Closed-loop supply chain network configuration by a multi-objective mathematical model. Saman Hassanzadeh Amin and Guoqing Zhang*

Transcription

1 Int. J. Business Performance and Supply Chain Modelling, Vol. 6, No. 1, Closed-loop supply chain network configuration by a multi-objective mathematical model Saman Hassanzadeh Amin and Guoqing Zhang* Department of Industrial and Manufacturing Systems Engineering, University of Windsor, Windsor, ON, N9B 3P4, Canada Fax: hassanzs@uwindsor.ca gzhang@uwindsor.ca *Corresponding author Abstract: Integration of forward and reverse channels results in closed-loop supply chain networks. In this research, a mixed-integer linear programming model is proposed to configure a closed-loop supply chain network. The network includes multiple products, plants, recovery technologies, demand markets, and collection centres. The objective function is minimisation of the total cost. The model can determine number and locations of open facilities, and flows of products in the network. In addition, we develop the model to multi-objectives by considering minimisation of defect rates and time of operations in collection centres. To solve the model, weighted-sums and distance methods are applied in copier remanufacturing example and the results are analysed. Moreover, value path approach is applied to compare the results of different methods. Keywords: closed-loop supply chain; CLSC; multi-objective programming; reverse logistics; RL; mixed-integer linear programming; MILP. Reference to this paper should be made as follows: Amin, S.H. and Zhang, G. (2014) Closed-loop supply chain network configuration by a multi-objective mathematical model, Int. J. Business Performance and Supply Chain Modelling, Vol. 6, No. 1, pp Biographical notes: Saman Hassanzadeh Amin is currently Research Associate and Sessional Instructor at Department of Industrial and Manufacturing Systems Engineering, University of Windsor, Canada. He received his PhD from University of Windsor, Canada in His research interests include application of operations research in supply chain management especially closed-loop supply chain and reverse logistics. He has published research articles in international journals such as Appl. Math. Model., Expert Syst. Appl., J. Syst. Sci. Syst. Eng., Int. J. Adv. Manuf. Technol., and Int. J. Prod. Res. Guoqing Zhang is a Professor in the Department of Industrial and Manufacturing Systems Engineering, University of Windsor. He received his PhD in Management Sciences from City University of Hong Kong in He has published articles in journals such as Computational Optimization and Applications, IIE Transactions, European Journal of Operational Research, and Operations Research. His recent research interests include optimisation in supply chain management, logistics, algorithms design and development, and business analytics. Copyright 2014 Inderscience Enterprises Ltd.

2 2 S.H. Amin and G. Zhang 1 Introduction There are two types of supply chains (SC): forward and reverse supply chains. The forward supply chain (FSC) is defined as a collection of activities in the process of converting raw materials to finished products (Cooper et al., 1997). On the other hand, reverse supply chain (RSC) contains activities of the collection and recovery of product returns in supply chain management (Melo et al., 2009; Bienstock et al., 2011). The integration of FSC and RSC forms a closed-loop supply chain (CLSC) (Guide and van Wassenhove, 2009). Several authors have investigated forward facility location models in terms of the number and location of facilities to open as well as the products to store in these locations. Some investigations have been done about facility location models in CLSC networks. The decision variables of both forward and reverse channels are determined in these models. In a well-known research, Fleischmann et al. (1997) categorised the field into three main areas including distribution planning, inventory, and production planning. They provided a survey based on this category. Jayaraman et al. (1999) investigated a RSC by an optimisation model. They determined optimal quantities of remanufactured products and cores (used parts). Fleischmann et al. (2001) proposed an optimisation model for a CLSC network including plants, disassembly centres, warehouses, and customers. They also provided some extensions such as integrated forward and reverse logistics system. But, they did not consider other objectives such as environmental-related objectives and uncertainty in the model. Kim et al. (2006) presented a mathematical model to determine the quantity of products and parts processed in a reverse logistics system. They supposed that parts are purchased from suppliers. Salema et al. (2007) extended the RSC model of Fleischmann et al. (2001) and considered uncertainty in parameters (demand and return) by defining scenario-dependent cases. Rubio et al. (2008) provided a categorisation of the reverse logistics papers that were published in international journals. Kannan et al. (2009) developed a genetic algorithm and particle swarm technique for CLSC configuration. The application of the model was shown by two examples: a plastic goods manufacturer and a tyre manufacturer. Francas and Minner (2007) designed a CLSC network by a two-stage stochastic model. They examined the effects of uncertain demand and return on the network configuration. Chanintrakul et al. (2009) provided a literature review for reverse logistics. Guide and van Wassenhove (2009) classified closed-loop supply chain networks to five phases: the golden age of remanufacturing, from remanufacturing to valuing the reverse logistics process, coordinating the RSC, closing the loop, prices and markets. Subramanian et al. (2010) proposed a mathematical model for a multi-echelon CLSC. Shi et al. (2010) applied Lagrangian relaxation method to develop a mathematical model for a remanufacturing system. The objective is maximisation of the profit. Shi et al. (2011) considered a multi-product CLSC system that the manufacturer has two channels for supplying products: producing brand-new products and remanufacturing returns into as-new ones. They considered uncertain demand and return by stochastic programming. Paksoy et al. (2011) developed a mathematical model for a reverse logistic system by considering different costs. They utilised a case study to show the model. Akcali and Cetinkaya (2011) reviewed several papers of RL and CLSC. They also categorised decision techniques. Amin and Zhang (2012a) proposed a general network based on commercial returns, end-of-use, and end-of-life returns. The network consists of manufacturer, collection, repair, disassembly, recycling, and disposal sites. Furthermore,

