A Multi-Objective Fuzzy Approach to Closed-Loop Supply Chain Network Design with Regard to Dynamic Pricing

Document Type: Original Manuscript


1 Department of Industrial Engineering, , Qazvin Branch, IslamicAzad University, Qazvin, Iran

2 Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran



During the last decade, reverse logistics networks received a considerable attention due to economic importance and environmental regulations and customer awareness. Integration of leading and reverse logistics networks during logistical network design is one of the most important factors in supply chain. In this research, an Integer Linear Programming model is presented to design a multi-layer reverse-leading, multi-product, and multi-period integrated logistics network by considering multi-capacity level for facilities under uncertainty condition. This model included three objectives: maximizing profit, minimizing delay of goods delivering to customer, and minimizing returned raw material from suppliers. This research gives financial incentives to encourage customers in order to return their used product. Considering that the remaining value of used products is the main incentive of a company to buy second-handed goods, a dynamic pricing approach is determined to define purchase price for these types of products, and based on that, the percentage of returned products were collected by customers. In addition, in this study, parameters have uncertainty features and are vague; therefore, at first, they are converted into exact parameters and, then, because model is multi-objective, the fuzzy mathematical programming approach is used to convert multi-objective model into a single objective; finally, the model by version 8 of Lingo is run. In order to solve a large-sized model, a non-dominated sorting genetic algorithm II (NSGA-II) was applied. Computational results indicate the effect of the proposed purchase price on encourage customers to return the used products.

Graphical Abstract

A Multi-Objective Fuzzy Approach to Closed-Loop Supply Chain Network Design with Regard to Dynamic Pricing


Main Subjects

Akçali, E., Çetinkaya, S., Üster, H. (2009). Network design for reverse and closed-loop supply chains: an annotated bibliography of models and solution approaches, Networks, Vol. 53, pp. 232-238.

Altiparmak F, Gen M, Lin L, Paksoy T. (2006). A genetic algorithm approach for multi- objective optimization of supply chain networks. Computers and Industrial Engineering.51,197–216.

Amiri, A. (2006). Designing a distribution network in a supply chain system: formulation and efficient solution procedure, European Journal of Operational Research, Vol. 171, pp. 567-576.

Aras, N., Aksen, D. (2008). Locating collection centres for distance- and incentive-dependent returns. International Journal of Production Economics. Vol. 111, 316-333.

Bagherinejad, J., Dehghani, M., (2016), A Non-dominated Sorting Ant Colony Optimization Algorithm Approach to the Bi-objective Multi-vehicle Allocation of Customers to Distribution Centres, Journal of Optimization in Industrial Engineering , VOL.19, 61-73

Bandyopadhyay,S., Bhattacharya, R., (2014). Solving a tri-objective supply chain problem with modified NSGA-IIalgorithm, Journal of Manufacturing Systems, VOL. 33 , 41– 50.

Deb, K., Agrawal, S., Pratab, A., and Meyarivan, T., "A Fast Elitist Non-Dominated Sorting Genetic Algorithm for Multi-Objective Optimization: NSGA-II. In Schoenauer", M., Deb, K., Rudolph, G., Yao, X., Lutton, E., Merelo, J. J., and Schwefel, H.P., editors, Proceedings of the Parallel Problem Solving from Nature VI Conference, (2000), pages 849-858, Paris, France. Springer.

Dubois, D., Fargier, H., Fortemps, P., (2003). Fuzzy scheduling: modelling flexible constraints vs. coping with incomplete knowledge, Eur. J. Oper. Res. 147, 231–252.

El-Sayed, M., Afia, N., El-Kharbotly, A., (2010), A stochastic model for forward-reverse logistics network design under risk. Computers & Industrial Engineering. Vol.58. PP. 423_31.

Fleischmann, M., Beullens, P., Bloemhof-Ruwaard, JM., &Wassenhove, L. (2001), The impact of product recovery on logistics network design. Production and Operations Management, Vol. 10, PP. 156-173.

Franca, R.B.,  Jones, E.C., Richards, C.N., Carlson, J.P., (2009). Multi-objective stochastic supply chain modeling to evaluate tradeoffs between profit and quality, Int. J. Product. Econ. Vol.127, pp. 292-299.

Guide, V.D.R., Teunter, R., van Wassenhove, L.N. (2003). Matching demand and supply to maximize profits from remanufacturing, Manufacturing and Service Operations Management, Vol. 5, pp. 303–316.

Guillen, G. Mele,F.D. Bagajewicz,M.J. Espuna,A. Puigjaner, L., (2005). Multiobjective supply chain design under uncertainty, Chem. Eng. Sci. 60, 1535–1553.

Hassanzadeh Amin,S., Zhang, G. (2013). A multi-objective facility location model for closed-loop supply chain network under uncertain demand and return. Applied Mathematical Modelling, Vol. 37, PP.4165–4176.

Jayaraman, V., Patterson, R., Rolland, E., (2003). The design of reverse distribution networks: Models and solution procedures. European Journal of Operational Research, Vol. 150. PP.128–149.

Jayaraman, V., Guide, V. D. R, Jr, Srivastava, R., (1999). A closed-loop logistics model for remanufacturing. Journal of the Operational Research Society. Vol. 50, PP.497–508.

