A Bi-Objective Green Closed Loop Supply Chain Design Problem with Uncertain Demand

Transcription

1 sustanablty Artcle A B-Obectve Green Closed Loop Supply Chan Desgn Problem wth Uncertan Demand Mng Lu 1 ID, Rongfan Lu 1, Zhanguo Zhu 2, *, Chengbn Chu 1,3 and Xaoy Man 4 1 School of Economcs and Management, Tong Unversty, Shangha , Chna; mnglu@tong.edu.cn (M.L.); lurongfan2017@tong.edu.cn (R.L.); chengbn.chu@ecp.fr (C.C.) 2 College of Economcs and Management, Nanng Agrcultural Unversty, Nanng , Chna 3 Laboratore Géne Industrel, Centrale Supélec, Unersté Pars-Saclay, Grande Voe des Vgnes, Châtenay-Malabry, France 4 Glorous Sun School of Busness and Management, Donghua Unversty, Shangha , Chna; manxaoy8996@163.com * Correspondence: zgzhu@nau.edu.cn Receved: 7 March 2018; Accepted: 21 March 2018; Publshed: 26 March 2018 Abstract: Wth the development of e-commerce, competton among enterprses s becomng fercer. Furthermore, envronmental problems can no longer be gnored. To address these challenges, we devse a green closed loop supply chan (GCLSC) wth uncertan demand. In the problem, two conflct obectves and recyclng the used products are consdered. To solve ths problem, a mathematcal model s formulated wth the chance constrant, and the ɛ-constrant method s adapted to obtan the true Pareto front for small szed problems. For larger szed problems, the non-domnated sortng genetc algorthm (NSGA-II) and the mult-obectve smulated annealng method (MOSA) are developed. Numerous computatonal experments can help manufacturers mae better producton and sales plans to eep compettve advantage and protect the envronment. Keywords: supply chan desgn; b-obectve optmzaton; chance constrant; algorthms 1. Introducton The development of e-commerce has maredly mproved the crculaton of commodtes, and consumers have more choces n ther preference. Moreover, competton n the commodty maret s becomng fercer. How to eep compettve has been a core problem for all enterprses. Many companes wll be gradually elmnated f they cannot effectvely mprove customer satsfacton (the ualty of products, logstcs speed, etc.) and cut ther cost (producton cost, operaton cost, etc.). To address these challenges, many studes about the desgn of the supply chan were dscussed over several decades. The problem of the supply chan s crucal for modern busness management. Strctly speang, the supply chan s not a chan of busnesses wth one-to-one, busness-to-busness relatonshps, but a networ of multple busnesses and relatonshps [1]. Customer satsfacton s mportant for the supply chan. For example, due to the fast logstcs, many people prefer purchasng boos on Amazon. Such an advanced logstcs servce level has brought plenty of advantages to Amazon, ncludng more page vews, hgher customer satsfacton, whch eep Amazon compettve wth ther counterparts. However, envronmental ssues have been exposed to the publc (e.g., electronc waste, whte polluton) wth socety s development n recent years. Governments around the world promulgated relevant laws and polces one after another. Some legslatons have forced producers to tae care of ther end of lfe (EOL) products [2]. As many people now, supply chan actvtes are the man sources of greenhouse gas emssons [3]. The actual solutons urge companes to ntegrate used products recovery actvtes Sustanablty 2018, 10, 967; do: /su

2 Sustanablty 2018, 10, of 22 nto ther regular supply chan. A few enterprses le Jngdong (a famous on-lne shoppng platform n Chna) have begun to recycle the used products for reproducng or reducng the waste to respond to the sustanable development strategy. Correspondng to ths phenomenon n real lfe, some research wors about green closed loop supply chan (GCLSC) have been conducted to address the challenges dervng from the envronment and customers. The closed-loop supply chan (CLSC) s the bass of the GCLSC networ desgn. CLSC has ganed consderable attenton recently. Accordng to the defnton [4], CLSC ncludes forward logstcs and reverse logstcs. Many manufacturng organzatons have recognzed the mportance of reverse logstcs. Based on these realtes and the sustanable development strategy, a GCLSC s desgned n ths paper consderng the uncertan demand and the total cost n the whole supply chan. The contrbutons of ths paper may nclude the followng. 1. To tacle the uncertanty n the demand, ths paper propose a b-obectve model wth the chance constrant. 2. The model n ths study consders customer satsfacton ncludng the speed of logstcs, the ualty of products and recyclng used products. 3. An exact ɛ-constrant method s adapted to obtan the exact Pareto front for small-scale problems after approxmaton. 4. An approxmaton method s ntroduced to handle the chance constrant. 5. A mult-obectve smulated annealng method (MOSA) and non-domnated sortng genetc algorthm (NSGA-II) are proposed for medum- and large-scale problems. The remander of ths paper s arranged as follows. In Secton 2, we revew the related lterature. In Secton 3, we descrbe the problem, and n Secton 4, we formulate a b-obectve mathematcal model. Then, a case study solved wth three methods s presented n Secton 5. In Secton 6, we mae the performance measurement. Conclusons are presented n Secton Lterature Revew Ths secton s gong to reconsder the lterature that has concentrated on the supply chan, CLSC and GCLSC n the last decade The Lterature of Supply Chan Zhang [5] studed a nonlnear complementarty formulaton of the supply chan networ eulbrum problem. Ths s a uncertan demand problem, and there are multple manufacturers who produced a homogeneous product and retalers facng random demands from customers. A smoothng Newton method that explots the networ structure was proposed, and convergence results were presented. Some numercal examples were provded, and the algorthm was applcable. Cardona et al. [6] addressed a problem of a two-echelon producton dstrbuton networ wth multple manufacturng plants, customers and a set of canddate dstrbuton centers. The study extended the exstng lterature by ncorporatng the uncertan demand and transportaton mode allocaton decsons, as well as provdng a networ desgn wthn a two-level supply networ settng. A two-stage nteger programmng was proposed consderng uncertan demand wth two obectves, where the nherent rs s modeled by scenaros. The choce of locatons was decded frstly, and the amount of producton was ensured n the second stage. The method, whch combned the ɛ-constrant and the L-shape, was used to solve ths problem. Perera et al. [7] nvestgated an ntegraton of lne balancng problem wthn the tactcal decson of the supply chan. An alternatve formulaton of the ont supply chan networ desgn was proposed. Then, the problem was decomposed nto a seuence of a smple assembly lne balancng problem and a mxed nteger lnear programmng model, whch was easer to solve than the prevously avalable non-lnear mxed nteger formulaton. The results showed that the new method was able to solve

