Modeling the Multi-period and Multi-product Closed-loop Supply Chain Network Design Problem Considering Reused Cost and Capacity Constraints

Document Type : Research Paper


Department of industrial engineering and management, Shahrood university of technology, Shahrood, Iran


The importance of remanufacturing used products into new ones has been widely recognized in the literature and in practice. This is due to both of economic opportunities and environmental aspects. This paper aims to design a new integrated multi-period & multi-product closed-loop supply chain network considering reused cost and capacity constraints for all stages. In this problem the stages of supplier, assembler, retailer, customer, collection center, refurbishing center, and disassembler is regarded consequently. The considered objective function is total cost factors that consists of 7 components: costs of associated with locating the plants and retailers, purchasing, transportation, collection of used products from customers, disposal for subassemblies, refurbishing, and finally refund to customers. First, parameters and decision variables of this problem are defined, then a mixed integer linear programming mathematical model is presented. The proposed mathematical model is run applying the GAMS software. Two real examples (shed light, and power-outlet) are considered to solve using the proposed mathematical model. These two examples were obtained based on data in two new references. Since this problem is known as NP-Hard, the model is run just for small-sized problem consists of four suppliers, two disassemblers, two retailers, and two periods. The results are analysed and some sensitivity analysis have been done for the effective factors. These result show that, the demand has a less effect on total cost. But Purchasing/refurbishing cost ratio has a high effect on the objective function. Finally, the capacity of collection and refurbishing centers has a high effect in primary changes and this effect gradually reduced. So having the proper capacity for collection and refurbishing centers and also creating balance between different stages can reduce overall cost.


