Designing an Integrated Logistics Network in a Supply Chain System

Transcription

1 SCE Journal of Civil Engineering (2013) 17(4): DOI /s ransportation Engineering Designing an Integrated Logistics Network in a Supply Chain System Hyangsook Lee*, i Zhang**, Maria Boile***, Sotiris heofanis****, and Sangho Choo***** Received February 15, 2012/Revised June 14, 2012/Accepted July 15, 2012 Abstract Many companies spend significant amounts of money and time on reverse logistics which mainly deal with transporting and handling returned products. herefore, efficient management of return products is an urgent and interesting issue facing the companies. his paper presents a facility location problem of the integrated logistics network aiming to improve the efficiency of both forward and reverse logistics. hree types of facilities are identified: Warehouses (forward logistics), collection centers (reverse logistics) and hybrid facilities (both forward and reverse logistics). Instead of the traditional static problem, the paper proposes a nonlinear mixed integer model addressing the dynamic integrated forward and reverse distribution network design problem for 3PLs (hird Party Logistics Providers). A bi-objective model is developed to minimize the total shipping cost and time simultaneously. An example is tested to evaluate the model. eywords: facility location problem, integrated freight logistics, distribution network, bi-objective model 1. Introduction As return rates and costs grow significantly, companies are confronted with challenges to improve their distribution networks in a more cost and time efficient manner, particularly with respect to reverse logistics. Currently, many companies use inefficient processes for transporting and handling returned products, which are slow and expensive. he design of the logistic distribution network typically has separated forward and reverse product flows, ignoring the relationship between them. herefore, integrating forward and reverse logistics is an interesting issue to improve the efficiency and productivity of the entire distribution operations. Up to now, little attention has been paid to this integrated concept, although it is known to be more effective (Fleischmann et al., 2001). Due to requirements for the sustainable logistics network design and needs of the efficient distribution system, good planning of the facility location problem to save reconstruction costs and produce less waste using limited resources effectively is necessary. his paper presents a network design problem determining the types of locations and facilities in an integrated forward and reverse logistics network for 3PLs. In general, many companies are outsourcing their distribution parts to 3PLs to improve logistics operations for both forward and reverse flows and take advantage in cost and revenue. In this study, existing potential sites are operated as one of the three types of facilities by minimizing the cost and time at different time periods. he three types of facilities are warehouses (handling forward flows), collection centers (handling reverse flows) and hybrid facilities (having the functions of both warehouse and collection centers). he paper applies the concept of hybrid facility to deal with both forward and reverse channels simultaneously. A nonlinear mixed integer formulation is proposed to model 3PL operations in a dynamic integrated distribution network. he model finds facility locations and determines shipping strategies between clients of 3PLs and customers. he two objectives of minimizing the total shipping cost and time are combined into one using a weighted time value. he structure of this paper is as follows. he next section presents an up-to-date literature review on forward logistics, reverse logistics and integrated logistics, respectively. he third section defines the research problem and formulates a bi-objective model. he fourth section discusses model applications and results. he last section concludes the paper with some final remarks. 2. Literature Review Forward and reverse flows are two major directions in distribution logistics networks. he facility location-allocation problem for forward logistics is a well researched topic and a lot *Research Fellow, Environmental Development Institute, Hongik University, Seoul , orea (Corresponding Author, hslee3060@gmail.com) **Graduate Student, Dept. of Civil, Architectural and Environmental Engineering, University of exas, Austin, X 77005, USA ( ms.zhang.ti@gmail.com) ***Research Director, Centre for Research and echnology Hellas, Hellenic Institute of ransport , Athens, Greece ( boile@ certh.gr) ****President, e-pos S.A , eratsini, Piraeus, Greece ( stheofanis@e-pos.gr) *****Member, Assistant Professor, Dept. of Urban Design & Planning, Hongik University, Seoul , orea ( shchoo@hongik.ac.kr) 806