3 Sustanablty 2018, 10, of 22 prevously-studed models wthn a fracton of the reported runnng tmes. The paper analyzed the nfluence of the nfluence of the cost structure, the demand and the structure of the assembly process on the supply chan networ. Esandarpour et al. [8] proposed a large neghborhood search heurstc to solve a problem of a mult-product supply chan networ consstng of four layers: supplers, producton plants, dstrbuton centers and customers. A mathematcal model was proposed consderng the capactes of facltes and dfferent transportaton modes wth the obectve of mnmzng the cost. Ths paper s the frst to use the large neghborhood search heurstc to solve the supply chan problem. Habb et al. [9] explored the problem of collecton-dsassembly n the reverse supply chan based on the stuaton of more and more polluton. Two optmzaton models wth or wthout coordnaton were developed, mnmzng the total cost. The expermental study showed that ont optmzaton of collecton and dsassembly wth coordnaton between them mproved the global performance of the reverse supply chan ncludng lower total cost correspondng to the component demand satsfacton. Supply chan optmzaton s a growng area due to the development of socety. There are plenty of papers on supply chans Related Research on the Closed-Loop Supply Chan Kannan et al. [10] addressed a CLSC problem ncludng two companes. A forward logstcs mult-echelon dstrbuton nventory model was ntegrated wth the reverse logstcs mult-echelon dstrbuton nventory model to mnmze the total cost. The problem was proposed based on two manufacturers. Genetc algorthm and partcle swarm optmzaton were proposed to solve ths problem. The proposed model was valdated by two actual examples, and both examples were located n the southern part of Inda. The results revealed that GA can get the optmum results. However, n ths paper, the demand was determnstc. Tur et al. [11] nvestgated a problem wth the optmzaton of a manufacturng-remanufacturng transport warehousng CLSC, whch was composed of two machnes for manufacturng and remanufacturng, manufacturng stoc, purchasng warehouse, transport vehcle and recovery nventory. The proposed system too nto account the return of used products from the maret. The paper proposed a dscrete flow model, mnmzng the total cost. An optmzaton program, based on a genetc algorthm, was developed to fnd the decson varables. The paper showed how the optmal values of decson varables depend on dfferent model ndcators, such as transportaton tme and unt remanufacturng cost. Eleonora et al. [12] nvestgated the ssue of mnmzng the envronmental burden of a CLSC, consstng of a pallet provder, a manufacturer and several retalers. A smulaton model was developed wth mult-obectve optmzaton ncludng some relevant envronmental ey performance ndcators and economc metrcs. Results showed that the asset-retrevng operatons contrbute to the envronmental mpact of the system to the greatest extent. The analyss was grounded on a real CLSC, and the results provded practcal ndcatons to logstcs and supply chan managers. Zhao et al. [13] redesgned the supply chan of agrcultural products n southwest Chna under the Belt. A system dynamcs smulaton was conducted by usng carbon emssons per product as an ndcator to obtan the optmal scenaro for manageral practce and desgn an ncentve mechansm to drve supply chan operatons. A case study was provded to demonstrate the applcaton of the system dynamcs. However, the paper gnored the margnal cost of such reducton and other maretng measures whle focusng on the effects of ncentve polces on the supply chan. Huynh et al. [14] developed a mathematcal framewor to draw up an nventory replenshment and capacty-plannng problem for a CLSC wth random returns. The obectve was to mnmze the cost. The paper examned the mpact of random loss of product n the supply chan system. There are ncreasng studes on CLSC along wth the ncreasngly promnent envronmental problems. The GCLSC s gradually becomng concerned and studed.

4 Sustanablty 2018, 10, of The Studes on the Green Closed-Loop Supply Chan Zohal et al. [15] addressed the problem of how a mult-obectve logstcs model n the gold ndustry can be created and solved through an effcent meta-heurstc algorthm. The developed model ncluded four echelons n the forward drecton and three stages n the reverse. Frst, an nteger lnear programmng model was developed to mnmze costs and emssons. Then, n order to solve the model, an algorthm based on ant-colony optmzaton was developed. Soleman et al. [16] addressed a desgn problem of GCLSC ncludng supplers, manufacturers, dstrbuton centers, customers, warehouse centers, return centers and recyclng centers. Three obectves were total proft optmzaton and reducton of lost worng days due to occupatonal accdents and maxmzng responsveness to customer demand, respectvely. In order to solve the model, genetc algorthm has been used, and multple scenaros wth dfferent aspects have been studed. Lu et al. [17] addressed a problem of green supply chan management (GSCM). Ths study proposed closed-loop orentaton (CLO) as the approprate strategc orentaton to mplement GSCM practces successfully and developed a vald measurement of CLO. The structural euaton modelng method was used to examne the relatonshps among CLO, GSCM practce and envronmental and economc performance. The results showed that both CLO and GSCM have postve effects on the envronmental performance and economc performance. Recently, green CLSC has become a revenue opportunty for manufacturers nstead of a cost-mnmzaton approach [4]. Green CLSC has become a goal of many ndustres, whch can create a cleaner envronment and gve them compettve advantages. However, related lterature wors that focus on GCLSC are very few. Addtonally, n the above-mentoned studes, we can fnd lterature wors that consder one or two smlar constrants n common wth ths paper, but a study wth smlar consderatons to ths paper has not been found. In ths paper, we consder a GCLSC problem wth uncertan demand. We use some certan approxmaton to approxmate the chance constrant and propose two heurstcs to solve t. 3. Problem Statement Accordng to the actual stuatons n famous e-commerce platforms n Chna, we dvde the forward logstcs nto four layers,.e., manufacturers, frst-class warehouses, second-class warehouses and customers. Most tradtonal supply chans are decentralzed and nearly have no cooperaton between manufacturer and retaler. Wth the maret becomng more and more complex, cooperaton s essental for every company n the free maret. Hence, a centralzed supply chan has gradually been adopted by many companes, such as Mengnu Dary (a famous dary company n Chna), whch has formed a large dary ndustry chan ncludng ml source constructon, research and development, producton and sales. Wth such a supply chan, Mengnu can ntegrate resources, mprove the product ualty effectvely and set a better corporate mage. If the manufacturer and retaler cooperate wth each other, they can get more profts. Addtonally, the retaler decdes the retal prce based on producton cost, operaton cost and other costs nstead of the wholesale prce [4]. Concernng the proft dstrbuton, we assume that there s a revenue sharng contract between manufacturers and retalers. Collectng a certan number of used products s an mportant part of GCLSC, and we can get two facts from the paper [18]. Frstly, the amount of recycled products s related to the recyclng prce. Secondly, t s economc to use tradtonal dstrbuton centers as collecton centers. Second-class warehouses wll recycle the used products mostly through the on-lne channel. Based on the classfcaton of return-obects proposed by Fleschmann et al. [19] and the man recovery optons categorzed by Therry et al. [20], four nds of basc reverse logstcs networs can be dentfed [21]: the drectly reusable networ (DRN), the remanufacturng networ (RMN), the repar servce networ (RSN) and the recyclng networ (RN). In ths artcle, we focus on the recyclng networ (RN).

