOS -Lj ) ,1 8
		Distribution center

Table 17 :

 17 Summary of statistics for the quantity of fruit exported, net profit, and holding

	time in each scenario
	SC 1 2 3	NP *(baht) 220,507,934b 91.81b 181b %RQ Decision variable (ctn) x1* x2 y 1 0c 19b 252,101,724a 92.06a 190a 1b 9c 142,760,415c 88.39c 124c 9a 51a	y 2 0 0 16a	Holding time TT ST 2.00b 0.16b 2.02b 0.07b 2.38a 1.03a

*For all decision variables and cost of exportation, a, b, and c different letters within a column indicate significantly different (P < 0.05). * There is an interaction between these factors

Table 18 :

 18 Summary

	Fitness value f1 best (NP) f2 best (%RQ)	DIP-ZO AWS-GA NSGA-II 211,202,497b 220,507,934a 84.12b 91.81a	DIP-ED 212,330,284b AWS-GA 86.50b	NSGA-II 220,417,601a 9 1 .92a

of the statistics for the fitness value of the main objective function in each type of quality loss. *All fitness value are compared by the paired sample t-test, and a, b different letters within a row indicate significantly different (P < 0.05)

Table 19 :

 19 Summary of the correlation values for the relationship of the holding time withNP and %RQ in both cases of DIP-ZO and DIP-ED models.

	Model	F1	The correlation value Factor F2	r (F1-F2)
	DIP-ZO DIP-ED	NP NP %RQ %RQ NP NP %RQ %RQ	TT ST TT ST TT ST TT ST	-0.5543 -0.9502 -0.5377 -0.9965 -0.6242 -0.9593 -0.5294 -0.9893
	4.1.

4 Studying the effects of the appropriate fruit distribution scheme on FDM

	Fruit distribution scheme is the most important strategy for fruit export

management to maximize NP and %RQ. It involves the fruit exportation planning by appropriately considering total logistics cost, total revenue, and the cost of quality loss.

Table 20 :

 20 Summary of the correlation values for the relationship between the decision variable and NP and %RQ.

	Model DIP-ZO DIP-ED	F1 NP NP NP NP %RQ %RQ %RQ %RQ NP NP NP NP %RQ %RQ %RQ %RQ	The correlation value Factor F2 x1 x2 y1 y2 x1 x2 y1 y2 x1 x2 y1 y2 x1 x2 y1 y2	r (F1-F2) 0.9905 -0.0429 -0.9713 -0.7952 0.9773 0.0742 -0.9730 -0.7755 0.9817 0.0611 -0.9629 -0.6388 0.9572 0.2230 -0.9677 -0.5805

Table 21 :

 21 Summary of the distribution scheme at the maximum points of NP and %RQ in case DIP-ZO and DIP-ED.

	Model DIP-ZO DIP-ED	NP 220,507,934 220,417,601	% RQ 91.81 91.92	x1 180 173	distribution scheme x2 y1 0 20 0 27	y2 0 0

Table 24 :

 24 Summary of statistics for the quantity of fruit exported, net profit, and holding time in each scenario.

	SC 1 2 3	NP *(baht) 220,507,934b 252,101,724a 142,760,415c	% RQ 91.81b 92.06a 88.39c	Inventory level (ctn) 32b 14c 59a
		However, reducing the inventory level may not be the best way to maximize

* 1

ACKNOWLEDGEMENTS

I cannot express enough thanks to my committee for their continued support and encouragement: Gilles NEUBERT, Co-director of the thesis; Aicha SEKHARI, Co-supervisor; Yacine OUZROUT, Director of the thesis. I offer my sincere appreciation for the learning opportunities provided by my committee. I would like to thank Erasmus Mundus the FUSION Project, University Lumière Lyon2, and DISP Lab, for their perfect support of my PhD scholarship. I would like to thank DISP lab teachers, researchers, Ph.D. students, administrative, and technical staff. I would like to thank Nopasit CHAKPITAK, Dean of International College of

this kind of algorithm means that we leave it up to chance whether we will be somewhat close to the optimal solution or miles away from it.