2 Designing an Integrated Logistics Network in a Supply Chain System of articles have been published over the past two decades. A large number of works (Sridharan, 1995; Dogan and Geotschalckx, 1999; Sabri and Beamon, 2000; Dasciand and Verter, 2001; Jayaraman and Pirkul, 2001; Syarif et al., 2002; Chopra, 2003; Jayaraman and Ross, 2003; Melachrinoudis et al., 2005; Altiparmak et al., 2006; Amiri, 2006; Chen et al., 2007; Cordeau et al., 2008; Dupont, 2008; siakis and Papageorgiou, 2008) have formulated models considering the capacitated/uncapacitated, single/multi-period, single/multi-product, single/multi-objective network designs and developed various solution techniques. lose and Drexl (2005) presented a good summary of major researches, which contributed to the current state of-the-art, focusing on fundamental assumptions, mathematical models and solution algorithms. here are also many studies concerning the process of reverse product flows. Stock (1992, 1998) gave a definition of reverse logistics and described reverse logistics programs. Following studies proposed analytical models dealing with the reverse logistics network design problem. Spengler et al. (1997) developed a Mixed Integer Linear Programming (MILP) model for an integrated dismantling and recycling planning system. A modified decomposition algorithm was used for finding the optimal solution. Marine and Pelegrin (1998) analyzed a new plant location problem, defined as the Return Plant Location Problem (RPLP), by extending the Simple Plant Location Problem (SPLP). Lagrangian decomposition using both heuristic and exact solution methods was applied, respectively, to test the research problems. Jayaraman et al. (2003) proposed a 0-1 Mixed Integer Programming (MIP) model for reverse distribution. Due to complexity of the model, a heuristic solution methodology was developed. Leickens and Vandaele (2007) studied a network design problem of reverse logistics with stochastic lead time. hey proposed an MILP model based on the modified multilevel warehouse location problem for a single product-single level network. Several examples were examined utilizing a Genetic Algorithm (GA) with the technique of differential evolution. Du and Evans (2008) addressed a bi-objective reverse logistics network problem for the post-sale service. wo objectives were presented; one is to minimize the overall costs and the other is to minimize the total tardiness of the cycle. he study found a set of non-dominated solutions from the facility capacity arrangement among potential facility locations, as well as the associated transportation flow between customers and service facilities. he solution approach consists of a combination of the three algorithms: scatter search, the dual simplex method, and the constraint method. Min et al. (2006) discussed a multi-echelon reverse logistics network problem for product returns. A nonlinear mixed integer programming model including facilities such as collection points and centralized return centers was proposed in the paper. he authors applied a GA to solve the reverse logistic problem. Salema et al. (2007) designed a reverse distribution network with capacity limits, multi-product management and uncertainly of product demands and returns. A MIP formulation was developed and solved by standard Brunch and Bound (B&B) technique. he generality of the model was corroborated and very satisfactory computational times were obtained. he model was limited to the solution of small size problems. As the problem size increased, the computational burden grew substantially. Aras et al. (2008) presented a collection center location problem for incentive-dependent returns under a pickup policy with capacitated vehicles. he incentive depends on conditions of the returned items. he authors formulated a mixed integer nonlinear facility location-allocation model and developed heuristic methods as solution approaches. All the aforementioned works focused on the independent forward and reverse flows, ignoring the interaction between them. Fleischmann et al. (1997) first pointed out that reverse distribution does not necessarily present a symmetric picture of forward distribution and it is more efficient to consider forward and reverse logistics flows at the same time. o improve the separate logistics operations, researchers started to consider an integrated forward-reverse distribution network in the 2000s. Hence, modeling approaches adopting the integrated system became an emerging