5 Sustanablty 2018, 10, of 22 In our studed problem, customer satsfacton ncludes logstcs speed, the ualty of products and the number of recycled used products. We manly consder the defect coeffcent of raw materal, whch has an mpact on the ualty [22]. As for logstcs, resdence tme n facltes and transportaton tme between facltes should be consdered. Dfferent transportaton modes, such as road, ral, nland navgaton or ar transport, mean dfferent transportaton tmes. Although arcraft s fast, t s also expensve. Moreover, the resdence tme s also related to the operaton system of facltes. For example, the applcaton of an ntellgent system can maredly reduce processng tme. As descrbed n the precedng paragraph, the reverse logstcs order s from the customer to the second-class warehouses and then to the second-class warehouses and fnally to the factory or others. In ths reverse logstcs, second-class warehouses play a role n recyclng, classfyng, nspectng (money can be gven to customers after nspectng the used products such as computers) and transportng. Frst-class warehouses tae the responsbltes of centralzng, dsposng and transportng. However, n order to smplfy the problem, we only consder the amount of used products recycled. As for the whole supply chan, our obectves are mnmzng the cost of the whole supply chan and maxmzng the satsfacton of customers. The cost ncludes producton cost, operaton cost, transportaton cost and constructon cost. The second obectve ncludes shppng tme, products ualty and recovery uantty. The GCLSC desgned n ths artcle s as shown n Fgure 1. Fgure 1. A green closed loop supply chan consderng recyclng. Some assumptons for ths problem are made as follows. 1. Our study manly focuses on the choce of warehouses. Therefore, we assume that manufacturer and customer locatons are fxed and nown. 2. The potental locatons of all enttes n the networ are dentfed, and the numbers of facltes that can be opened are lmted. 3. We do not consder the transshpment of goods between the same echelon. We assume that there are only flows between two dfferent echelons. For example, the producton cannot be transported from one frst-class warehouse to another frst-class house, but can be transported from a frst-class warehouse to a second-class warehouse. 4. In order to smplfy the model, the prce of recycled products s consstent regardless of ualty. 4. Mathematcal Formulaton In ths secton, a model wth the chance constrant s formulated for a generalzed problem.

6 Sustanablty 2018, 10, of Notaton Indces: : ndex of manufacturer; : ndex of frst-class warehouse; : ndex of second-class warehouse; l: ndex of customer demand pont; r: ndex of raw materal; o: ndex of operaton; : ndex of transportaton method; Sets: I: set of manufacturers; J: set of frst-class warehouses; K: set of second-class warehouses; L: set of customer demand ponts; R: set of raw materals; O: set of operatons; Q: set of transportaton methods; Problem parameters: D l : the products maxmum uantty of customer demand pont l; d l : the products mean uantty of customer demand pont l; π l : the maxmum probablty the second-class warehouses fal to meet customer demand l w r : the defect coeffcent of raw materal r to product ualty of manufacturer ; TC e : OP o : OF o : OS o : u: the upper bound of recyclng prce; v: the lower bound of recyclng prce; the unt transportaton cost when recyclng; the operaton cost of manufacturer usng operaton system o, non-negatve; the operaton cost of frst-class warehouse usng operaton system o, non-negatve; the operaton cost of second-class warehouse usng operaton system o, non negatve; TC : the unt transportaton cost from manufacturer to frst-class warehouse by vehcle, non-negatve; TF : TS l : PC r : tm o : the unt transportaton cost from frst-class warehouse to second-class warehouse by vehcle, non-negatve; the unt transportaton cost from second-class warehouse to customer demand pont l by vehcle, non-negatve; the producton of manufacturer cost usng raw materal r, non-negatve; the stay tme of products wth the manufacturer under the operaton cost OP o, non-negatve; t f o : the stay tme of products n the frst-class warehouse under the operaton cost OP o, non-negatve; ts o : the stay tme of products n the second-class warehouse under the operaton cost OP o, non-negatve; t 1 : t 2 : the transportaton tme from manufacturer to frst-class warehouse under the transportaton cost TC, non-negatve; the transportaton tme from frst-class warehouse to second-class warehouse under the transportaton cost TC, non-negatve;

7 Sustanablty 2018, 10, of 22 t 3 l : p m : the transportaton tme from second-class warehouse to customer demand pont l under the transportaton cost TC l, non-negatve; the recyclng prce; b: parameter denotng the ncentve senstvty of return amounts; β: parameter between zero and one, dependng on the proporton of products that are possble to recycle; α m : parameter denotng the coeffcent of the amounts of recyclng products, whch changes wth the recyclng prce; δ: a scalng parameter to adust the dmenson of tme; γ: a scalng parameter to adust the dmenson of product ualty; ε: a scalng parameter to adust the dmenson of the amounts of recyclng products; a: postve nteger, denotng the mnmal traffc volume; s: postve nteger, denotng the mnmal producton of manufacturer ; f : postve nteger; c: postve number, and c = u v f ; h: postve nteger, and h = [ p m v c ]; M: a suffcently large postve number; Decson varables: X r : the producton yeld of manufacturer usng raw materal r; H : FW : SW l : Y 1 : Y 2 : Y 3 o : Y 4 o : the amounts of products shpped from manufacturer to frst-class warehouse usng transportaton vehcle ; the amounts of products shpped from frst-class warehouse to second-class warehouse usng transportaton vehcle ; the amounts of products shpped from second-class warehouse to customer demand pont l usng transportaton vehcle ; bnary varable; euals one f constructng frst-class warehouse, zero otherwse; bnary varable; euals one f constructng second-class warehouse, zero otherwse; bnary varable; euals one f manufacturer uses operaton system o, zero otherwse; bnary varable; euals one f frst-class warehouse uses operaton system o, zero otherwse; Yo 5 : bnary varable; euals one f second-class warehouse uses operaton system o, zero otherwse; T 1 : T 2 : T 3 l : T 4 r : T 5 m: 4.2. Problem Model bnary varable; euals one f usng transportaton vehcle between manufacturer and frst-class warehouse, zero otherwse; bnary varable; euals one f usng transportaton vehcle between frst-class warehouse and second-class warehouse, zero otherwse; bnary varable; euals one f usng transportaton vehcle between second-class warehouse and customer demand pont l, zero otherwse; bnary varable; euals one f manufacturer uses raw materal r to produce products, zero otherwse; bnary varable; euals one f recyclng used products wth prce m, zero otherwse; mn f 1 = OBJ1 + OBJ2 + OBJ3 + OBJ4 (1) Euaton (1) s the frst obectve,.e., mnmzng the total costs.