Main Subjects

Amini, A., Alinezhad, A., and Salmanian, S. (2016). Development of Data Envelopment Analysis for the Performance Evaluation of Green supply chain with Undesirable Outputs. International journal of supply and operations management, Vol. 3(2), pp. 1267-1283.
Amin, S. H., and Zhang, G. (2012). An integrated model for closed-loop supply chain configuration and supplier selection: Multi-objective approach. Expert Systems with Applications, Vol. 39(8), pp. 6782-6791.
Bjørn, A. and Hauschild, M.Z. (2013). Absolute versus Relative Environmental Sustain-ability: What can the Cradle-to-Cradle and Eco-efficiency Concepts Learn from Each Other?, Journal of Industrial Ecology, Vol. 17(2), pp. 321-332.
Cardenas-Barron, L. E., and Sana, S. S. (2014). A production-inventory model for a two-echelon supply chain when demand is dependent on sales teams' initiatives. International Journal of Production Economics, Vol. 155, pp. 249-258.
Chen, Y.T., Chan, F.T.S., Chung, S.H., Park, W.Y. (2017). Optimization of product refurbishment in closed-loop supply chain using multi-period model integrated with fuzzy controller under uncertainties. Robotics and Computer–Integrated Manufacturing, in press, available at:
Das, K., Posinasetti, N. R., (2015). Addressing environmental concerns in closed loop supply chain design and planning. International Journal of Production Economics, Vol. 163, pp. 34-47.
Demirel, N. Ö., and Gökçen, H. (2008). A mixed integer programming model for remanufacturing in reverse logistics environment. The International Journal of Advanced Manufacturing Technology, Vol. 39(11-12), pp. 1197-1206.
Dutta, P., Das, D., Schultmann, F., and Frohling, M. (2016). Design and planning of a closed-loop supply chain with three way recovery and buy-back offer. Journal of Cleaner Production, Vol. 135, pp. 604-619.
Elbounjimi, M., Abdulnour, G., Ait-kadi, D., (2014). Green Closed-loop Supply Chain Network Design: a literature review. International journal of operations and logistics management, Vol. 3(4), pp. 275-286.
Elbounjimi, M., Abdulnour, G., Ait-kadi, D., (2015). A Mixed Integer Linear Programming Model for the Design of Remanufacturing Closed–loop Supply Chain Network. International journal of supply and operations management, Vol. 2(3), pp. 820-832.
Ellen, M. F. (2014). Towards the circular economy -Accelerating the scale-up across global supply chains. Available at:
El Saadany, A. M., and Jaber, M. Y. (2010). A production/remanufacturing inventory model with price and quality dependant return rate. Computers & Industrial Engineering, Vol. 58(3), pp. 352-362.
Fleischmann, M., Beullens, P., BLOEMHOF‐RUWAARD, J. M., and Wassenhove, L. N. (2001). The impact of product recovery on logistics network design. Production and operations management, Vol. 10(2), pp. 156-173.
Fleischmann, M., Bloemhof-Ruwaard, J. M., Dekker, R., Van der Laan, E., Van Nunen, J. A., and Van Wassenhove, L. N. (1997). Quantitative models for reverse logistics: A review. European journal of operational research, Vol. 103(1), pp. 1-17.
Gaura, J., Aminib, M., Rao, A.K., (2017). Closed-loop supply chain configuration for new and reconditioned products: An integrated optimization model. Omega, Vol. 66(Part B), pp. 212–223.
Georgiadis, P., and Besiou, M. (2010). Environmental and economic sustainability of WEEE closed-loop supply chains with recycling: a system dynamics analysis. The International Journal of Advanced Manufacturing Technology, Vol. 47(5-8), pp. 475-493.
Govindan, K., Soleimani, H. (2017). A review of reverse logistics and closed-loop supply chains: a Journal of Cleaner Production focus. Journal of Cleaner Production, Vol. 142 (20), pp. 371-384.
Govindan, K., Soleimani, H. and Kannan. D. (2015). Reverse logistics and closed -loop supply chain: A comprehensive review to explore the future. European Journal of Operational Research, Vol. 240(3), pp. 603-626.
Guide, V. D. R., Jayaraman, V., and Linton, J. D. (2003). Building contingency planning for closed-loop supply chains with product recovery. Journal of operations Management, Vol. 21(3), pp. 259-279.
Guide Jr, V. D. R., and Van Wassenhove, L. N. (2009). OR FORUM—the evolution of closed-loop supply chain research. Operations research, Vol. 57(1), pp. 10-18.
Guo, J., and Ya, G. (2015). Optimal strategies for manufacturing/remanufacturing system with the consideration of recycled products. Computers & Industrial Engineering, Vol. 89, pp. 226-234.
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(5), pp. 497-508.
M. Jeihoonian, M. K. Zanjani, and M. Gendreau. (2017). Closed-loop supply chain network design under uncertain quality status: case of durable products. International Journal of Production Economics, Vol. 183(Part B), pp. 470-486.
Kannan, G., Sasikumar, P., and Devika, K. (2010). A genetic algorithm approach for solving a closed loop supply chain model: A case of battery recycling. Applied Mathematical Modelling, Vol. 34(3), pp. 655-670.