Whenever we fail to solve with the methods mentioned above, using traditional optimisation methods, human beings have a natural tendency to follow the way nature has solved complex optimisation problems. Some natural processes, such as biological, physical processes are modelled artificially to develop optimisation tools for solving problems. A considerable amount of literature is available on non-traditional optimisation tools. These methods include genetics algorithm (GA) (Holland, J., 1975 and b Holland, J., 1992 ), genetic programming (GP) [START_REF] Koza | Genetic Programming: on the Programming of Computers by Means of Natural Selection[END_REF], evolution strategies (ES) [START_REF] Vent | Ingo, Evolutionsstrategie-Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. 170 S. mit 36 Abb[END_REF], simulated annealing (SA) [START_REF] Metropolis | Equation of state calculations by fast computing machines[END_REF], ant colony optimisation (ACO) [START_REF] Dorigo | Optimization, learning and natural algorithms[END_REF], differential evolution (DE) [START_REF] Storn | Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces[END_REF], cultural algorithm (CA) [START_REF] Reynolds | An introduction to cultural algorithms[END_REF] Reynolds, R.G., 1994, particle swarm optimisation (PSO) [START_REF] Kennedy | Particle swarm optimization[END_REF], evolutionary programming (EP) [START_REF] Fogel | Artificial intelligence through simulated evolution[END_REF], Tabu search [START_REF] Gendreau | An introduction to tabu search[END_REF], and others. The working principles of some of these nontraditional optimisation tools are explained below in brief.

Genetic algorithm ( GA) , a population-based search and optimisation algorithm that works based on the mechanics of natural genetics and Darwin's principle of natural selection was introduced by Holland. It starts with a population of randomly generated solutions. The design variables can be represented using either binary numbers or real values, and accordingly, the GA is called binary-coded GA or real-coded GA, respectively. For more detail, it will be described in 2.5.2

Cultural Algorithm is a modified version of GA. Besides its population of solutions, it maintains a belief space, which contains an elitist solution. As iteration proceeds, the belief space may also get updated. The elite solution modifies the fitness values of the population before forming the mating pool. As useful information is added with the help of an elite solution, this algorithm is expected to be faster than the conventional GA.

CHAPTER III MATERIAL AND METHODOLOGY

The main objective of this research is to develop a multi-objective integrated distribution and inventory planning (DIP) of fruit exportation that considers a fitting exchange between the two fundamental goals of maximising net profit (NP) and % remaining quality (%RQ) for value chain analysis. We apply MI and ND based on two case studies of ZO and ED into the DIP model. The optimal Pareto fronts of both cases are studied for the effects of quality loss on NP and to analyse the value chain in terms of the competitive advantage in FDM.

In this chapter, we design the experiment into the following.

1) Input data: we present various input factors incorporated into the DIP model. These factors consist of common logistics costs in section 3 . 1, the cost of mechanical injury in section 3.2, the cost of natural decay in section 3.3, and greenhouse gas emissions during each activity in section 3.4.

2) Problem setup: we discuss the state problem of fruit exportation in 3.5.1 and model formulation in case of a quality loss with zero-order kinetics (DIP -ZO) and exponential decay (DIP -ED) in section 3.5.2.

3) Formal model: we give the numerical study base on the history data of fruit exportation in section 3.6. The numerical set consists of the quantity of supply and demand of fruit export in section 3. 6. 1, and the material and market price of fruit exportation in section 3.6.2. 4) Solving method: we propose two multi-objective optimisation methods in section 3.7: the posterior methods using an adjusted weight-sum approach with genetic algorithm (GA) (AWS-GA) in section 3.7.1, and NSGA-II in section 3.7.2.