8 Sustanablty 2018, 10, of 22 + OBJ1 = l TC H + TS l SW l + TC e β l TF FW d l α m Ym 5 m (2) Euaton (2) states the transportaton cost between facltes. The frst three parts are the transportaton costs from manufacturers to frst-class warehouses, from frst-class warehouses to second-class warehouses and from second-class warehouses to customer ponts, respectvely. The fourth part s the transportaton cost of recyclng used productons. OBJ2 = Euaton (3) states the producton cost of productons. OBJ3 = o OP o Y 3 o + o PC r X r (3) r OF o Y 4 o + o OS o Yo 5 (4) The four parts of Euaton (4) are the operaton cost of manufacturers, frst-class warehouse and second-warehouse, respectvely. OBJ4 = β l Euaton (5) states the recyclng cost. d l (α m Tm 5 p m ) (5) m max f 2 = OBJ5 + OBJ6 + OBJ7 (6) Euaton (6) s the second obectve of ths paper,.e., maxmzng the customers satsfacton ncludng shppng tme, producton ualty and the amount of recyclng productons. OBJ5 = ( o tm o Y 3 o + o t f o Y 4 o + o t 1 T1 + ts o Yo 5 + t 2 T2 + t 3 l T3 l ) δ l (7) Euaton (7) states the total transportaton tme from manufacturers to customer ponts. OBJ6 = γ (1 w r ) (8) r where γ s to mae the value of OBJ6an order of magntude wth the value of OBJ5. Accordng to w r, whch denotes the the defect coeffcent of raw materal r for product ualty [22], we can assume that 1 w r denotes the ualty. The bgger the 1 w r, the better the ualty. OBJ7 = ε β l d l (α m Tm) 5 (9) m where ε s to mae the value of OBJ7 an order of magntude wth the value of OBJ5. Accordng to the exstng paper [18], the coeffcent of recyclng products s 1 e bp, where b s the ncentve senstvty of return amounts and p m s the recyclng prce. However, n ths paper, n order to lnearze the model, we dvde the regon of prce, whch s between v and u, nto n parts, f v + hc p m v + (h + 1)c, v+(h+1)c v+hc (1 e α = bpm )dp m c and p m = hc+(h+1)c 2 + v.

9 Sustanablty 2018, 10, of 22 H Y 1 M 0 Q, I, J (10) The constrant (10) ensures the number of products, whch are shpped from manufacture to frst-class warehouse, eual to zero f frst-class warehouse s not constructed. FW Y 1 M Y 2 0 Q, J, K (11) FW (1 Y 1) M Y2 M 0 Q, J, K (12) FW Y 1 M (1 Y 2 ) M 0 Q, J, K (13) The constrants (11) (13) ensure the number of products, whch are shpped from frst-class warehouse to second-class warehouse, eual to zero f frst-class warehouse or second-class warehouse s not constructed. SW l Y 2 M 0 Q, K, l L (14) The constrant (14) ensures the number of products, whch are shpped from second-class warehouse to customer demand pont l, eual to zero f second-class warehouse s not constructed. H T 1 M 0 Q, I, J (15) T 1 a H 0 Q, I, J (16) The constrants (15) and (16) lmt the mnmum amount of traffc between manufacturers and frst-class warehouses, n other words, the number of transshpment productons are no less than a. FW T 2 M 0 Q, J, K (17) T 2 a FW 0 Q, J, K (18) The constrants (17) and (18) lmt the mnmum amount of traffc between frst-class warehouses and second-class warehouses. SW l Tl 3 M 0 Q, K, l L (19) T 3 l a SW l 0 Q, K, l L (20) The constrants (19) and (20) lmt the mnmum amount of traffc, whch s a, between second-class warehouses and customer ponts. H = X r I (21) r H = H = r X r = H = FW J (22) SW l K (23) l FW = H (24) FW (25) SW l (26) l

10 Sustanablty 2018, 10, of 22 The constrants (21) (26) ensure the flow s balanced. Pr( SW l D l ) 1 π l (27) The constrant (27) ensures that, wth a probablty of at least 1 π l, the amounts of products shpped from second-class warehouses to customer demand pont l are suffcent to meet the demand of customer l. v p m u (28) The constrant (28) states the prce lmtaton. X r Tr 4 M 0 r R, o O, I (29) T 4 r s X r 0 r R, o O, I (30) The constrants (29) and (30) ensure the producton cost r and the defcent coeffcent w r eual zero f raw materal r s not used. Yo 3 = 1 I (31) o Yo 4 = Y1 J (32) o Yo 5 = Y2 K (33) o The constrants (31) (33) state one faclty can only choose one operaton systems. T 1 = Y1 I, J (34) T 2 Y1 J, K (35) T 2 Y2 J, K (36) T (2 Y1 Y 2 ) M J, K (37) T 2 1 (2 Y1 Y 2 ) M J, K (38) Tl 3 = Y2 K, l L (39) The constrants (34) (39) ensure only one vehcle can be chosen between facltes. Tr 4 = 1 I (40) r The constrant (40) guarantees only one raw materal can be chosen when producng. Tm 5 = 1 m f (41) m The constrant (41) states only one prce can be chosen when recyclng. SW l d l + µ l (42)

