Fluent Essays

Write a two-page paper, plus the title page and a reference page on the following statement: Describe one direct and one indirect impact of reverse logistics operations on some local or regional area and compare it to some aspect of the world environment. Incorporate at least one peer reference from articles listed within the online APUS library.  You must cite the peer reviewed reference within the paper. •Written Communication: Written communication is free of errors that detract from the overall message. •APA formatting: Resources and citations are formatted according to APA style and formatting. •Length of paper: typed, double-spaced pages with no less than a two-page paper. •Font and font size: Times New Roman, 12 point. lable at ScienceDirect Journal of Cleaner Production 201 (2018) 1081e1091 Contents lists avai Journal of Cleaner Production journal homepage: www.elsevier.com/locate/jclepro A goal programming model for sustainable reverse logistics operations planning and an application Alperen Bal a, Sule Itir Satoglu b, * a Yalova University, Engineering Faculty, Industrial Engineering Department, Yalova, Turkey b Istanbul Technical University, Faculty of Management, Industrial Engineering Department, Istanbul, Turkey a r t i c l e i n f o Article history: Received 2 January 2018 Received in revised form 15 July 2018 Accepted 10 August 2018 Available online 13 August 2018 * Corresponding author. Istanbul Teknik Universite Macka, Sisli, Istanbul, Turkey. E-mail address: [email protected] (S.I. Satoglu). https://doi.org/10.1016/j.jclepro.2018.08.104 0959-6526/© 2018 Elsevier Ltd. All rights reserved. a b s t r a c t Global concerns about climate change and its environmental consequences, social factors and economic constraints require pursuit of a new approach to the supply chain planning at the strategic, tactical and operational levels. Recovery of waste electric and electronic equipment (WEEE) has become an important issue in the developing economies, as legislations that mandate manufacturers and importers to take back the wastes of their electrical and electronic products (WEEE) has been promulgated. Therefore, this study addresses the process of collecting WEEE products from service points, transporting them to recycling facilities, and recovery of the waste materials. Our framework considers triple-bottom-line approach and employs goal programming to reach economic, social and environmental targets. A multi-facility, multi-product and multi-period mathematical model is proposed, considering the real conditions, for the first time in the literature. In addition, this goal programming approach is illustrated on a WEEE reverse supply chain of the household appliances. © 2018 Elsevier Ltd. All rights reserved. 1. Introduction Global concerns about climate change and its environmental consequences, social factors and economic constraints require pursuit of a new approach to the supply chain planning at the strategic, tactical and operational levels. In this day and age, it is not enough to think only from economic perspective. Especially private companies aim cost minimization, but it is also necessary for them to consider the environmental protection and the social impact. At this point, governments consider to amplify social benefit and make legislations to reduce unfavorable environmental impact. Sustainability is either used to sustain an implementation or to emphasize environmental awareness both in academic and non- academic resources. Although both definitions are correct, they are incomplete. The approach used in analyzing sustainability is described as triple bottom line (TBL) accounting. The TBL concept states that for a system to be sustainable, economic, environmental and social requirements must be reached at a minimum (Jeurissen, 2000). As Linton et al. (2007) expressed, to achieve a sustainable supply chain, each fragment of it should have environmentally si, Isletme Fakultesi, 34369, friendly procedures including product design, manufacturing, us- age, recycling, and transporting among suppliers, manufacturers, and customers. Recovery of WEEE products has become an important issue in the developing economies. However, companies are reluctant or not capable of entering this market. Manufacturers, on the other hand, are under pressured according to the market trend and obliged to implement environmental regulations (Kumar and Putnam, 2008). A regulatory control of waste electric and elec- tronic equipment that mandates manufacturers and importers to take back their products has been promulgated (Ministry of Environment and Urbanization, 2012). Based on the aforementioned considerations, this paper ad- dresses the issue of the collecting waste products from service points and transporting them to recycling facilities. Our