DIP model for fruit exportation

The integrated distribution and storage-planning problem for fruit exportation considered in this research consist of choosing the optimal transit route and storage time. In order to maximise profits under restrictions in terms of quality loss during transportation and storage, variability in raw material prices, selling prices, supply and demand, including environmental responsibility. The multi-objective function framework was developed to analyse the relationship between profitability and the quality of exported fruit. It is relevant to understanding the importance of the design choice of having such a complex supply chain for fruit exportation instead of just considering a single objective function.

Problem statement

We considered a case study of the seasonal fruit exportation supply chain, as shown in the details of Figure 2. Collectors gather fresh fruit from farmers to load fruit into containers. Then, the fruit is immediately distributed from the collectors to distribution centres with a cold-chain system by truck (short route) or cargo ship (long route). In order to maximise total profit from the sale to retailers at distribution centres each day, exporter need to choose the optimal transit route and storage time to maximize the profits under restrictions in quality loss during transportation and storage, and variability in raw material prices, selling prices and supply and demand, including environmental responsibility.

The main problem in fruit exportation is planning distribution and inventory to maximise NP and %RQ of the fruit supply chain. We propose an integrated distribution and inventory planning (DIP), which considers the quality loss of fruit from MI in two cases of ND: zero-order (DIP -ZO) and exponential decay as well as (DIP-ED) as a multiobjective, mixed-integer model.

To facilitate analysis and discussion, the scope of the work follows the principle questions below:

1. What is the effect of quality loss on the net profit of fruit exportation?

2. How does the type of product decay affect the overall solution quality?

3. How can an appropriate balance be found between the multi-objectives for maximizing NP and %RQ in terms of distribution and inventory planning and GHG emission?

4. How can an appropriate trade-off be found between quality loss, logistics costs and GHG emission? days), the delivery charge (90,000 and 50,000 baht/ctn and Gj (route1 = 1.5 and route2 = 1.2), and which we justify as the following.

Chinese festival

And then, we substitute E(P)i in eq.67 to estimate PMi of fruit exports each day. All results of the material price determination for each day of SC1, SC2, and SC3 are represented in Figure 30-Figure 31, respectively.

Selling price

We consider the data history of the selling price of fruit at the Chinese

NSGA-II

In this part, we applied a fast and elitist multi-objective GA: NSGA-II to optimize the multi-objective problems in FDM. The approach runs the single-point crossover and bitwise mutation for binary-coded GAs and the simulated binary crossover (SBX) operator and polynomial mutation. We use the idea of elitism when creating a new population by crossover and mutation. The best chromosome is copied to the new population to prevent the loss of its best chromosome. This method can also vary rapidly increase the performance of GA, because it prevents losing the best-found solution. (Deb, K., et.al., 2002).

Figure 34 describes the algorithm for NSGA-II, which has seven main steps.

Step1: Define population size, the number of generations as stopping criteria, dimension of decision variables with its design bounds, and objective/fitness functions.

Step2: Initialise random population

Step3: Sort non-dominated solutions from the initial random population with individual rank and crowding distance corresponding to fitness values or position in front.

While Stopping Criteria ( there has been no improvement in the population for X iterations or generation number = 50,000).

Step4: Do tournament selection based on individual rank and crowding distance.

If individuals have the same non-domination rank, then the individual with large crowding distance will be selected.

Step5: Do genetic operation which consists of crossover and mutation to generate an offspring population.

Step6: Sort non-dominated solutions from the combined population ( Parent population + offspring population).

CHAPTER IV RESULTS AND DISCUSSION

Numerical results

In this section, we present results from the numerical analysis to develop an in-depth understanding of the effects of quality loss in fruits exportation due to MI and ND. Six parts organize the section. Firstly, the optimal Pareto front of simulation results based on different fruit supply and demand are presented to verify the DIP model in 4.1.