field. Fleischmann et al. (2001) presented a logistics network design problem considering the integrated forward and return flows to analyze the impact of product returns on networks. hey assumed four types of participants, plants, warehouses, disassembly centers and customers. he new network showed significant cost savings, compared to a sequential design of the two networks. Salema et al. (2006) extended Fleischmann et al. (2001) s work defining a single product model under unlimited capacity and a multi-product model under capacity limitations. he proposed MILP formulations optimized forward and reverse networks simultaneously, based upon the warehouse location-allocation model. Salema et al. (2007) presented a generalized model for designing a capacitated multi-product reverse logistics network with uncertainly, which allows easier application to the real cases. An MILP model integrating the traditional forward chain with reverse one was formulated and solved by Standard B&B techniques. Lu and Bostel (2007) developed a facility location model for logistics systems by capturing simultaneous forward-reverse flows. he model focused on remanufacturing activities that convert used/defective products or parts to new ones via intermediate centers and remanufacturing centers. A 0-1 MIP model for a two-level location problem was developed and solved by algorithms based upon Lagrangian heuristics. Fuente et al. (2008) proposed an Integrated Model for Supply Chain Management (IMSCM) which simultaneously handles forward and reverse logistics. he model re-defined demand management procedures, order management procedures, manufacturing management procedures, procurement management procedures, distribution management procedures, client management procedures, etc. he application of IMSCM identified new business opportunities by providing sub-processes and activities for the reverse logistic chain in the existing supply chain. Vol. 17, No. 4 / May

3 Hyangsook Lee, i Zhang, Maria Boile, Sotiris heofanis, and Sangho Choo Some studies applied the concept of hybrid facility to the integrated system to cover both forward and reverse product processes in a distribution facility. Operating hybrid facilities can save money and improve the efficiency and service level by sharing resources such as equipment and storage spaces, while having inherent complexity. Lee et al. (2008) presented a multiproduct distribution network design problem of 3PLs with reverse logistics operations. hey focused on integrating forward and reverse channels in a network including distribution facilities such as warehouses, collection centers and hybrid warehouse-collection centers. A static model concerning the determined forward and return flows was formulated to find strategies for distributing products. GA with two greedy algorithms solved the problem. o and Evans (2007) proposed an MIP model for the design of a dynamic integrated distribution network. A hybrid warehouse-repair facility deals with both forward and reverse products at the same time. A model for dynamic supply chain management by 3PLs was formulated considering the uncertainty of the demand and return rate. A GA-based heuristic was developed for the solution purpose. Sahyouni et al. (2007) developed three generic facility location models to design forward and reverse logistics networks throughout different stages of the product's life cycle. Subsequently, the models were extended to the uncapacitated fixed-charge location problem that integrates the forward and reverse distribution activities through bidirectional facilities. A Lagrangian relaxation-based solution algorithm was used for solving the problems. Min and o (2008) presented a dynamic reverse logistics network problem to improve logistics operations including both forward and reverse flows for 3PLs. Customers can return products to one of the warehouse/repair facilities near their locations. A nonlinear mixed integer programming model was developed under capacity limitations and service requirements and the model was solved by a GA. he proposed model and solution procedure allowed integration of existing forward logistics and reverse logistic networks by using warehouse s space for return product handling. Lee and Dong (2008) presented a heuristic approach in the logistic network for end-of-lease computer product recovery. Hybrid processing facilities deal with both forward and returned product flows. hey developed a deterministic programming model to minimize the total cost of recovery operations, for systematically managing forward and reverse logistics flows. he integrated distribution network design was decomposed into a