framework considers triple-bottom-line approach and employs goal pro- gramming to reach economic, social and environmental targets. A goal-programming model has been developed in tactical opera- tions planning of the reverse supply chains with multi-facility, multi-product and multi-period. The proposed mathematical model can be used for transportation and recovery operations de- cision making with a TBL perspective and it can be extended to different types of reverse supply chains. In addition, we illustrate our approach on a WEEE reverse supply chain of the household mailto:[email protected] http://crossmark.crossref.org/dialog/?doi=10.1016/j.jclepro.2018.08.104&domain=pdf www.sciencedirect.com/science/journal/09596526 http://www.elsevier.com/locate/jclepro https://doi.org/10.1016/j.jclepro.2018.08.104 https://doi.org/10.1016/j.jclepro.2018.08.104 https://doi.org/10.1016/j.jclepro.2018.08.104 A. Bal, S.I. Satoglu / Journal of Cleaner Production 201 (2018) 1081e10911082 appliances. The paper is structured as follows. Section 2 offers a sustain- ability based literature review to assess the optimization papers in forward/reverse logistics network design. To further explain the TBL accounting, the proposed framework is illustrated and eco- nomic, environmental and social perspectives are discussed in section 3. To design reverse logistics network, a goal-programming model is developed in section 4. Section 5 explains Augmented ε-constraint methodology and section 6 presents the Case Study. Later, results and discussion on the case study are presented. Lastly, conclusion of the paper and further research are explained in sec- tion 8. 2. Literature review A significant amount of sustainable supply chain research has been conducted considering various sustainability indicators related to TBL for managerial decision making in supply chain management (SCM) (Carter and Rogers, 2008) and operations management (Drake and Spinler, 2013; Kleindorfer et al., 2005), in particular. Compared to the extensive research on environmental aspects and especially economic issues, the social aspects are neglected in the sustainable SCM literature. Yura (1994) elaborated social issues, Brent et al. (2007) and Abreu and Camarinha-Matos (2008) studied on socio-economic issues and Clift (2003) detailed socio-environmental interfaces. Paksoy et al. (2010) proposed a closed loop supply chain design using multi-objective mixed- integer linear programming. The model minimizes cost and greenhouse gas emissions at the same time. Tseng and Hung (2014) considered both social costs caused by the carbon dioxide emis- sions and operational cost in an apparel manufacturing supply chain network. Transportation planning in reverse and closed-loop supply chain design is also discussed at the tactical level, and Table 1 Reviewed Articles about sustainable supply chain design. (Notation e BD: benders decom GP: goal programming, MILP: mixed integer linear programming, MINLP: mixed integer n optimization, S: social, SMILP: stochastic mixed integer linear programming SO: stochas Network structure Anvari and Turkay, 2017 Forward Arampantzi and Minis, 2017 Forward Feit�o-Cesp�on et al., 2017 Reverse Safaei et al., 2017 Closed-loop Sarkar et al., 2017 Closed-loop Yu and Solvang, 2017 Reverse Demirel et al., 2016 Reverse Govindan et al., 2016a Closed-loop Govindan et al., 2016b Reverse Shaw et al., 2016 Closed-loop Ene and Oztürk, 2015 Reverse Zhou and Zhou, 2015 Reverse Hashemi et al., 2014 Closed-loop Ozceylan et al., 2014 Closed-loop Roghanian and Pazhoheshfar, 2014 Reverse Soleimani and Govindan, 2014 Reverse Amin and Zhang, 2013 Closed-loop Diabat et al., 2013 Closed-loop Ozceylan and Paksoy, 2013 Closed-loop Ramezani et al., 2013 Closed-loop Alumur et al., 2012 Reverse Das and Chowdhury, 2012 Reverse Kannan et al., 2012 Reverse Ozkır and Başligıl, 2012 Closed-loop Fonseca et al., 2010 Reverse Ramudhin et al., 2010 Forward Lee and Dong, 2009 Reverse Aras and Aksen, 2008 Reverse Demirel and Gokçen, 2008 Closed-loop Pati et al., 2008 Reverse mathematical models are proposed (Dekker et al., 2013). A large number of multi-facility multi-product deterministic facility location problems were studied in the literature. However, operational planning has attracted little attention. Also, sustain- ability approach requires multiple objectives to be achieved. Gonela et al. (2015) proposed a stochastic mixed integer linear program- ming model for bioethanol supply chain and evaluated the results under different sustainability concerns. Krumwiede and Sheu (2002) developed a reverse logistics decision-making model for third-party logistics providers to help engage in the reverse logis- tics business. Hung Lau and Wang (2009) investigated the feasi- bility of current reverse logistics theories and models for