Secondly, the Pareto-optimal fronts between % RQ for cases of zero kinetic and exponential decay and net profit are used to analyze the effect of quality loss on the net profit of fruit exportation and evaluate the performance algorithm in 4.2. Thirdly, we expanded the results from 4.2 to discuss the effects of quality loss in fruit on appropriate holding time in 4.3, the fruit distribution scheme in 4.4, and the interdependence between fruit quality, net profit, and total GHG emission to study the environmental impact in 4.5. All results are discussed and used to propose a way to improve the value chain of fruit exportation in 4.6. Sixth, we represent the differences between the developed DIP model and the other operational research model to discuss strong points and weak points of this research. Seventh, we conclude all experimental results in 4.7.

Scenario result

This section presents scenario results to develop insight into the benefits of scheduling fresh fruit exportation on NP and %RQ in FDM. We focus on presentation in two main parts. Firstly, we demonstrate the effect of quality loss on NP in each scenario of fruit demand rate uncertainty to study the effects of fruit quality on NP of fruit exportation. Secondly, we discuss the results from the first part to conclude the key points of the scenario results and to verify the usability of the DIP model for optimization of the fruit exportation problem under the various situation.

Although fruit transportation by refrigerated truck (j =1, and CT1= 441.5 kg CO2 e/ctn) has higher GHG gas emissions than fruit transportation by cargo ship (j=2, and CT2= 236.5 kg CO2e/ctn), choosing the shorter time for transportation is still the best way to optimize the appropriate balance between GHG emissions and NP and %RQ. This result can be explained by the fact that using cold chain systems to preserve fruit quality in FDM needs to use a lot of storage energy (at 5.4 MJ/t*d for blueberry storage at 1 C, and 1.9 MJ/t*d for mangosteen storage at 13 C). Cold chain systems also release a lot of GHG gas during storage (at CM1=1,089.3 kg CO2 e/ctn*d for blueberry and CM2=63.6 kg CO2e/ctn*d for mangosteen). Furthermore, storing fruit in order to wait for higher selling prices via using transit storage with the longer route or cooling room storage causes spoilage, which also has an impact on the total GHG emissions with CW = 1.90 kg CO2 e/kg. As mentioned above, the results reveal that the optional transportation and storage schedule not only have the ability to increase %RQ and NP directly but also can indirectly help to reduce the CO2 e emissions in FDM. Temperature control is essential for controlling fruit quality and fruit safety. It does, however, lead to additional energy consumption. As such, temperature-controlled distribution is related to all three foodspecific aspects that are the focus in our discussion: quality, safety and sustainability

Tactical planning

We consider the effects of % RQ on NP from 4. 1. 2, which shows the preservation of %RQ > 91.81 in the case of DIP-ZO and %RQ> 91.92 in case of DIP-ED as a way to achieve the maximization of NP. The %RQ depends on the degree of %MI and %ND, which are different in each transportation route and storage time, respectively.

Figure 49 and Figure 50 present the relative importance of %MI and %ND on NP in the case of DIP-ZO and DIP-ED, respectively. We obtain that the relative importance of the %MI on NP in both cases of DIP-ZO and DIP-ED is rather independent of the NP of FDM with r 2 = -0. 9531, and -0. 9317 respectively while the relative importance of the %ND on NP in both cases DIP-ZO, and DIP-ED is less. They represent the correlation value at 0.5543 and 0.5408, respectively, as shown in Table 25. In the case of DIP-ZO, we found that NP can ascend to 220 Million baht when aiming at 0.42% of ND w hile in the case of DIP-ED, NP can ascend up to 220

Million baht when aiming at 0.42% of ND. The result is consistent with the studied effect of appropriate holding time of fruit on FDM in 4.1.3, which represents that a decrease in storage time less than 1.600 days and 0.195 days in the cases of DIP-ZO and DIP-ED and transportation time with 2day in both cases can be achieved through NP and % RQ maximization.