11 Sustanablty 2018, 10, of 22 f (µ l ) = mn λ>0 (e λµ l/d l (1 + E[Z2 l ] bl 2 (e λb l λb l 1)) π l ) (43) f (µ l ) = 0 (44) Accordng to the exstng research [23], we use the constrant (42) to approxmate the constrant (27). µ l s some real number, and the value of µ l can be found by Euatons (43) and (44); where Z l s a random varable to model devatons from the mean demand of demand pont l, and λ s a postve number. In addton, t s assumed that there exsts some postve real number b l such that Z l b l wth probablty one. w r, H, FW, SW l 0 r R, Q, I, J, K, l L (45) The constrant (45) gves the range of varables. 5. Soluton Approach In ths secton, we ntroduce three methods to solve the lnear model after approxmaton. The frst method s the ɛ-constrant method, whch s sutable for small-scale problems. The other two methods are heurstcs ncludng NSGA-II and MOSA suted for larger scale problems ɛ-constrant Method From the above descrpton, we can now that the two obectves are conflctng: one obectve ncreases, whle the other obectve decreases. Therefore, there cannot exst a sngle optmum that smultaneously optmzes both obectves, but a set of Pareto optmal solutons. If a feasble soluton s not domnated by any other feasble soluton, t s called Pareto optmal or non-domnated, and ts obectve vector s called as a non-domnated pont. All the non-domnated ponts mae up the Pareto front, denoted by Ϝ. The ɛ-constrant method has been wdely used to solve the mult-obectve problem snce ts ncpent practce [24]. The structure of the feasble soluton cannot affect the usage of the ɛ-constrant method, whose basc dea s to focus on a sngle obectve and restrct the remanng obectves. Therefore, we need to obtan the mnmum and maxmum of the obectve that s taen nto account as a constrant The ɛ-constrant Method Framewor For a b-obectve optmzaton problem, the followng concepts are needed when usng the ɛ-constrant method [25]. Ideal pont: Let f I =( f I 1, f I 2 ) wth f I 1 = mn{ f 1(X)} and f I 2 = mn{ f 2(X)}, X Z V ; Nadr pont: Let f N =( f1 N, f 2 N) wth f 1 N = mn{ f 1 (X) : f 2 (X) = f2 I} and f 2 N = mn{ f 2 (X) : f 1 (X) = f1 I}, X Z V ; Extreme pont: f E ={ f1 I, f 2 N} and f E = { f1 N, f 2 I } are two extreme ponts on the Pareto front. In ths paper, the two obectves are total cost and the combnaton of tme, ualty and the amounts of recycled used products. The total cost could be regarded as a constrant n the desgn of the method. The detaled exact ɛ-constrant method s shown as follows: 1. Compute the deal pont f I = ( f I 1, f I 2 ) and nadr pont fn = ( f N 1, f N 2 ).

12 Sustanablty 2018, 10, of Set Ϝ = {( f1 N, f 2 I)} and ɛ = f 1 N ( = 2000 for ths problem). 3. Whle ɛ f1 I, do: (a) solve the ɛ-constrant problem wth Ob1 ɛ as a constrant and the Ob2as the sngle obectve functon to optmalty, and add the optmal soluton value ( f1, f 2 ) to Ϝ. (b) set ɛ = f1. 4. Obtan the Pareto front Ϝ by removng domnated ponts from Ϝ, f exstng An Example wth the ɛ-constrant Method To llustrate the soluton procedures of the problem by the ɛ-constrant method wth CPLEX 12.6, we consder a small nstance wth I = 2, J = 4, K = 6, L = 14, respectvely. In other words, there are two manufacturers, four frst-class warehouses, sx second-class warehouses and fourteen demand ponts. We assume that two types of raw materals, two types of operaton systems and three types of transportaton methods, whch can be chosen by managers. We obtan the deal pont ( f I 1, f I 2 ) = (84,995, 70,748) and nadr pont ( f N 1, f N 2 ) = (175,177, 31,913). Consderng the customers satsfactory mnmzaton as the only obectve and total cost, the teraton procedure s carred out from the extreme pont (175,177, 70,748). Fnally we obtan 29 non-domnated solutons, lsted n Columns 2 and 4 of Table 1. The dstances between each soluton and ts correspondng deal value are presented n Columns 3 and 5. When the value of customers satsfacton ncreases progressvely to approach the deal value, the dstance between the resultng cost and ts deal value grows conseuently. Table 1. Summary of the domnant solutons. Soluton ID Obectve 1 Obectve 2 Cost Opt 1 Satsfacton Opt 2 (1) mn Ob.2 84, % 31, % (2) Ob , % 48, % (3) Ob , % 54, % (4) Ob , % 56, % (5) Ob , % 57, % (6) Ob , % 58, % (7) Ob , % 60, % (8) Ob , % 61, % (9) Ob , % 62, % (10) Ob , % 63, % (11) Ob , % 64, % (12) Ob , % 64, % (13) Ob , % 65, % (14) Ob , % 66, % (15) Ob , % 66, % (16) Ob , % 67, % (17) Ob , % 67, % (18) Ob , % 68, % (19) Ob , % 68, % (20) Ob , % 69, % (21) Ob , % 69, % (22) Ob , % 69, % (23) Ob , % 70, % (24) Ob , % 70, % (25) Ob , % 70, % (26) Ob , % 70, % (27) Ob , % 70, % (28) Ob , % 70, % Ideal 84, % 70, % Nadr 175, % 31, %

13 Sustanablty 2018, 10, of 22 It s very tme-consumng when usng the ɛ-constrant method to solve ths small-scale nstance, not to menton the mddle or large scales. For real-world practce, t s essental to solve the much larger scale problem. Hence, developng heurstc algorthms s extremely necessary Mult-Obectve Smulated Annealng Method In order to address the complexty of problems, Krpatrc et al. [26] proposed smulate annealng (SA) frst, whch used the concept of the annealng process to see for the optmal soluton from the feasble doman. Ths algorthm terates from a set of ntal solutons wth a hgh temperature, T max, and fnshes wth a fnal temperature, T mn. The new solutons generated n each teraton are receved wth probablty, prob, whose value s a functon of the temperature. An annealng rate α (0, 1) s used to determne the speed of annealng. The bgger value of α means optmzng at a slower pace, whch can approach the optmal solutons gradually. Snce there s more than one obectve n ths paper, a modfed SA algorthm s developed to fnd approprate Pareto solutons rather than gettng one result used n a sngle obectve envronment. Based on the framewor of Bandyopadhyay et al. [27], the mult-obectve smulated annealng (MOSA) method s used to solve our problem. The procedure of MOSA s ndcated n Fgure 2. Fgure 2. The procedure of mult-obectve smulated annealng (MOSA) Non-Domnated Soluton Genetc Algorthm NSGA-II s an evolutonary algorthm, ntegratng a fast non-domnated sortng procedure and an eltst-preservng approach. The approach s wdely used to solve the mult-obectve problems effectvely, and the procedure s shown as Fgure 3. In ths paper, the chromosome can be dvded nto three parts. The frst part and second are bnary varables, whch denote the facltes and operaton system (ncludng transportaton modes), respectvely. The thrd part s the number of productons between facltes. The genetc operatons are as follows.