electronics industry taking into account developing countries like China. A mixed integer programming model is proposed by Shih (2001) for reverse logistics network design considering cost pa- rameters including sale revenue of reclaimed materials. Kara et al. (2007) calculated collection cost of waste appliances in reverse logistics network using discrete event simulation. Mutha and Pokharel (2009) designed a multi-echelon network including a consolidation warehouse into the system before they are sent to the reprocessing center for inspection or dismantling. Tuzkaya et al. (2011) proposed a two staged multi objective model for reverse the logistics network design problem and presented its application in the Turkish white appliances industry. Bal and Satoglu (2017) used sustainability perspective as well as legal requirements to set up a goal-programming model to opti- mize a global white appliance manufacturers’ reverse logistics system. Coskun et al. (2016) proposed a goal-programming model to re-design green supply chain network considering three different customer segments. The results demonstrated that the increase in the number of green consumers expanded the tendency of the retailers to cooperate with the suppliers to redesign the supply chain, to fit the consumers expected greenness level. A position, E: economic, En: environmental, FMoO: fuzzy multi objective optimization on-linear programming, MoSO: multi objective stochastic optimization, RO: Robust tic optimization). Objective Modelling approach Case study EEnS MILP Yes EEnS GP Yes EEnS MoSO Yes E MILP Yes EEn MINLP No EEn MoSO No E MILP Yes EEnS MILP Yes EEnS FMoO Yes En BD No E MILP No E MINLP Yes E MILP No E MINLP No E MILP No E SO No EEn MoSO No EEn MILP No E MILP No E MoSO No E MILP Yes E MILP No En MILP Yes E MILP No ES MoSO Yes EEn GP No E SMILP No E MINLP No E MILP No EEn GP Yes A. Bal, S.I. Satoglu / Journal of Cleaner Production 201 (2018) 1081e1091 1083 similar research was carried out by Ghosh and Shah (2015). They verified that supply chain stakeholders are provided better op- portunities to launch green initiatives by green consumer markets. In Table 1, the papers are summarized concerning economic (E), environmental (En) and social (S) objectives. Economic objectives are considered at all of the papers. Sixteen papers used only eco- nomic objectives. Both economic and environmental objectives are used by Sarkar et al. (2017), Yu and Solvang (2017), Pati et al. (2008), Amin and Zhang (2013), Diabat et al. (2013), Ramudhin et al. (2010). However, these studies but do not have any social objective. Especially recently published papers are using social objectives in addition to economic and environmental objectives (Anvari and Turkay (2017), Arampantzi and Minis (2017), Feit�o-Cesp�on et al. (2017), Govindan et al. (2016a), Govindan et al. (2016b)). In spite of many papers with economic objectives, sustainability approach is not widely studied in the literature. Multi-objective optimization has been used increasingly in recent years. In addition, there are only a few papers using goal programming (Arampantzi and Minis (2017), Ramudhin et al. (2010), Pati et al. (2008)), in the literature. Arampantzi and Minis (2017) consid- ered only forward logistics network design, especially facility Fig. 1. Schematically representatio location problem and capacity extension decisions. Anvari and Turkay (2017) also studied the facility location problem that in- corporates the TBL approach for sustainability. Colapinto et al. (2015) presented a comprehensive review of the GP studies. This technique has been frequently used for solving multi-criteria decision problems concerned with engineering design, management and social sciences. Design of the hybrid manufacturing systems (Satoglu and Suresh, 2009), paper recycling system (Pati et al., 2008), closed-loop battery supply chains (Subulan et al., 2015a), tire closed-loop supply chains (Subulan et al., 2015b) were performed by means of GP or fuzzy GP. To the best of authors’ knowledge, this is the first study in the literature that proposes a goal programing model for reverse supply chains based on a TBL approach and performs a case study in household goods (WEEE) recovery industry. Our detailed literature review supports this finding. 