location-allocation problem and a revised network flow problem with a two-stage heuristic approach. Lee and Dong (2009) focused on the dynamic network design for integrated forward and reverse logistics operations with uncertainty. hey formulated a model aiming to maximize profit, customer responsiveness and service quality. Hybrid processing facilities control both logistics channels in the network. A deterministic model was extended to a stochastic model to explicitly account for uncertain forward and reverse products. Pishvaee et al. (2010) proposed an optimization model for the integrated logistics network design with multiple capacity levels, where some distribution centers cover collection/inspection process. A bi-objective MIP formulation was presented to minimize the total cost and the responsiveness of a logistics network. For solving the model, the authors used an efficient multi-objective memetic algorithm with dynamic local search mechanism and found the non-dominated set of solutions. his paper formulates a dynamic bi-objective model to minimize the total shipping cost and time in an integrated logistics system including hybrid centers. he main differences of this model compared to the existing ones are that potential facilities are determined as one of the warehouse, collection center and hybrid facility with time periods, and time parameters for returning and repairing products are considered simultaneously. he proposed model analyzes how the types of potential facilities are changed according to the different time periods during a long period of time. Also, values of uncertain parameters such as return and repair ratios are varied via sensitivity analyses. 3. Problem Definitiona and Modeling Approach he structure of the integrated forward and reverse logistics network is given in Fig. 1. here are suppliers, potential facilities (i.e., warehouses, hybrid facilities, collection centers) and customers in the network. Suppliers are the plants and customers refer to the customers of 3PL s clients. hree types of potential facilities exist between suppliers and customers: warehouses, hybrid facilities and collection centers. Warehouses handle only forward products, collection centers deal with only reverse products, and hybrid facilities cover both forward and reverse products. Hybrid facilities have the same function with warehouses in the forward channel and collection centers in the reverse channel, respectively. hese combined facilities have advantage of increasing savings by sharing handling equipment and infrastructure. All return products are sent back to suppliers and then some are repaired or disposed by considering their conditions. After these steps, the products are stored within the capacity of Fig. 1. Integrated Forward and Reverse Logistics Network Structure for 3PLs 808 SCE Journal of Civil Engineering

4 Designing an Integrated Logistics Network in a Supply Chain System suppliers and sold according to the demand of customers in the next time period. o simplify the problem, some assumptions are defined as follows: 1. he number and location of potential sites are known. 2. In both forward and reverse channels, a customer can be served by more than one facility. 3. Vehicle routing problems are ignored. 4. Only factories can repair products. 5. At time zero, no facility is open at any potential site. A bi-objective model is developed to minimize the total shipping cost and time. he first objective is to minimize the total shipping cost (C) including Set-up Cost (SC), Fixed Operating Cost (FOC) and Variable Cost (VC) for transporting and handling products, and the second objective is to minimize the total shipping time (). Minimize {C + }: C = { SC( j, t) + FOC( j, t) + VCpijkt (,,,,)}, t 1 SC( j, t) = sw jt A( 1 A jt 1 ) + sh jt C jt ( 1 C jt 1 ) Subject to: j J + sc jt E jt ( 1 E jt 1 ) j J j J FOC( j, t) = ow jt A jt + oh jt C jt + oc jt E jt j J j J j J VCpijkts (,,,,, ) = X pijkt cf pijkt Y pkjit cr pkjit =, t 1 + vot p p Pi Ij Jk p Pi Ij Jk s S p Pi Ij Jk Pi Ij Jk X pijkt tf pijkt Fr pkt Y pkjits tr pkjit p Pi Ij Jk Fp pkt Y pkjits ( tr pkjit + rt pit ) s S (a) γ p X Q jt A jt + R jt C jt, j J, (6) p Pi Ik (b) γ p Y pkjit L jt E jt + U jt C jt, j J, (7) p Pi Ik (c) X pijkt M it, i I, (8) p Pj Jk (d) X pijkt x pkt, p P, k, (9) i Ij J (e) Y pkjit r pkt, p P, k, (10) i Ij J (f) A jt + C jt + E jt 1, j J, (11) (g) + = 1, p P, k, (12) Fr pkt Fp pkt (h) Fp pkt, Fr pkt, X pijkt, Y pkjit 0, p Pi, I, j Jk, t, (13) (1) (2) (3) (4) (5) (i) A jt, C jt, E jt { 01, }, j J, (14) Constraint (a) is the capacity constraint at warehouses and hybrid facilities for forward products. It ensures that the demand