14 Sustanablty 2018, 10, of 22 Genetc Operator 1: 1. Randomly select two chromosomes; 2. Exchange the faclty locatons of the two chromosomes; 3. Change the second and thrd parts accordngly; 4. Recalculate the obectves. Genetc Operator 2: 1. Randomly select two chromosomes; 2. Exchange the faclty operaton system of the two chromosomes; 3. Change the frst and thrd parts accordngly; 4. Recalculate the obectves. Genetc Operator 3: 1. Randomly select a chromosome; 2. Change the number of transportaton producton; 3. Change the frst and second parts accordngly; 4. Recalculatng the obectves. Fgure 3. The procedure of non-domnated sortng genetc algorthm (NSGA-II). 6. Performance Measurement In ths subsecton, we frst tune the parameter values n NSGA-II and MOSA. Then, we mae a comparson between the two proposed algorthms usng three ndces, manly n two aspects: the dstance from the true Pareto front and the dversty of the solutons. All these algorthms are coded n MATLAB R2014b and are conducted on a PC wth a 3.90-GHz Intel Core CPU processor and 4 GB RAM memory.

15 Sustanablty 2018, 10, of Introducton of Indcators Three ndcators are ntroduced n ths secton for algorthms performance measurement, whch have been wdely adopted n prevous studes. The frst one s dstance from reference set ndcator I D. It s used to measure the dstance between the approxmate Pareto front and the true Pareto front [28]. A smaller I D means the approach performs better. For an approxmate non-domnated soluton set A and a reference soluton set R, I D s calculated by the followng expresson: I D (A, R) = 1 R mn d(x, y) y R x A where d(x, y) presents the dstance between solutons x (n set A) and y (n set R), d(x, y) = M ( f (x) f (y) =1 f max f mn where M s the number of obectves and f mn, f max, [1, M] are mnmum and maxmum values of the -th obectve n set R, respectvely. More precsely, the reference set R n the ndcator expresson refers to the true Pareto front. However, t s extremely dffcult to obtan the true Pareto front, especally for large-scale nstances. In ths stuaton, R s formed by the total solutons obtaned from the two heurstcs. The second one s the average e-domnance D. For two gven non-domnated soluton sets A, B, t s used to get the domnance relatons between them [29]. The ndcator D s defned below. ) 2 D = 1 ( R { mn max f1 (y) y R x A f 1 (x), f } 2(y) ) f 2 (x) where y x represents the relaton that soluton y domnates soluton x. C(A, B) [0, 1], where C(A, B) = 0 means that all the solutons n A are domnated by the solutons n B and C(A, B) = 1 means the opposte. Both C(A, B) and C(B, A) should be calculated for sets A and B, and A s udged better than B n the set coverage ndcator when C(A, B) > C(B, A). The thrd one s maxmum spread ndcator MS. Ths ndcator llustrates the spread performance of the non-domnated soluton set [30]. It s calculated by comparng wth the reference set R mentoned n the frst ndcator, and set A s consdered to cover a wder range of obectve values when the ndcator acheves a larger value Parameter Tunng MS(A) = M =1 ( f (x) f mn max x A f max f mn mn x A f (x) f mn f max f mn The performance of MOSA partly depends on the parameter set n the algorthm, ncludng populaton sze, the ntal temperature, teraton generatons and the coeffcent of coolng. Snce parameters of the proposed heurstcs should be tuned under approprate scale problem frstly, n our study, our tunng scale combnaton s I = 2, J = 4, K = 6, L = 14. We consder all four parameters mentoned above and carry out 36 parameter combnatons wth the followng values: pop = {200, 250}, T m = {200, 250}, ter = {20, 25, 30}, temp = {0.94, 0.96, 0.97}. The exact Pareto fronts of these nstances can be obtaned wth the ɛ-constrant method. Parameter analyss usng the exact Pareto front as the reference set s desrable and accurate. For each nstance combnaton, ten ndependent runs are mplemented consderng the probablty randomness of the ) 2

16 Sustanablty 2018, 10, of 22 obtaned results. The mean value of the dstance from reference set ndcator I D s calculated for each parameter combnaton. The results are lsted n Table 2, and we select the parameter combnaton wth the smallest I D value for the MOSA, mared n bold, whch s ; where I D s ndcated n the followng experments,.e., the parameters of MOSA are set as {pop = 250, T m = 250, ter = 20, temp = 0.97}. The parameters, populaton sze, the number of generatons, the probablty of cross and the probablty of mutaton have an nfluence on the performance of NSGA-II. In ths paper, we tae the four parameters mentoned above nto account and consder the 36 combnatons wth the followng values: pop = {150, 200}, gen = {100, 150}, p c = {0.2, 0.5, 0.8}, p m = {0.2, 0.5, 0.8}. Smlar to MOSA, the reference set s the true front obtaned by the method of ɛ-constrant, and we get the best parameter combnaton through calculatng the mean value of ndcator I D. The results are lsted n Table 3. The smallest ndcator I D s The best parameter combnaton of NSGA-II s set as {pop = 150, gen = 150, p c = 0.8, p m = 0.5}. Table 2. Computatonal results for parameter tunng of MOSA. {pop, T m, ter, temp} I D {pop, T m, ter, temp} I D {200, 200, 20, 0.94} {250, 200, 20, 0.94} {200, 200, 20, 0.96} {250, 200, 20, 0.96} {200, 200, 20, 0.97} {250, 200, 20, 0.97} {200, 200, 25, 0.94} {250, 200, 25, 0.94} {200, 200, 25, 0.96} {250, 200, 25, 0.96} {200, 200, 25, 0.97} {250, 200, 25, 0.97} {200, 200, 30, 0.94} {250, 200, 30, 0.94} {200, 200, 30, 0.96} {250, 200, 30, 0.96} {200, 200, 30, 0.97} {250, 200, 30, 0.97} {200, 250, 20, 0.94} {250, 250, 20, 0.94} {200, 250, 20, 0.96} {250, 250, 20, 0.96} {200, 250, 20, 0.97} {250, 250, 20, 0.97} {200, 250, 25, 0.94} {250, 250, 25, 0.94} {200, 250, 25, 0.96} {250, 250, 25, 0.96} {200, 250, 25, 0.97} {250, 250, 25, 0.97} {200, 250, 30, 0.94} {250, 250, 30, 0.94} {200, 250, 30, 0.96} {250, 250, 30, 0.96} {200, 250, 30, 0.97} {250, 250, 30, 0.97} Table 3. Computatonal results for parameter tunng of NSGA-II. {pop, gen, p c, p m } I D {pop, gen, p c, p m } I D {150, 100, 0.8, 0.2} {200, 100, 0.8, 0.2} {150, 100, 0.8, 0.5} {200, 100, 0.8, 0.5} {150, 100, 0.8, 0.8} {200, 100, 0.8, 0.8} {150, 100, 0.5, 0.2} {200, 100, 0.5, 0.2} {150, 100, 0.5, 0.5} {200, 100, 0.5, 0.5} {150, 100, 0.5, 0.8} {200, 100, 0.5, 0.8} {150, 100, 0.2, 0.2} {200, 100, 0.2, 0.2} {150, 100, 0.2, 0.5} {200, 100, 0.2, 0.5} {150, 100, 0.2, 0.8} {200, 100, 0.2, 0.8} {150, 150, 0.8, 0.2} {200, 150, 0.8, 0.2} {150, 150, 0.8, 0.5} {200, 150, 0.8, 0.5} {150, 150, 0.8, 0.8} {200, 150, 0.8, 0.8} {150, 150, 0.5, 0.2} {200, 150, 0.5, 0.2} {150, 150, 0.5, 0.5} {200, 150, 0.5, 0.5} {150, 150, 0.5, 0.8} {200, 150, 0.5, 0.8} {150, 150, 0.2, 0.2} {200, 150, 0.2, 0.2} {150, 150, 0.2, 0.5} {200, 150, 0.2, 0.5} {150, 150, 0.2, 0.8} {200, 150, 0.2, 0.8}