3 Closed-loop supply chain network configuration 3 they developed the model for a secondary market. Amin and Zhang (2012b) developed an optimisation model for CLSC configuration and supplier selection, simultaneously. The model has been extended for a multi-objective situation. Hasani et al. (2012) developed an optimisation model under uncertain demand and purchasing cost. Lundin (2012) examined the effects of design changes of a CLSC network by a mathematical model. Amin and Zhang (2013) considered uncertainty and selection problem in CLSC configuration. In the majority of CLSC papers, the total cost is minimised. On the other hand, a minority of authors have considered other objectives (in addition to the total cost) by multi-objective models. Minimisation of the supply chain costs, energy use, and residual waste have been considered in the paper of Krikke et al. (2003). Sheu et al. (2005) considered maximisation of the manufacturing chain-based net profit, and the reverse chain-based net profit. Ahluwalia and Nema (2006) developed a model for minimisation of the total cost, and environmental risk. Sheu (2008) considered maximisation of the supply chain-based net profit and minimisation of the reverse chain-based net cost. Pati et al. (2008) developed a goal programming model for a recyclable wastepaper CLSC network by considering minimisation of the reverse logistics cost, maximisation of the product quality, and maximisation of environmental benefits. Du and Evans (2008) considered two objectives for a reverse logistics network: minimisation of the overall costs, and minimisation of the total tardiness of cycle time. Selim and Ozkarahan (2008) took into account minimisation of the total cost and investment with maximisation of the total service level. Pishvaee et al. (2010) developed a multi-objective model for a CLSC system. They considered minimisation of the total cost, and maximisation of the responsiveness of a logistics network. Pishvaee and Torabi (2010) considered minimisation of the overall costs, and the delivery tardiness. To our knowledge, no investigation has considered multi-objective mathematical models in selection of collection centres during CLSC network configuration. In this paper, an optimisation model is proposed to configure a CLSC network including multiple plants, products, recovery technologies, demand markets, and collection centres. The new products are sent from plants to demand markets. Then, some of them are returned. The returned products are divided in collection centres. Some of them are disposed. On the other hand, the rests are carried to the plants. Plants can manufacture new products and remanufacture returned products. Minimisation of the total cost is the objective function. Besides, some constraints such as capacity and demand are considered. Copier remanufacturing example is used to show the application of the proposed model. We also extend the model to take into account other objectives in addition to the total cost. The second and third objectives are minimisation of defect rates and time of operations in collections sites, respectively. This research is among the first investigations that consider costs, defect rates, and time of operations in collection centres, simultaneously during CLSC configuration. Two methods (weighted-sums and distance methods) are utilised to solve the multi-objective model. Moreover, the effects of multi-objectives are analysed and efficient solutions are calculated. Ultimately, value path approach is utilised to compare the results. This article is organised as follows. The problem is described in Section 2. Then, the model is formulated in Section 3. In Section 4, copier remanufacturing example is presented. An extension to consider multi-objective is provided in Section 5. Finally in Section 6, conclusions are discussed.