3. Proposed framework for operations planning In this section, we present the proposed decision making framework (see Fig. 1). This decision-making framework can be n of the decision framework. A. Bal, S.I. Satoglu / Journal of Cleaner Production 201 (2018) 1081e10911084 applied for operations planning in any sustainable supply chain. In our case, operations planning problem requires definition of the system boundary and determination of the model assumptions utilizing the knowledge in the related literature and experts working on reverse supply chain networks. In our network we consider customers, WEEE collection sites, recycling facilities, raw material markets, and government. The framework of the model is completed by considering economic, environmental and social factors. Since we optimize conflicting objectives in the Pareto optimal set we need to implement a decision maker strategy where experts are involved. One of the challenging sides of analyzing sustainability is the conflict between essential factors. It is absolutely necessary for companies to maintain their profitability so that they can sustain their existence, but also the responsibility for nature and society must not be ignored. Some guidance (e.g. ISO 14001) and regula- tions exist regarding environmental responsibility which force the companies. As for the performance of the supply chain, not only economic and environmental aspects but also social factors are important (Ramudhin et al., 2010). Nevertheless, social perspective remains an area that received less attention (Seuring and Müller, 2008). Economic parameters: The most important thing for investors is the profit of the investment. We did the primary considerations for parameters selection in the economic dimension in this context. We focused on the cost of running reverse logistics operations, but not the initial investment cost. The cost items include the fixed cost of recycling the products, labor cost, transportation cost and pen- alty cost of uncollected products. Besides, revenue item is consid- ered as the monetary value of the recycled materials such as aluminum, copper etc. (Shih, 2001). Environmental parameters: We derived emission and waste rates used in the model from recognized data sources including web sites (www.myclimate.org, footprint.wwf.org.uk, www.nature. org), research articles (Eskandarpour et al., 2015; Neumüller et al., 2015) and reports (Trends in Global CO2 emissions: 2016, In- ventory of US greenhouse gas emissions and sinks: 1990e2015). In addition, we considered performance characteristics of the trucks from manufacturers such as Volvo (Martersson, 2010). Based on (Martersson, 2010), we have calculated the emission of carbon di- oxide for a 40-ton truck for which the payload is 27 tons and the fuel consumption is 0.35 L per kilometer, as follows: 0.35 l/km � 2.7 kg/l per 27 tons z 0.035 kg/ton-km. The proposed model considers not only emission from trans- portation but also facility operations. Because a facility creates emission from power consumption, employee transportation, pa- per consumption and use of computers as well. In Table 2, we show compared data of Euro6 and Euro 5 emission standards for the heavy duty engines (Williams and Minjares, 2016). Social parameters: International Guidance Standard on Social Responsibility-ISO 26000 (ISO, 2010) is a good reference for social criteria identification. ISO 26000 sets the frameworks of social Table 2 Euro 5 and Euro 6 standards for heavy-duty diesel engines: steady state testing (Notation e CO: carbon monoxide, ELR: European load response, ESC: European stationary cycle, HC: hydrocarbon, NOx: nitrogen oxide, PM: particulate matter, PN: particle number, WHSC: world harmonized stationary testing). Test CO (g/kWh) HC (g/kWh) NOx (g/kWh) PM (g/kWh) PN (1/kWh) Euro VI WHSC 1.5 0.13 0.40 0.01 8.0 � 1011 Euro V ESC&ELR 1.5 0.46 2.0 0.02 PM ¼ 0.13 g/kWh for engines < 0.75 dm3 swept volume per cylinder and a rated power speed > 3000 min�1. responsibility in seven major topics: organizational governance, human rights, labor practices, the environment, fair operating practices, consumer issues, community involvement and develop- ment. Also, Anvari and Turkay (2017) divides social factors into five categories: demand satisfaction, resource equity, job opportunity, regional development, security level at the location, medical facility access level. These factors are used for selection of a facility loca- tion. However, it can also be considered as the local development goal, and we determined keeping the number of workers at a certain level for an operating facility as a social goal. The main reason behind this is the variability in the demand of WEEE to be recycled (Bal et al., 2018) which can cause layoffs at some period. For both employers and governments, it is important to keep workforce level at a certain level. Governments do not wish the workforce level to decrease. On the other hand, employers often do not wish to pay compensation by layoffs and confront with unions. Thus, we aimed to provide more regular work opportunity to employees. 