cannot exceed the capacity of the facilities for forward flows. Constraint (b) is the capacity constraint at hybrid facilities and collection centers for reverse products. It ensures that return products cannot exceed the capacity of facilities for reverse flows. Constraint (c) indicates the limited production capacity of suppliers. Constraint (d) refers to customer s forward demand satisfaction and constraint (e) refers to customer s reverse demand satisfaction. Constraint (f) ensures that only one type of facility can be opened in the same time period at each potential site. Constraint (g) states that there are two types of returns, return and repair. Constraint (h) ensures the non-negativity of the corresponding decision variables. Constraint (i) ensures that decision variables are binary. 4. Model est and Results An integrated forward and reverse logistics network is tested for evaluating the proposed model. he model is solved using the Mixed Integer Nonlinear Programming (MINLP) solver in the mathematical programming software package GAMS version 24. All the test problems are executed on a PC with Pentium IV 2.00 GHz CPU with 3.00 GB of RAM. 4.1 Example We assume twp plants, three potential sites and five customers in the integrated logistics network. en time periods are considered in the example and the types of facilities can be changed along with different time periods in a cost and time efficient manner. he model determines the types of facilities at potential sites, forward and reverse flows and their shipping costs. Information on data (shipping demand, facility capacity, set-up cost and operating cost, shipping time, product volume, etc.) is illustrated in able 1. he capacity of each plant is set at 5,000 and 4,000 in all time periods. Warehouses and hybrid facilities are used for forward products and collection centers and hybrid centers are utilized for reverse products, respectively. he same capacity of each facility is assumed for different time periods. he set-up cost and the fixed operating cost are not changed regardless of the time period and the amount of flow is given. he variable cost to serve a unit of product, including the transportation and handling costs, is assumed according to the potential facilities and time periods. he cost ranges of the forward and reverse shipping and repair are also provided. Various reverse and repair demands are experienced based on the different product return and repair rates. Return rates range from 2% to 30% with 2%~5% intervals and repair rates range from 15% to 30% with a 5% interval. 4.2 Results An integrated network with hybrid facilities covering both Vol. 17, No. 4 / May

5 Hyangsook Lee, i Zhang, Maria Boile, Sotiris heofanis, and Sangho Choo able 1. Example Data Forward Demand (unit product) ime period Forward flow 1 3, , , , , , , , , ,540 otal demand 33,360 Capacity of the facility (unit product) Facility type Potential site 1 Potential site 2 Potential site 3 Warehouse 2,000 1,800 2,500 Hybrid center for forward products 2,000 2,400 2,800 Hybrid center for reverse products Collection Center Cost ($) Warehouse Set-up cost 1,800 Operating cost 1,600 Set-up cost and fixed Set-up cost 2,500 Hybrid center operating cost Operating cost 2,000 Collection Center Set-up cost 1,000 Operating cost 600 Variable cost Variable cost for forward products 15 ~ 40 Variable cost for reverse products 20 ~ 50 Shipping ime (mins) Shipping time for forward products 280 ~ 560 Shipping time Shipping time for return products 310 ~ 590 Shipping and repairing time for repair products 3,600 ~ 3,800 Note: the unit occupied capacity per product and value of time are assumed as follows. Unit occupied capacity: 1.2 Value of time: 0.2 $ per minute able 2. otal Cost with and without Hybrid Facility Return rate (%) otal cost with hybrid facility ($) otal cost without hybrid facility ($) Cost savings ($) 2.0 3,284,583 3,315,707 31, ,393,308 3,433,593 40, ,501,931 3,544,398 42, ,610,476 3,661,384 50, ,719,020 3,773,283 54, ,827,506 3,890,555 63, ,935,993 4,006,185 70, ,039,466 4,087,434 47, ,147,513 4,194,706 47,193 forward and reverse flows showed benefit, compared with a nonintegrated network. able 2 compares the total cost with/without hybrid facilities according to the different return rates. he cost savings range from $31,123 to $47,193 suggesting a costefficient solution. For sensitivity analyses, we varied return rates from 2% to 30%, assuming the return/repair ratio is 0.7/0.3. As the return rate grew, the total cost increased accordingly. When return rates grew from 2% to 10% with a 2% interval, the total cost increased from 7.1% to 29.5%. In cases of return rates from 15% to 30% with a 5% interval, the total cost increased from 48.3% to 101.2%. hese results indicate that reverse flows require much more costs than forward flows. he impact of return rates on the total cost is shown in Fig. 2. When the return rate was fixed at 4% and the return/repair ratio was varied from 0.9/0.1 to 0.1/0.9, the changes in the total cost are depicted in Fig. 3. he figure shows that the total cost increases accompanying the growth of the repair rate. When the return/repair ratio changed from 0.9/0.1 to 0.8/0.2, the total cost increased 3.1%; when the ratio changed to 0.5/0.5, the total cost 810 SCE Journal of Civil Engineering