4 4 S.H. Amin and G. Zhang 2 Problem definition A CLSC network is shown in Figure 1. The network consists of plants, collection centres, and demand markets. It is supposed that the plants are able to manufacture new products and remanufacture returned products. In the forward channel, the new products are sent to demand markets. Then in the reverse channel, the returned products are carried to collection centres to determine the condition of the returned products by some operations such as inspection. As a result, the products are separated in collection centres to returns and disposal. Then, the returns are carried to plants to be remanufactured. It is assumed that locations of demand markets and collection centres are fixed. Besides, capacities of plants and collection centres are known in advance. Furthermore, we assume that there are different recovery technologies in collection centres. Different technologies may lead to diverse processing costs. The objective is minimisation of the total cost to identify open facilities (plants and collection centres) and to know how many products exist in each part of the network. Figure 1 The CLSC network Plants 1... b... B Forward channel Reverse channel Collection centres 1... f... F Disposal centre Demand markets 1... e... E 3 Model formulation A mixed-integer linear programming model can be proposed for the CLSC network. The definitions of sets, parameters, and decision variables are as follows: 3.1 Sets A B C Set of recovery technologies (1 a A). Set of plants locations (manufacturing and remanufacturing) (1 b B). Set of products (1 c C).

5 Closed-loop supply chain network configuration 5 E F Set of demand markets locations (1 e E). Set of collection centres locations (1 f F). 3.2 Parameters G c Production cost of product c. H c Transportation cost of product c per km between plants and demand markets. I c Transportation cost of product c per km between demand markets and collection centres. J c Transportation cost of product c per km between collection centres and plants. K c Transportation cost of product c per km between collection centres and disposal centre. L b Fixed cost for opening plant b. M fa Fixed cost for installing technology a at collection centre f. N ca Cost saving of product c (because of product recovery) using technology a. O ca Disposal cost of product c using technology a. P b Capacity of plant b. Q fa Capacity of collection centre f using technology a. D be The distance between location b and e generated based on the Euclidean method. D ef and D fb are defined in the same way. D f is the distance between collection centre f and disposal centre. d ec Demand of customer e for product c. r c Return of product c. α ca Minimum disposal fraction of product c using technology a. 3.3 Decision variables X bec Quantity of product c produced by plant b for demand market e. Y efca Quantity of returned product c from demand market e to collection centre f using technology a. S fbca Quantity of returned product c from collection centre f to plant b using technology a. T fca Quantity of returned product c from collection centre f to disposal centre using technology a. Z b 1, if a plant is located and set up at potential site b, 0, otherwise. 1, if technology a is installed at potential collection site f, 0, otherwise. W fa

6 6 S.H. Amin and G. Zhang Min z = L Z + M W + ( G + H D ) X 1 b b fa fa c c be bec b a f b e c a e f c a f b c a f c ( ) + N + I D Y ( ) ( ) ca c ef efca + N + J D S ca c fb fbca + O + K D T ca c f fca (1) s.t. X bec dec e, c, (2) b Sfbca + Xbec PZ b b b, (3) a f c e c Yefca Xbec e, c, (4) a f b α Y T f, c, a (5) ca efca fca e Yefca QfaWfa f, a, (6) e c Yefca = Sfbca + Tfca f, c, a, (7) e b Sfbca = rc c, (8) a f b Z, W {0,1} b, f, a, (9) b fa X, Y, S, T 0 b, e, f, c, a, (10) bec efca fbca fca The total cost is minimised in the objective function. The first and second parts of the objective function represent the fixed costs of opening plants and installing technologies at collection centres, respectively. The production and transportation costs of new products are written in the third part. The recovery and transportation costs of returned products are taken into account in the fourth part. Additionally, the total recovery and transportation costs of returned products from collection centres to plants are written in the fifth part. Moreover, the sixth part represents transportation and disposal costs. Demand is considered in constraint (2) and it shows that the number of manufactured products must be greater than demand. Constraint (3) is capacity constraint of manufacturing and remanufacturing plants. Constraint (4) ensures that forward channel is