17 Sustanablty 2018, 10, of Comparson of the Proposed Algorthms In the computatonal experments, we generate 108 nstances n total. Among 108 nstances, there are 36 small-szed nstances wth the parameter combnatons: I = {1, 2}, J = {3, 4}, K = {5, 6, 7}, L = {12, 14, 16}; 36 mddle-scale nstances wth the followng values: I = {2, 3}, J = {5, 6}, K = {8, 9, 10}, L = {18, 20, 22}; 36 large-szed nstances wth the followng parameters: I = {2, 3}, J = {5, 6}, K = {9, 10, 11}, L = {24, 26, 28}. Both NSGA-II and MOSA are appled to all 108 nstance combnatons. Each example s calculated ten tmes ndependently wth ten random parameters combnatons. For all the nstances, the average results of ten ndependent runs are recorded, and we apply the three ndcators to measure the performance of the algorthms. In addton, the average runnng tme of each algorthm n every nstance test s also recorded as an ndcator, to evaluate the computatonal effcency. For nstance combnaton, t s rather dffcult or tme-consumng to get the true front, so that we apply the solutons generated by the two heurstcs to the reference set. The results of three ndcators of three scales are lsted n Tables 4 6, respectvely. Table 4. Computatonal results for 36 small-scale nstance combnatons. Instance NSGA-II (Referred to as A) MOSA (Referred to as B) I D C (AR) MS Tme I D C (BR) MS Tme {1, 3, 5, 12} {1, 3, 5, 14} {1, 3, 5, 16} {1, 3, 6, 12} {1, 3, 6, 14} {1, 3, 6, 16} {1, 3, 7, 12} {1, 3, 7, 14} {1, 3, 7, 16} {1, 4, 5, 12} {1, 4, 5, 14} {1, 4, 5, 16} {1, 4, 6, 12} {1, 4, 6, 14} {1, 4, 6, 16} {1, 4, 7, 12} {1, 4, 7, 14} {1, 4, 7, 16} {2, 3, 5, 12} {2, 3, 5, 14} {2, 3, 5, 16} {2, 3, 6, 12} {2, 3, 6, 14} {2, 3, 6, 16} {2, 3, 7, 12} {2, 3, 7, 14} {2, 3, 7, 16} {2, 4, 5, 12} {2, 4, 5, 14} {2, 4, 5, 16} {2, 4, 6, 12} {2, 4, 6, 14} {2, 4, 6, 16} {2, 4, 7, 12} {2, 4, 7, 14} {2, 4, 7, 16} Average

18 Sustanablty 2018, 10, of 22 From the prevous descrpton, the smaller the value of frst ndcator I D s, the better the algorthm s, and t s opposte for the remanng two ndcators. For the small-scale problem shown n Table 4, NSGA-II and MOSA s average values of the frst ndcator are , , whch means NSGA-II s about 37.79% better than MOSA consderng the ndcator I D. Smlarly, the mean values of NSGA-II and MOSA are and for the average e-domnance ndcator. The values and are of the thrd ndcator of the two algorthms. Addtonally, the NSGA-II performs better, by about 64.61% and 3.89% for the second and thrd ndcators. After tang the average value, we can fnd that NSGA-II s 35.43% better than MOSA consderng the ualty of solutons. As for the runnng tmes of the two algorthms, the mean tmes are seconds and seconds, respectvely. The results reflect that NSGA-II s more effcent, about 18.29% faster than MOSA. Table 5. Computatonal results for 36 mddle-scale nstance combnatons. Instance NSGA-II (Referred to as A) MOSA (Referred to as B) I D C (AR) MS Tme I D C (BR) MS Tme {2, 5, 8, 18} {2, 5, 8, 20} {2, 5, 8, 22} {2, 5, 9, 18} {2, 5, 9, 20} {2, 5, 9, 22} {2, 5, 10, 18} {2, 5, 10, 20} {2, 5, 10, 22} {2, 6, 8, 18} {2, 6, 8, 20} {2, 6, 8, 22} {2, 6, 9, 18} {2, 6, 9, 20} {2, 6, 9, 22} {2, 6, 10, 18} {2, 6, 10, 20} {2, 6, 10, 22} {3, 5, 8, 18} {3, 5, 8, 20} {3, 5, 8, 22} {3, 5, 9, 18} {3, 5, 9, 20} {3, 5, 9, 22} {3, 5, 10, 18} {3, 5, 10, 20} {3, 5, 10, 22} {3, 6, 8, 18} {3, 6, 8, 20} {3, 6, 8, 22} {3, 6, 9, 18} {3, 6, 9, 20} {3, 6, 9, 22} {3, 6, 10, 18} {3, 6, 10, 20} {3, 6, 10, 22} Average Concernng the mddle-szed problem, the results of three ndcators are lsted n Table 5. As for the dstance from the reference set ndcator, the values of the two heurstcs are and ; hence, NSGA-II performs better, by about 56.67%, than MOSA. We can fnd that the values of NSGA-II are smaller for the frst ndex comparng every nstance. Whle we use the average e-domnance