6 Designing an Integrated Logistics Network in a Supply Chain System Fig. 2. otal Cost Change according to Different Return Rates($) increased 12.4%; and when the ratio changed to 0.1/0.9, the total cost increased 24.6%. We found that the number of open warehouses decrease as the return rate increase since warehouses deal with only forward flows. he model in this example suggests that all warehouse facilities need to be closed at a return rate of 20%. his implies that when the return rate is high, it is cost effective to close warehouses and utilize hybrid facilities. Under 20% of the return Fig. 3. otal Cost Change according to Different Return/Repair Ratios($) rate, no collection centers were selected. It s because when the return rate is not high enough, the hybrid facility itself covers both the forward and reverse flows simultaneously. However, collection centers started to work at a return rate of 20% due to capacity limitation of the hybrid facilities for handling reverse flows. he types and locations of potential facilities at return rates of 2%, 10% and 25% during 10 time periods are illustrated in able 3. able 3. Facility Distributions according to Different Return Rates Return rate 2% 10% 25% Binary variable A jt C jt E jt A jt C jt E jt A jt C jt E jt t=1, j= t=1, j= t=1, j= t=2, j= t=2, j= t=2, j= t=3, j= t=3, j= t=3, j= t=4, j= t=4, j= t=4, j= t=5, j= t=5, j= t=5, j= t=6, j= t=6, j= t=6, j= t=7, j= t=7, j= t=7, j= t=8, j= t=8, j= t=8, j= t=9, j= t=9, j= t=9, j= t=10, j= t=10, j= t=10, j= Vol. 17, No. 4 / May

7 Hyangsook Lee, i Zhang, Maria Boile, Sotiris heofanis, and Sangho Choo 5. Conclusions he paper explored a facility location problem in an integrated forward and reverse distribution network. A nonlinear mixed integer model was formulated to minimize the total shipping cost and time simultaneously. he model determine several potential facilities as one of the warehouses, collection centers and hybrid facilities and find product flows (forward and reverse flows) using optimization programming. We could analyze how the types of facilities were changed in different time periods. Also, uncertain parameters such as return and repair ratios were varied for sensitivity analyses. he results indicate that an integrated network with hybrid facilities has benefit, compared with a non-integrated network, suggesting a cost-efficient solution. As return and repair rates grew, the total cost increased accordingly since reverse flows generally require more costs than forward flows. he types of facilities were changed according the time period and the return rate. If the return rate was low, it was cost effective to utilize hybrid facilities and close collection centers because hybrid facilities deal with the forward and reverse flows simultaneously. However, in cases of high return rates, collection centers started to work due to capacity limitation of the hybrid facilities for handling reverse flows. An example is tested to demonstrate the applicability and validity of the developed model. he paper examined a relatively small network, focusing on determining potential sites in different time periods over a long period of time and experiencing various return and repair rates as different scenarios. he developed model can cover any types of logistic networks defining plants, customers and potential facilities. his research will be extended to the more complicated networks and the consideration of stochastic return rates in the future. Notations Indices: I: Set of suppliers i: Supplier (i I) J: Set of potential facilities j: Potential facility (j J) : Set of customers k: Customer (k ) P: Set of product types p: Product type (p P) : Set of time periods t: time period (t ) Parameters: Cost parameters cf pijkt : he unit variable cost of serving product p from supplier i via warehouse or hybrid facility j to customer k in period t, including transportation and handling costs (p P, i I, j J, k, ) 812 cr pkjit : he unit variable cost of serving returned product p from customer k via