7 Closed-loop supply chain network configuration 7 greater than reverse one. Minimum disposal fraction is considered in constraint (5). Capacity constraint of installing technologies at collection centres is considered in constraint (6). Constraint (7) represents that the quantity of returned products to plants and quantity of products in disposal centre for each collection centre and each product is equal to the quantity of returned products from demand market. Constraint (8) represents the quantity of returned products. Constraint (9) ensures the binary decision variables. Furthermore, constraint (10) represents the non-negativity of the decision variables. 4 Copier remanufacturing example In this section, copier remanufacturing is considered as an example for the proposed model. Copier is a machine that makes paper copies of documents and other visual images. Some researchers such as Fleischmann et al. (2001) have investigated copier remanufacturing systems. Some companies such as Canon collect used copy machines from customers and remanufacture them. They check the quality standards of used copiers in collection sites to make sure the returned products have specific quality standards. The products that do not have minimum quality are sent to disposal centre. The goal of this section is to show the mathematical model by a realistic example. In this example, a deterministic model is examined. Data of costs and minimum disposal fraction are adopted from Fleischmann et al. (2001). The data are written in Table 1. Uniform distribution between 0 and 200 units of distance on the x and y coordinates is utilised to generate the locations for plants, demand markets, collection centres, and disposal centre (Then, they are considered as fixed points). Table 1 Data for the example A = 3 (number of recovery technologies) I c = ($/km) O ca = 2.5 ($) B = 4 (number of potential plants) J c = ($/km) P b = 250,000 (products) C = 3 (number of products) K c = ($/km) Q f a = 100,000 (products) E = 5 (number of demand markets) L b = 5,000,000 ($) d ec = 15,000 (products) F = 4 (number of potential collection centres) M fa = 500,000 ($) r c = 45,000 (products) G c = 15 ($) N ca = 7 ($) α ca = 0.4 H c = ($/km) The problem has been solved by CPLEX CPLEX is an optimisation software package that can solve different types of optimisation problems including mixed-integer linear programming models. In addition, a personal computer (32-bit operating system, 2.33 GHz CPU, and 4.00 GB) is used to run the software. The problem has been solved in seconds. It has 1,857 non-zero elements, 122 single equations, 437 single variables, and 16 discrete variables. The value of objective function (total cost) is 12,911,152. The optimal network is illustrated in Figure 2. As it can be observed from the figure, the plants 1, 4, and collection centres 1, 2, 3 are open. Furthermore, recovery technologies 1 and 3 are utilised. Figure 3 illustrates the sensitivity analysis of the demand. It can be seen that by increasing demand, value of the objective function (total cost) will be increased.

8 8 S.H. Amin and G. Zhang Figure 2 Optimal closed-loop supply chain network (product 1) (see online version for colours) Figure 3 Sensitivity analysis of demand (see online version for colours) Objective value Demand 5 Extension: multi-objectives model Not only, the total cost is important in CLSC network configuration, but also quality and time of operations in collection centres should be taken into account. To this goal, new parameters are defined. R fca is parameter of defect rate (percent) of product c in collection centre f using technology a. As a result, the second objective function is defined in equation (11). To consider the time of operations, U fca is defined as time (minutes) of operations of product c in collection centre f using technology a. Thus, third objective function can be written in equation (12).

9 Closed-loop supply chain network configuration 9 (11) Min z = R Y + S + T a f c e b 2 fca efca fbca fca (12) Min z = U Y + S + T a f c e b 3 fca efca fbca fca 5.1 Solution methods In this section, two methods are utilised to solve the multi-objective model. The first one is weighted-sums method, and second one is distance method. Using these methods, the problem can be transformed to a single-objective optimisation problem. For more information about multi-objective models and algorithms, you can refer to Collette and Siarry (2003) Weighted-sums method In this method, different weights are assigned to the objective functions. Generally, decision makers determine the values of weights. In this case, there are three weights (w 1, w 2, and w 3 ) because of three objective functions. It is noticeable that w 1, w 2, w 3 0 and w 1 + w 2 + w 3 = 1. equation (13) shows the formula for our problem. Min z = w1z 1+ w2z2 + w3z3 (13) s.t. equations (2) (10) Distance method Distance to a reference objective is a useful method to transform the problem to a mono-objective one. In this method, ideal values of objective functions are defined (V 1, V 2, V 3 in our case). Then, the summation of distances between ideal values and objective functions are calculated in the main objective function. Equation (14) shows a transformed problem. Min z = V1 z1 + V2 z2 + V3 z3 (14) s.t. equations (2) (10). 5.2 Discussion In this section the example is solved by the two methods and results are analysed. The data for the second objective (defect rate) and the third objective (time of operations) are written in Table 2. As mentioned before, CPLEX is utilised to solve the problem. Generally, it is easy to use weighted-sums method. This method can be applied to approximate the Pareto front, but it is not appropriate to determine the exact points of Pareto front. The performance of distance method depends on the selection of ideal values (reference sets). Good ideal values can lead to optimal solutions. The advantage of distance method is to discover efficient solutions in both convex and concave problems.