4. Proposed goal programming model In this paper, we address the operations planning problem for a reverse supply chain considering four goals. The proposed model determines the timing and amount of WEEE collection from the pre-determined points considering cost & revenue items, emission, available workforce, collection target, capacity of the recycling fa- cility and distance. There are four goals determined according to the cost minimization, environmental effect reduction, workforce balance and catching legal targets. The model handles operations planning problem, which has a TBL accounting perspective within a multi-product, multi-facility and multi-period case. Model Assumptions. � Products are collected from the central point of the city. Inner- city routing is out of the scope of this study. � Cost of recycling does not change with years. � The numbers of collection sites are known and locations of the recycling facilities are predetermined. � The specific facility that can recover a product type is predetermined. � Cost parameters are foreknown as material, operation, recycling, transportation, hiring, laying off and fixed cost. � The holding cost, stock out cost and storage cost are disregarded. Model notation. Sets: i: set of all types of products, i21:::I j: set of all types of raw recycled materials, j21;:::J k: set of all cities, k21:::K l: set of all facilities, l21:::L t: set of all periods, t21:::T p: set of periods, p21:::T Scalars: BG : big number EOQ : economic order quantity for a city ðA full � truck loadÞ FTLðvehicleÞ : full truck load per transport vehicle Gðgram=unit vehicle=KmÞ : amount of emission per unit transport per km MRð\%Þ : minimum collection rate RBð$=personÞ : employment cost of a worker RCð$=personÞ : hiring cost of a worker in $ RDð$=personÞ : layoff cost of a worker in $ RTð$=vehicleÞ : fixed cost of transportation in $ WMð\%Þ : maximum workforce level; ðWM � 100\%Þ http://www.myclimate.org http://footprint.wwf.org.uk http://www.nature.org http://www.nature.org A. Bal, S.I. Satoglu / Journal of Cleaner Production 201 (2018) 1081e1091 1085 MH (Hour): Number of work hours per month per one worker. Parameters: ßtðgramÞ : target value of CO2 emission due to all transportation process CAPltðunit productÞ : capacity of facility l in period t dklðkmÞ : distance between demand location k and recycling facility location l DMiktðunitÞ : amount of product i sold in region k at period t EiðgramÞ : amount of emission stem from recycling of a product i εtðgramÞ : target value of CO2 emission due to all recycling processes at period t FAiðhourÞ : required person � hour workforce to recycle product i FtðunitÞ : collection target at period t LtðpersonÞ : target number of worker in period t MSijð$=kg mterialÞ : monetary value of material j recycled from product i Oitð\%Þ : the percentage at which product i should be collected accordin to the legislation PRið$=vehicle=KmÞ : cost of transportation of product i RAið$=unit productÞ : recycling operation cost of product i RPið$=unit productÞ : penalty cost of uncollected product i RSijðkg=unit productÞ : amount of material j recycled from product i SMitðunit productÞ : amount of product i sold in period t TRitð$Þ : target total cost of recycling of product i in period t Employment targetlt : Number of people targeted to be employed at facility � l;in period � t: Decision variables: Hlt : number of workers hired at facility l during period t Mlt : number of redundant workers at facility l during period t Wlt : number of workers employed at facility l in period t Xikt : collected � recycled number of product i in period t from region k Ykt � 1; if product i is collected in period t from region k 0; otherwise f þit , f � it ; tr þ it , tr � it ; e � t ;e þ t , p þ lt ;p � lt : Deviational variables. Objectives: Min Z1 ¼ X t X i f �it (1) Min Z2 ¼ X t X i trþit (2) Min Z3 ¼ X l X t p�lt (3) Min Z4 ¼ X t eþt (4) Subject to : X i X k X l XiktRAi þWltRBþHltRC þMltRDþ X i X k X l dkl PRi xikt FTL þ X i X k xikt FTL RT þ X i X k ðDMikt �XiktÞRPi � X i X j X k XiktRSijMSij ¼ X i � TRit þtrþit �tr � it � ; ðct2TÞ (5) X k X t Xikt ¼ X t OitSMit þ f þit � f � it ; ðci2IÞ (6) X i X k XiktEi þ X k X l Xikt FTL Gdkl ¼ εt þ bt þ eþt � e�t ; ðct2TÞ (7) Wlt ¼ Employment targetlt þ pþlt � p � lt ; ðct2T; cl2LÞ (8) Wlt � X i XiktFAi=MH; ðct2T; cl2LÞ (9) Wlt � X i XiktFAi � WM=MH; ðct2T; cl2LÞ (10) Wlt�1 þ Hlt � Mlt ¼ Wlt; ðct2T; cl2LÞ (11) X i X k Xikt � CAPlt; ðct2T; cl2LÞ (12) EOQ � X i Xikt � BGð1 � YktÞ ; ðct2T; ck2KÞ (13) X i Xikt � BG � Ykt; ðct2T; ck2KÞ (14) X i Xikt � MR � X i DMikt; ðct2T; ck2KÞ (15) Xp t¼1 Xikt � Xp t¼1 DMikt; ðcp ¼ 1; …; 12Þðci2I ; ck 2KÞ (16) All variables � 0 (17) Xikt; Hlt; Mlt; Wlt 2Z þ ðci; k; l; tÞ; Ykt2f0; 1g (18) Objective functions (1), (2), (3), (4) minimizes the negative de- viation from WEEE collection target, minimizes positive deviation from cost target, negative deviation from employment target and positive deviation from total emission target that stems from both transportation and