19 Sustanablty 2018, 10, of 22 ndcator to evaluate the performance, the value of every MOSA nstance s smaller, whch means MOSA performs worse, and the means are and for NSGA-II and MOSA, respectvely. NSGA-II s about 77.20% better overall for second ndcator. Whle consderng the thrd ndcator, we can fnd there are only fve nstances, {2, 5, 10, 20}, {2, 6, 8, 18}, {2, 6, 8, 22}, {3, 5, 8, 20}, {3, 6, 10, 22}, whose value of MOSA s bgger. However, on average, and for NSGA-II and MOSA state that NSGA-II performs better about 7.16%. It s easy to get the mean value, 47.01%, whch llustrates that NSGA-II s about 47.01% better than MOSA from the perspectve of solutons. The average runnng tme of 36 nstances s seconds for NSGA-II and s seconds for MOSA. NSGA-II s about 46.55% faster than MOSA. Table 6. Computatonal results for 36 large-scale nstance combnatons. Instance NSGA-II (Referred to as A) MOSA (Referred to as B) I D C (AR) MS Tme I D C (BR) MS Tme {2, 5, 9, 24} {2, 5, 9, 26} {2, 5, 9, 28} {2, 5, 10, 24} {2, 5, 10, 26} {2, 5, 10, 28} {2, 5, 11, 24} {2, 5, 11, 26} {2, 5, 11, 28} {2, 6, 9, 24} {2, 6, 9, 26} {2, 6, 9, 28} {2, 6, 10, 24} {2, 6, 10, 26} {2, 6, 10, 28} {2, 6, 11, 24} {2, 6, 11, 26} {2, 6, 11, 28} {3, 5, 9, 24} {3, 5, 9, 26} {3, 5, 9, 28} {3, 5, 10, 24} {3, 5, 10, 26} {3, 5, 10, 28} {3, 5, 11, 24} {3, 5, 11, 26} {3, 5, 11, 28} {3, 6, 9, 24} {3, 6, 9, 26} {3, 6, 9, 28} {3, 6, 10, 24} {3, 6, 10, 26} {3, 6, 10, 28} {3, 6, 11, 24} {3, 6, 11, 26} {3, 6, 11, 28} Average Lewse, the large-scale nstance experment has smlar conclusons shown n Table 6. For the frst and second ndcators, MOSA s worse than NSGA-II for every nstance. The mean values of the dstance from the reference set ndcator are and for the two algorthms, whch state that the NSGA-II s about 57.56% better than MOSA. For the average e-domnance ndcator, the average values are and , respectvely, whch llustrates that MOSA s worse than NSGA-II by about

20 Sustanablty 2018, 10, of %. Concernng the thrd ndcator, we can fnd that there are only three nstances, {2, 5, 9, 24}, {3, 5, 9, 26}, {3, 5, 10, 26}, whose value of MOSA s bgger. It s obvous that the NSGA-II s better for the mean values, whch are and for NSGA-II and MOSA. When consderng the ualty of solutons, NSGA-II s on average46.73% better than MOSA for the three ndcators. From the perspectve of runnng tme, the two algorthms runnng tmes are and , respectvely, whch llustrates that NSGA-II s faster by about 51.25% than MOSA. Consderng the above descrpton synthetcally, the mean values of three ndcators are , , for NSGA-II and , , for MOSA. The average runnng tmes of the two algorthms are and seconds, respectvely. Furthermore, NSGA-II s about 43.06% better than MOSA on average for 108 nstances n terms of the ualty of soluton. From the perspectve of runnng tme, NSGA-II s about 38.70% faster than MOSA. 7. Conclusons In ths paper, we study the GCLSC problem. Smlar to E-commerce servce, the GCLSC s dvded nto four parts ncludng manufacture, frst-class warehouse, second-class warehouse and customer pont. Furthermore, the locatons and number of manufacturer and customer ponts are nown, and several canddate locatons of facltes are avalable. Recyclng happens between customer ponts and second-class warehouses. A b-obectve model wth the chance constrant was proposed consderng uncertan demand n ths paper. From the perspectve of customers, they are very concerned about the ualty of goods and the logstcs speed, as well as the performance on envronmental protecton, so one obectve s to maxmze the satsfacton, whch conssts of the logstcs speed, ualty of goods and the amount of recyclng products n ths paper. Recyclng more products means that the contrbuton of enterprses to envronmental protecton s more remarable, whch wll also mprove the satsfacton of the customer. The other conflct obectve s to mnmze the total cost. To fnd a trade-off relaton between these two obectves, we establsh a b-obectve mathematcal programmng model oned wth the chance constrant. An approxmaton method s used to handle the chance constrant. Addtonally, an exact ɛ-constrant method s ntroduced to obtan exact Pareto fronts for small-scale nstances. Two heurstc algorthms, NSGA-II and MOSA, are proposed to solve the GCLSC problem effcently, especally for mddle- and large-scale nstances. Computatonal experments are conducted, and the results llustrate the effcency of the algorthms. Addtonally, we can conclude that NSGA-II performs better than MOSA n ths problem. Our research solves the problem of GCLSC under certan demand and provdes gudance for manufacturers. Future research drectons, as well as research lmtatons of ths paper may cover the followng aspects: () nventory constrant; nventory plays an mportant role when mang the producton plan; the mathematcal model can be extended to be closer to the actual stuaton; () t s also nterestng to consder a decentralzed supply chan, then t should be a two-stage decson problem where supplers and retalers only consder ther own costs and profts. In ths way, the problem becomes a two-stage stochastc programmng problem, and we can use a sample approxmaton approach to solve t. Acnowledgments: Ths wor was supported by the Natonal Natural Scence Foundaton of Chna (NSFC) under Grants , , and Supported by the Fundamental Research Funds for the Central Unverstes. Author Contrbutons: Mng Lu and Zhanguo Zhu conceved of and desgned the experments. Rongfan Lu performed the experments. Rongfan Lu and Xaoy Man analyzed the data. Chengbn Chu contrbuted analyss tools. Rongfan Lu wrote the paper. Conflcts of Interest: The authors declare no conflcts of nterest. References 1. Lambert, D.M.; Cooper, M.C. Issues n supply chan management. Ind. Mar. Manag. 2000, 29, Govndan, K.; Soleman, H.; Kannan, D. Reverse logstcs and closed-loop supply chan: A comprehensve revew to explore the future. Eur. J. Oper. Res. 2015, 240,

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22 Sustanablty 2018, 10, of Ztzler, E.; Thele, L.; Laumanns, M.; Fonseca, C.M.; Fonseca, V.G.D. Performance assessment of multobectve optmzers: An analyss and revew. IEEE Trans. Evolut. Comput. 2003, 7, Ztzler, E.; Deb, K.; Thele, L. Comparson of multobectve evolutonary algorthms: Emprcal results. Evolut. Comput. 2000, 8, c 2018 by the authors. Lcensee MDPI, Basel, Swtzerland. Ths artcle s an open access artcle dstrbuted under the terms and condtons of the Creatve Commons Attrbuton (CC BY) lcense (