10 10 S.H. Amin and G. Zhang Table 2 Data for the multi-objective example R fca defect rate U fca time of operations f.c. a f.c a The optimal network using weighted-sums method (w 1 = w 2 = w 3 = 1/3) is illustrated in Figure 4. Results show that the plants 1 and 3 are open. Besides, the collection centre 1 is active. Therefore, the results have been changed rather the single-objective function. The value of the first objective function (total cost) is 12,974,000. Therefore, the total cost has increased (it was 12,911,152 in the mono-objective problem). The problem also has been solved by distance method (V 1 = 12,000,000, V 2 = 1,000,000, and V 3 = 4,000,000). We observed that the optimal network by distance method is similar to Figure 4. Table 3 shows the results of assigning different weights to the objective functions. It can be seen that by changing the weights of objective functions, open facilities (plants and collection centres) may be changed. Figure 4 Optimal closed-loop supply chain network (see online version for colours) Note: Weighted-sums method, w 1 = w 2 = w 3 = 1/3.

11 Closed-loop supply chain network configuration 11 Table 3 Results of the multi-objective model (weighted-sums method) Weights w 1 w 2 w 3 Open plants Open collection centres , 4 1, 2, , , , , , , 2 1, 4 Efficient solutions can be calculated by multi-objective programming models. An efficient solution has the property that it is impossible to improve any one objective values without sacrificing on at least one other objective. A collection of efficient solutions forms Pareto front or trade-off surface (Collette and Siarry, 2003; Wadhwa and Ravinsdran, 2007). Some efficient solutions are written in Table 4. Each of the cases shows a unique situation. Managers can utilise Table 4 in decision-making process. The values of objective functions are illustrated in Figure 5. Table 4 Efficient solutions Multi-objective method First objective Second objective Third objective Weighted-sums method Case 1 (w 1 = 1, w 2 = 0, w 3 = 0) 12,911,000 1,744,000 10,410,000 Case 2 (w 1 = 1/3, w 2 = 1/3, w 3 = 1/3) 12,974,000 1,455,000 4,600,000 Case 3 (w 1 = 0.2, w 2 = 0.7, w 3 = 0.1) 12,929,000 1,425,000 4,650,000 Case 4 (w 1 = 0.7, w 2 = 0.1, w 3 = 0.2) 12,928,000 1,580,000 4,950,000 Case 5 Distance method 12,974,000 1,455,000 4,600,000 Figure 5 The values of objective functions (see online version for colours)

12 12 S.H. Amin and G. Zhang In this paper, we use value path approach which has been introduced by Schilling et al. (1983). This approach can illustrate the tradeoffs among the objectives in problems with more than two objective functions. The approach has been applied in some papers (e.g., Weber and Current, 1997; Wadhwa and Ravinsdran, 2007). The values of the approach are written in Table 5. They are calculated based on the value of each objective function divided by the best solution of each objective values. Therefore, the minimum value for each axis is 1. The value path approach is shown in Figure 6 using the results of Table 5. A vertical axis is assigned for each of the three objective functions. It can be observed that weighted-sums method (w 1 = 1, w 2 = 0, w 3 = 0) minimises first objective function (total cost) but it has 22% more defect rates (second objective) and 1.26% more time of operations (third objective) than the best solutions for those objective functions. Table 5 Value path approach Multi-objective method First objective Second objective Third objective Weighted-sums method (w 1 = 1, w 2 = 0, w 3 = 0) (w 1 = 0.2, w 2 = 0.7, w 3 = 0.1) (w 1 = 0.7, w 2 = 0.1, w 3 = 0.2) Distance method Figure 6 The value path approach (see online version for colours)