Kaya, O., Urek, B., (2016). A mixed integer nonlinear programming model and heuristic solutions for location, inventory and pricing decisions in a closed loop supply chain. Computers & Operations Research, Vol. 65, pp. 93-63.
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(16), pp. 3689-3719.
Lee, J. E., Gen, M., and Rhee, K. G. (2009). Network model and optimization of reverse logistics by hybrid genetic algorithm. Computers & Industrial Engineering, Vol. 56(3), pp. 951-964.
Lund, R. T. (1996). The remanufacturing industry: hidden giant, United States: Boston University.
Maliki, F., Anwar Brahami, M., Dahane, M., and Sari, Z. (2016). A supply chain Design Problem Integrated Facility Unavailabilities Management. International journal of supply and operations management, Vol. 3(2), pp.1253-1266.
Masoudipour, E., Amirian, H., and Sahraeian, R. (2017). A novel closed-loop supply chain based on the quality of returned products. Journal of Cleaner Production, Vol. 151, pp. 344-355.
Meindl, P., and Chopra, S. (2001). Supply Chain Management: Strategy, Planning, And Operation, edition- 5, india: Pearson Education India.
Min, H., Ko, C. S., and Ko, H. J. (2006). The spatial and temporal consolidation of returned products in a closed-loop supply chain network. Computers & Industrial Engineering, Vol. 51(2), pp. 309-320.
Moshtagh, M. S., and Taleizadeh, A. A. (2017). Stochastic integrated manufacturing and remanufacturing model with shortage, rework and quality based return rate in a closed loop supply chain. Journal of Cleaner Production, Vol. 141, pp. 1548-1573.
Neto, J. Q. F., Bloemhof-Ruwaard, J. M., van Nunen, J. A., and van Heck, E. (2008). Designing and evaluating sustainable logistics networks. International Journal of Production Economics, Vol. 111(2), pp. 195-208.
Özceylan, E., Paksoy, T., and Bektaş, T. (2014). Modeling and optimizing the integrated problem of closed-loop supply chain network design and disassembly line balancing. Transportation research (part E): logistics and transportation review, Vol. 61, pp. 142-164.
Pishvaee, M. S., Rabbani, M., and Torabi, S. A. (2011). A robust optimization approach to closed-loop supply chain network design under uncertainty. Applied Mathematical Modelling, Vol. 35(2), pp. 637-649.
Qiang, Q., Ke, K., Anderson, T., and Dong, J. (2013). The closed-loop supply chain network with competition, distribution channel investment, and uncertainties. Omega, Vol. 41(2), pp. 186-194.
Quariguasi Frota Neto, J., Walther, G., Bloemhof, J. A. E. E., Van Nunen, J. A. E. E., and Spengler, T. (2010). From closed-loop to sustainable supply chains: the WEEE case. International Journal of Production Research, Vol. 48(15), pp. 4463-4481.
Richter, K. (1996a). The EOQ repair and waste disposal model with variable setup numbers. European Journal of Operational Research, Vol. 95(2), pp. 313-324.
Rogers, D. S., and Tibben-Lembke, R. S. (1998). Going backwards: reverse logistics trends and practices. University of Nevada, Reno: Center for Logistics Management.
Schrady, D. A. (1967). A deterministic inventory model for reparable items. Naval Research Logistics Quarterly, Vol. 14(3), pp. 391-398.
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): Logistics and Transportation Review, Vol. 41(4), pp. 287-313.
Stindt, D. and Sahamie, R. (2014). Review of research on closed loop supply chain management in the process industry. Flexible Services and Manufacturing Journal, Vol. 26(1-2), pp. 268-293.
Tahirov, N., Hasanov, P., Jaber, M. Y., (2016). Optimization of closed-loop supply chain of multi-items with returned subassemblies. International Journal of Production Economics, Vol. 174, pp. 1-10.
Tang, Y., Zhou, M., Zussman, E., and Caudill, R. (2002). Disassembly modeling, planning, and application. Journal of Manufacturing Systems, Vol. 21(3), pp. 200-217.
Teunter, R. (2004). Lot-sizing for inventory systems with product recovery. Computers & Industrial Engineering, Vol. 46(3), pp. 431-441.
Torkaman, S., Fatemi Ghomi, S.M.T, and Karimi, B. (2017). Multi-stage multi-product multi-period production planning with sequence-dependent setups in closed-loop supply chain. Computers & Industrial Engineering, Vol. 113, pp. 602-613.
Wang, H. F., and Hsu, H. W. (2010). A closed-loop logistic model with a spanning-tree based genetic algorithm, Computers & operations research, Vol. 37(2), pp. 376-389.
Yang, G.-F., Wang, Z.-P., and Li, X.-Q. (2009). The optimization of the closed-loop supply chain network. Transportation Research (Part E), Vol. 45 (1), pp. 16–28.
Zavvar Sabegh, M.H., OzturkOglu, Y., and Kim, T. (2016). Green supply chain Management Practices’ Effect on the Performance of Turkish Business Relationships. International journal of supply and operations management, Vol. 2(4), pp. 982-1002.