collection center or hybrid facility j to supplier i in period t, including transportation and handling costs (p P, k, j J, i I, ) d pkt : Forward demand of customer k for product p in period t (p P, k, ) L jt : he maximum production capacity of collection center j for handling reverse products in period t (j J, ) M it : he maximum production capacity of supplier i in period t (i I, ) oc jt : he fixed operating cost of collection center j in period t (j J, t ) oh jt : he fixed operating cost of hybrid facility j in period t (j J, t ) ow jt : he fixed operating cost of warehouse j in period t (j J, t ) Q jt : he maximum production capacity of warehouse j for handling forward products in period t (j J, t ) R jt : he maximum production capacity of hybrid facility j for handling forward products in period t (j J, t ) r pkt : Reverse demand of customer k for product p in period t (p P, k, t ) sc jt : he set-up cost of installing collection center j in period t (j J, t ) sh jt : he set-up cost of installing hybrid facility j in period t (j J, t ) sw jt : he set-up cost of installing warehouse j in period t (j J, t ) U jt : he maximum production capacity of hybrid facility j for handling reverse products in period t (j J, t ) : Per unit occupied capacity by product p (p P) γ p ime parameters Fp pkt : Fraction of repairs of product p from customer k in period t (p P, k, t ) Fr pkt : Fraction of returns of product p from customer k in period t (p P, k, t ) rt pit : Repair time of product p at supply plant i in period t (p P, i I, t ) tf pijkt :Shipping time of forward product p from supplier i via facility j to customer k in period t (p P, i I, j J, k, t ) tr pkijt : Shipping time of reverse product p from customer k via facility j to supplier i until customers get credits back in period t (p P, k, j J, i I, t ) vot : Value of time, $/min Decision variables: A jt : 1, if warehouse j is open in period t (j J); 0, otherwise C jt : 1, if hybrid center j is open in period t (j J); 0, otherwise E jt : 1, if collection center j is open in period t (j J); 0, otherwise X pijkt : Forward flow: amount of demand of product p served SCE Journal of Civil Engineering

8 Designing an Integrated Logistics Network in a Supply Chain System from supplier i via warehouse or hybrid facility j to customer k in period t (p P, i I, j J, k, ) Y pkjit : Reverse flow: amount of demand of product p at customer k sent back to supplier i via collection center or hybrid facility j in period t (p P, k, j J, i I, ) References Altiparmak, F., Gen, M., Lin, L., and Paksoy,. (2006). A genetic algorithm approach for multi-objective optimization of supply chain networks. Computers and Industrial Engineering, Vol. 51, No. 1, pp Amiri, A. (2006). Designing a distribution network in a supply chain system: Formulation and efficient solution procedure. European Journal of Operational Research, Vol. 171, No. 2, pp Aras, N., Aksen, D., and anugur, A.G. (2008). Locating collection centers for incentive dependent returns under a pick-up policy with capacitated vehicles. European Journal of Operational Research, Vol. 191, No. 3, pp Chen, C. L., Yuan,. W., and Lee, W. C. (2007). Multi-criteria fuzzy optimization for locating warehouses and distribution centers in a supply chain network. Journal of the Chinese Institute of Chemical Engineers, Vol. 38, No. 5, pp Chopra, S. (2003). Designing the distribution network in a supply chain. ransportation Research Part E, Vol. 39, No. 2, pp Cordeau, J.F., Laporte, G., and Pasin, F. (2008). An iterated local search heuristic for the logistics network design problem with single assignment. International Journal of Production Economics, Vol. 113, No. 2, pp Dasciand, A. and Verter, V. (2001). A continuous model for productiondistribution system distribution system design. European Journal of Operational Research, Vol. 129, No. 2, pp Dogan,. and Geotschalckx, M. (1999). A primal decompositon method for the integrated design of multi-period productiondistribution systems. IIE ransactions, Vol. 31, No. 11, pp 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 Dupont, L. (2008). Branch and bound algorithm for a facility location problem with concave site dependent costs. International Journal of Production Economics, Vol. 112, No. 1, pp Fleischmann, M., Beullens, P., Bloemhof-Ruwaard, J. M., and Van Wassenhove, L. N. (2001). he impact of product recovery on logistics network design. Production and Operations Management, Vol. 10, No. 2, pp Fleischmann, M., Bloemh f-ruwaard, J. M., Dekker, R., Laan, E., Nunen, J. A. E. E., and Wassenhove, L. N. (1997). Quantitative models for reverse logistics: A review. European Journal of Operational