13 Closed-loop supply chain network configuration 13 6 Conclusions In this research, we proposed a mixed-integer linear programming model to configure a CLSC network including multiple plants, products, technologies, demand markets, and collection centres. The total cost (fixed costs of opening facilities, production, and transportation costs) is minimised in the model. Besides, it is extended by two methods (weighted-sums method and distance method) to consider three objectives (minimisation of total cost, defect rates, and time of operations), concurrently. We also applied the model for a copier remanufacturing example. The results are analysed and different efficient solutions are calculated. In addition, value path approach is applied to demonstrate the efficient solutions of multi-objective methods. In this paper, a deterministic model is considered. But, some parameters such as demand, return, and minimum disposal fraction are uncertain parameters in practice. As future works, some techniques such as fuzzy sets theory, stochastic programming, and robust optimisation can be applied to analyse the effects of uncertainty and vagueness on the CLSC network configuration. Another future research is investigating on the mathematical properties of the model to develop appropriate solution approaches. References Ahluwalia, P.K. and Nema, A.K. (2006) Multi-objective reverse logistics model for integrated computer waste management, Waste Management and Research, Vol. 24, No. 6, pp Akcali, E. and Cetinkaya, S. (2011) Quantitative models for inventory and production planning in closed-loop supply chains, International Journal of Production Research, Vol. 49, No. 8, pp Amin, S.H. and Zhang, G. (2012a) A proposed mathematical model for closed-loop network configuration based on product life cycle, The International Journal of Advanced Manufacturing Technology, Vol. 58, No. 5, pp Amin, S.H. and Zhang, G. (2012b) An integrated model for closed-loop supply chain configuration and supplier selection: multi-objective approach, Expert Systems with Applications, Vol. 39, No. 8, pp Amin, S.H. and Zhang, G. (2013) A three-stage model for closed-loop supply chain configuration under uncertainty, International Journal of Production Research, Vol. 51, No. 5, pp Bienstock, C.C., Amini, M. and Retzlaff-Roberts, D. (2011) Reeengineering a reverse supply chain for product returns services, Int. J. Business Performance and Supply Chain Modelling, Vol. 3, No. 4, pp Chanintrakul, P., Coronado Mondragon, A.E., Lalwani, C. and Wong, C.Y. (2009) Reverse logistics network design: a state-of-the-art literature review, Int. J. Business Performance and Supply Chain Modelling, Vol. 1, No. 1, pp Collette, Y. and Siarry, P. (2003) Multi Objective Optimization: Principles and Case Studies, Springer-Verlag, New York. Cooper, M.C., Lambert, D.M. and Pagh, J.D. (1997) Supply chain management: more than a new name for logistics, The International Journal of Logistics Management, Vol. 8, No. 1, pp.1 9. Du, F. and Evans, G.W. (2008) A bi-objective reverse logistics network analysis for post-sale service, Computers & Operations Research, Vol. 35, No. 8, pp Fleischmann, M., Beullens, P., Bloemhof-Ruwaard, J.M. and van Wassenhove, L.N. (2001) The impact of product recovery on logistics network design, Production and Operations Management, Vol. 10, No. 2, pp