recycling operations. Constraint (5) defines cost that the manufacturer must pay for. The fact that reverse supply chain may not (always) make revenue, the objective is to minimize the reverse logistics cost. Cost items are composed of the fixed cost of recycling operation in the recycling facilities, employment cost, fixed and variable cost of transportation, penalty cost of uncollected items. On the other hand, income is earned out of sales of the material obtained from recycled WEEE. TR defines the target cost, and since the goal is to catch a break-even point, this is set to zero. Constraint (6) denotes legal collection goal taking into account actual sales (Smit) and the amount of product (Xikt) decided to collect in that period. There is a legal requirement that at least Oit percent of the sold goods are recycled. Constraint (7) describes environmental effect of each products’ recycling operation in the facility and each truck sent to collect the products. The total emission goal ðεtÞ is set with regard to total emission expected from all operations. Minimization of the negative deviation ðp�lt Þ from the employ- ment target is aimed at the third objective. Related with this objective, Constraint (8) stipulates that the number of workers in A. Bal, S.I. Satoglu / Journal of Cleaner Production 201 (2018) 1081e10911086 each facility (Wlt) should be close to the employment target. The structural Constraints (9), (10) ensures workforce is greater than required person-hour work and does not exceed the allowed maximum workforce level. Constraint (11) implies that sum of the workers employed in the previous period and those hired in the current period minus the redundant workers is equal to the current number of workers employed. Here, Wlt denotes the number of workers employed and Hlt denotes the number hired, in period-t. Constraint (12) defines the capacity for each facility. Thus, recy- cled products in each period cannot exceed the capacity of the fa- cilities. Economic order quantity is provided by Constraints (13), (14). These two constraints are modeled as conditional con- straints and ensure that a truck is sent to a collection point if at least the amount of products is equal to the economic order quantity. Here, Ykt is a binary variable and makes constraint (14) equal to Xikt which is greater than EOQ. Then, the constraint (13) becomes 0 due to ð1 � YktÞ. Otherwise, 0 is assigned to Xikt. EOQ is determined as a full-truck load that must be satisfied to collect WEEE from a city. Constraint (15) provides that at least some certain percent of the demand is collected in each city and each period. This constraint prevents the model to collect no products so as to produce zero emission. On the other hand, constraint (16) ensures that the total collected amount of product in a period cannot exceed the total demand from first period to a relevant period. Constraint (17) im- poses non-negativity restrictions while set of integrality re- strictions for decision variables Xikt; Hlt; Mlt; Wlt; Ykt are imposed by constraint (18). 5. Solution methodology In the literature, many different and improved versions of the Augmented ε-constraint method exist (Ehrgott and Ryan, 2002; Laumanns et al., 2006; Hamacher et al., 2007; Mavrotas, 2009; Mavrotas and Florios, 2013). Since the Augmented ε-constraint method 2 (AUGMECON2) (Mavrotas and Florios, 2013) was proved to have better performance than the others, we preferred to use this method as our solution algorithm. We applied AUGMECON2 as shown below (Mavrotas and Florios, 2013): min f1ðxÞ þ eps � � s2 fmax2 � fmin2 þ 10�1 � s3 fmax3 � fmin3 þ 10�2 � s4 fmax4 � fmin4 � (19) Subject to : (20) f2ðxÞ þ s2 ¼ fmin2 þ t � ðfmax2 � fmin2Þ=q2 (21) f3ðxÞ þ s3 ¼ fmin3 þ t � ðfmax3 � fmin3Þ=q3 (22) f4ðxÞ þ s4 ¼ fmin4 þ t � ðfmax4 � fmin4Þ=q4 (23) x2S and si2R þ: (24) In this formulation, f1 corresponds to ‘Legal Function’, f2 corre- sponds to ‘Cost Function’, f3 corresponds to ‘Social Function’ and f4 corresponds to ‘Environmental Function’. Surplus variables of the respective constraints are represented by s2, s3, and s4, respectively. The maximum and minimum value of objective functions from the payoff table are fmaxi and fmini respectively. The range of fi is fmaxi � fmini , t is the counter of the interval (if fi is divided to 4 then t changes from 1 to 4) and qi is the length of the equal intervals of the objective function fi, and ε is relatively a small number be- tween 10�6 and 10�3 (Mavrotas and Florios, 2013). The identifica- tion of Pareto-optimal solutions is essential in multi-objective optimization. Thus we used CPLEX solver of the GAMS® software to generate a set of Pareto optimal solutions. 6. Case study We illustrate our proposed model on a case study with real data and analyze the results. Some operational …