Research, Vol. 103, No. 1, pp Fuente, M. V., Ros, L., and Cardos, M. (2008). Integrating forward and reverse supply chains: Application to a metal-mechanic company. International Journal of Production Economics, Vol. 111, No. 2, pp Jayaraman, J. and Ross, A. (2003). A simulated annealing methodology to distribution network design and management. European Journal of Operational Research, Vol. 144, No. 3, pp Jayaraman, V., Patterson, R. A., and Rolland, E. (2003). he design of reverse distribution networks: Models and solution procedures. European Journal of Operational Research, Vol. 150, No. 1, pp Jayaraman, V. and Pirkul, H. (2001). Planning and coordination of production and distribution facilities for multiple commodities. European Journal of Operational Research, Vol. 133, No. 2, pp lose, A. and Drexl, A. (2005). Facility location models for distribution system design. European Journal of Operational Research, Vol. 162, No. 1, pp o, H. J. and Evans, G. W. (2007). A genetic algorithm-based heuristic for the dynamic integrated forward/reverse logistics network for 3PLs. Computers & Operations Research, Vol. 34, No. 2, pp Lee, D. H. and Dong, M. (2008). A heuristic approach to logistics network design for end-of-lease computer products recovery. ransportation Research Part E, Vol. 44, No. 3, pp Lee, D. H. and Dong, M. (2009). Dynamic network design for reverse logistics operations under uncertainly. ransportation Research Part E, Vol. 45, No. 1, pp Lee, D. H., Wen, B., and Meng, D. (2007). Multiproduct distribution network design of third party logistics providers with reverse logistics operations. ransportation Research Record, Vol. 2008, No. 3, pp Lieckens,. and Vandaele, N. (2007). Reverse logistics network design with stochastic lead times. Computers & Operations Research, Vol. 34, No. 2, pp Lu, A. and Bostel, N. (2007). A facility location model for logistics systems including reverse flows: he case of remanufacturing activities. Computers & Operations Research, Vol. 34, No. 2, pp Marin A. and Pelegrin, B. (1998). he return plant location problem: Modeling and resolution. European Journal of Operational Research, Vol. 104, No. 2, pp Melachrinoudis, E., Messac, A., and Min, H. (2005). Consolidating a warehouse network: A physical programming approach. International Journal of Production Economics, Vol. 97, No. 1, pp Min, H., o, H.J. and o, C.S. (2006). A genetic algorithm approach to developing the multi-echelon reverse logistics network for product returns. Omega, Vol. 34, No. 1, pp Min, H. and o, H. J. (2008). he dynamic design of a reverse logistics network from the perspective of third-party logistics service provider. International Journal of Production Economics, Vol. 113, No. 1, pp Pishvaee, M. S., Farahani, R. A., and Dullaert, W. (2010). A memetic algorithm for bi-objective integrated forward/reverse logistics network design. Computers & Operations Research, Vol. 37, No. 6, pp Sabri, E. H. and Beamon, B. M. (2000). A multi-objective approach to simultaneous strategic and operational planning in supply chain design. Omega, Vol. 28, No. 5, pp Sahyouni,., Savaskan, R.C., and Daskin, M. S. (2007). A facility location model for bidirectional flows. ransportation Science, Vol. 41, No. 4, pp Salema, M. I. G., Barbosa-Povoa, A. P., and Novais, A. Q. (2006). A warehouse-based design model for reverse logistics. Journal of the Operational Research Society, Vol. 57, No. 1, pp Salema, M. I. G., Barbosa-Povoa, A. P., and Novais, A. Q. (2007). An optimization model for the design of a capacitated multi-product reverse logistics network with uncertainty. European Journal of Vol. 17, No. 4 / May

9 Hyangsook Lee, i Zhang, Maria Boile, Sotiris heofanis, and Sangho Choo Operational Research, Vol. 179, No. 3, pp Spengler,., Pucher, H., Penkuhn., and Rentz, O. (1997). Environmental integrated production and recycling management. European Journal of Operational Research, Vol. 97, No. 2, pp Sridharan, R. (1995). he capacitated plant location problem. European Journal of Operational Research, Vol. 87, No. 2, pp Stock, J. R. (1992). Reverse logistics, Council of Logistics Management, Oak Brook III. Stock, J. R. (1998). Development and implementation of reverse logistics programs, Council of Logistics Management, Oak Brook III. Syarif, A., Yun, Y. S., and Gen, M. (2002). Study on multi-stage logistics chain network: A spanning tree-based genetic algorithm approach. Computers & Industrial Engineering, Vol. 43, No. 1, pp siakis, P. and Papageorgiou, L. G. (2008). Optimal production allocation and distribution supply chain networks. International Journal of Production Economics, Vol. 111, No. 2, pp SCE Journal of Civil Engineering