14 14 S.H. Amin and G. Zhang Fleischmann, M., Bloemhof-Ruwaard, J.M., Dekker, R., van der Laan, E., van Nunen, J.A.E.E. and van Wassenhove, L.N. (1997) Quantitative models for reverse logistics: a review, European Journal of Operational Research, Vol. 103, No. 1, pp Francas, D. and Minner, S. (2009) Manufacturing network configuration in supply chains with product recovery, Omega, Vol. 37, No. 4, pp Guide Jr., V.D.R. and van Wassenhove, L.N. (2009) The evolution of closed-loop supply chain research, Operations Research, Vol. 57, No. 1, pp Hasani, A., Zegordi, S.H. and Nikbakhsh, E. (2012) Robust closed-loop supply chain network design for perishable goods in agile manufacturing under uncertainty, International Journal of Production Research, Vol. 50, No. 16, pp Jayaraman, V., Guide Jr., V.D.R. and Srivastava, R. (1999) A closed-loop logistics model for remanufacturing, Journal of the Operational Research Society, Vol. 50, No. 5, pp Kannan, G., Noorul Haq, A. and Devika, M. (2009) Analysis of closed loop supply chain using genetic algorithm and particle swarm optimization, International Journal of Production Research, Vol. 47, No. 5, pp Kim, K.B., Song, I.S. and Jeong, B.J. (2006) Supply planning model for remanufacturing system in reverse logistics environment, Computers & Industrial Engineering, Vol. 51, No. 2, pp Krikke, H., Bloemhof-Ruwaard, J. and van Wassenhove, L.N. (2003) Concurrent product and closed-loop supply chain design with an application to refrigerators, International Journal of Production Research, Vol. 41, No. 16, pp Lundin, J.F. (2012) Redesigning a closed-loop supply chain exposed to risks, International Journal of Production Economics, Vol. 140, No. 2, pp Melo, M.T., Nickel, S. and Saldanha-da-Gama, F. (2009) Facility location and supply chain management a review, European Journal of Operational Research, Vol. 196, No. 2, pp Paksoy, T., Bektaş, T. and Özceylan, E. (2011) Operational and environmental performance measures in a multi-product closed-loop supply chain, Transportation Research Part E: Logistics and Transportation Review, Vol. 47, No. 4, pp Pati, K.R., Vrat, P. and Kumar, P. (2008) A goal programming model for paper recycling system, Omega, Vol. 36, No. 3, pp Pishvaee, M.S. and Torabi, S.A. (2010) A possibilistic programming approach for closed-loop supply chain network design under uncertainty, Fuzzy Sets and Systems, Vol. 161, No. 20, pp Pishvaee, M.S., Farahani, R.Z. and Dullaert, W. (2010) A memetic algorithm for bi-objective integrated forward/reverse logistics network design, Computers & Operations Research, Vol. 37, No. 6, pp Rubio, S., Chamorro, A. and Miranda, F.J. (2008) Characteristics of the research on reverse logistics ( ), International Journal of Production Research, Vol. 46, No. 4, pp Salema, M.I.G., Barbosa-Povoa, A.P. and Novais, A.Q. (2007) An optimization model for the design for a capacitated multi-product reverse logistics network with uncertainty, European Journal of Operational Research, Vol. 179, No. 3, pp Schilling, D.A., ReVelle, C. and Cohon, J. (1983) An approach to the display and analysis of multiobjective problems, Socio-Economic Planning Science, Vol. 17, No. 2, pp Selim, H. and Ozkarahan, I. (2008) A supply chain distribution network design model: an interactive fuzzy goal programming-based solution approach, International Journal of Advanced Manufacturing Technology, Vol. 36, Nos. 3 4, pp Sheu, J.B. (2008) Green supply chain management, reverse logistics and nuclear power generation, Transportation Research Part E: Logistics and Transportation Review, Vol. 44, No. 1, pp

15 Closed-loop supply chain network configuration 15 Sheu, J.B., Chou, Y.H. and Hu, C.C. (2005) An integrated logistics operational model for green-supply chain management, Transportation Research Part E, Vol. 41, No. 4, pp Shi, J., Zhang, G. and Sha, J. (2011) Optimal production planning for a multi-product closed loop system with uncertain demand and return, Computers & Operations Research, Vol. 38, No. 3, pp Shi, J., Zhang, G., Sha, J. and Amin, S.H. (2010) Coordinating production and recycling decision with stochastic demand and return, Journal of Systems Science and Systems Engineering, Vol. 19, No. 4, pp Subramanian, P., Ramkumar, N. and Narendran, T.T. (2010) Mathematical model for multi-echelon, multi-product, single time period closed loop supply chain, Int. J. Business Performance and Supply Chain Modelling, Vol. 2, Nos. 3 4, pp Wadhwa, V. and Ravindran, A.R. (2007) Vendor selection in outsourcing, Computers & Operations Research, Vol. 34, No. 12, pp Weber, C.A. and Current, J.R. (1997) A multiobjective approach to vendor selection, European Journal of Operational Research, Vol. 68, No. 2, pp