Operational planning that considers these five variables can help exporters to achieve comprehensive cost advantages. The operations cover the solution in all activities of fruit distribution from production, transportation, inventory, to consumer.

However, to maximize the benefits of the implementation of the export plan from the author's perspective, all stakeholders in fruit exportation must cooperate to avoid quality loss during the operation. For instance, the farmer must be careful during harvesting, grading, and handling, and should also receive training in good agricultural practice (GAP). While, the collectors also must be careful during the sorting, cleaning, packing, handling in the fruit packing process, including the training on Good manufacturing practice (GMP). Drivers' driving behaviours and environmental conditions during fruit transportation should be monitored by GPS tracking to prevent quality loss during transportation. Finally, the exporter must work together with the other stakeholders, and the integration of farmers and collaboration among farmers and collectors should be encouraged to increase understanding about the importance of fruit quality preservation.

A comparative study between the DIP model and the other operational research model

Out of all of the experiments mentioned, the DIP model can be applied to solve the FDM problem that corresponds to the mechanism of loss of quality in fruits in both MI and ND. An assessment of MI helps to reflect the estimated cost of quality loss from long-distance transportation in fruit exports. At the same time, the assessment of ND related to lag time for the appearance of quality deterioration (DFD) and kinetics of quality loss ( zero-order kinetics or exponential decay) , which they are different depending on the total holding time and type of fruit.

We compare the difference of quality loss assessment between DIP model both case of zero order and exponential decay, and the other operation research model such as Amorim, P., and et al., (2019), [START_REF] Amorim | Multi-objective integrated production and distribution planning of perishable products[END_REF]et al., (2012), and[START_REF] Rong | An optimization approach for managing fresh food quality throughout the supply chain[END_REF]et al., (2011), as show the details of Figure 55 and Figure 56. They represent the differences in assessing quality loss in the following.

short-distance transportation problems, which the MI due to transportation is not the main factor to consider. The MI evaluation can help exporter to analyse actual total cost in longdistance transport of fruit exportation. The cost is also helpful in choosing the optimal transportation route, including the development of a packaging system for transportation.

Regarding the sustainability indicators in FDM model, most of the research papers focused more on the study of environmental impacts in the form of greenhouse gas emission (GHG) than on social impacts since the environment can be quantified easily.

While the assessment of GHG emission in operation research model usually specifies the scope of activities that need to be studied. They do not consider comprehensive in all the activities of distribution management.

To overcome weakness in the operation research model, this research proposes a multi-objective integrated distribution and inventory planning model ( DIP model) for scheduling fresh fruit exporting operations which consider the cost from both logistics and quality loss in fruits, as well as the total GHG emissions in fruit distribution.

The DIP model addresses a bi-objective function to maximise the total net profit (NP) and the percentage of the remaining quality of fruit (%RQ) in fruit distribution. The total NP is determined by the difference between total revenue and logistics cost, which depend on overall supply, demand, and fruit price each day. %RQ is assessed extensively for both the case of MI and ND so that the results obtained from the assessment are consistent with the actual costs of quality loss from longtransportation and storage in global fruit exportation.

The degree of MI is estimated by considering the vibration level each route of transportation (the refrigerated truck (short route) and cargo ship(long route)). While the cost of MI is different depending on the fluctuation of fruit material price each day.

The degree of ND is estimated through the kinetics shelf life model, taking into account the product stability or lag time of the date of fruit deterioration begins to appear (DFD)

based on two cases of kinetics model: zero-order kinetics (DIP-ZO) and exponential decay (DIP-ED). While the cost of ND is quantified in the form of the cumulative holding cost by modifying Economic Order Quantity (EOQ) models [START_REF] Ferguson | Note: An application of the EOQ model with nonlinear holding cost to inventory management of perishables[END_REF].

We proposed the numerical study based on the data history of fruit supply, demand, and selling price in fruit exportation. While the balance of supply and demand in the form of excess supply function will be applied to determine the price of fruit material.