Jimenez, M., Arenas, M., Bilbao, A. and Guez, M. V. (2007). Linear programming with fuzzy parameters: an interactive method resolution, European Journal of Operational Research, Vol. 177, PP. 1599-1609.

Jimenez, M., (1996), Ranking fuzzy numbers through the comparison of its expected intervals, International Journal of Uncertainty, Fuzziness and Knowledge Based Systems, Vol. 4 (4), PP. 379–388.

Karbasian,  M., Dashti, M., 2011. Designing four multi-objective models for dispersion facilities location problems considering Data Envelopment Analysis and maximum covering.  International Journal of Management Science and Engineering Management.  6,  298-306.

 Keyvanshokooh, E., Fattahi, M., Seyed-Hosseini, S.M., Tavakoli-Moghaddam, R., (2013), A dynamic pricing approach for returned products in integrated forward/reverse logistics network design, Applied Mathematical Modelling, Vol. 37(24), PP.10182-10202

Klibi, W., Martel, A. Guitouni, A. (2010). The design of robust value-creating supply chain networks: a critical review, European Journal of Operational Research, Vol. 203. PP. 283–293.

Ko, H.J., Evans, G.W., (2007), A genetic-based heuristic for the dynamic integrated forward/reverse logistics network for 3PLs, Comput. Oper. Res. Vol. 34. PP. 346–366.

Krikke, HR., Van Harten, A., Schuur, PC., (1999), Reverse logistic network re-design for copiers. OR Spectrum , Vol. 21. PP.381–409.

Lai, Y.J., Hwang, C.L., (1993), Possibilistic linear programming for managing interest rate risk, Fuzzy Sets and Systems. Vol. 54 ,PP. 135–146.

Lai, Y.J., Hwang, C.L., (1992), A new approach to some possibilistic linear programming problems, Fuzzy Sets Syst. Vol. 49, PP. 121–133.

Lee, D. & Dong, M. (2008). A heuristic approach to logistics network design for end-of lease computer products recovery. Transportation Research Part E. Vol.44, PP.455-474.

Listes, O., Dekker, R., (2005), A stochastic approach to a case study for product recovery network design, Eur. J. Oper. Res.Vol.160, PP. 268–287.

Marı´n,A, PelegrinB, (1998), There turn plant location problem: modelling, and resolution. European Journal of Operational Research, Vol. 104(2), PP. 375–392.

Meade, L., Sarkis, J., & Presley A. (2007). The theory and practice of reverse logistics. International Journal of Logistics System Management, Vol. 3, pp. 56–84.

Meepetchdee Y, Shah N. (2007) Logistical network design with robustness and complexity considerations. International Journal of Physical Distribution & Logistics Management.37, 201–22.

Melachrinoudis E, Messac A, Min H. (2005). Consolidating a warehouse network: a physical programming approach. International Journal of Production Economics.97,1–17.

Min, H., Ko, H.J., Ko, C.S., (2006), A genetic algorithm approach to developing the multi-echelon reverse logistics network for product returns. Omega, Vol. 34. PP.5–69.

Min, H.,  Ko, H.J., (2008), The dynamic design of a reverse logistics network from the perspective of third-party logistics service providers, Int. J. Product. Econ. Vol.113. PP.176–192.

Pishvaee, M.S., Torabi, S.A.(2010). A possibilistic programming approach for closed-loop supply chain network design under uncertainty. Fuzzy sets and systems,161, 2668–2683.

Pishvaee., M.S., Zanjirani Farahani, R., Dullaert, W. (2010). A memetic algorithm for bi-objective integrated forward/reverse logistics network design. Computers & Operations Research. 37, 100–1112.

Pishvaee, M.S., Jolai, F., Razmi, J. (2009). A stochastic optimization model for integrated forward/reverse logistics network design. Journal of Manufacturing Systems. 28, 107_114.

Pishvaee, M.R., Kianfar, K., Karimi, B., (2010), Reverse logistics network design using simulated annealing, Int. J. Adv. Manuf. Technol. Vol. 47 .PP.269–281.

Ramezani. M., Bashiri, M., Tavakkoli-Moghaddam, R., (2013). A new multi-objective stochastic model for a forward/reverse logistic network design with responsiveness and quality level. Applied Mathematical Modelling. Vol. 37. PP. 328–344.

 Sabri, EH, Beamon, BM. (2000). A multi-objective approach to simultaneous strategic and operational planning in supply chain design. Omega. 28,581–98.

Saffari,H., Makui, A., Mahmoodian, V., Pishvaee, M.S.(2015). Multi-objective robust optimization model for social responsible closed-loop supply chain solved by non-dominated sorting genetic algorithm, Journal of Industrial and Systems Engineering, Vol. 8, No. 3, pp 42-59

Salema, M.I.G., Barbosa-Povoa, A.P., Novais, A.Q., (2007),  An optimization model for the design of a capacitated multi-product reverse logistics network with uncertainty, Eur. J. Oper. Res. Vol. 179. PP. 1063–1077.

Salema, M.I., Po’voa, A.P.B., Novais, A.Q., (2006), A warehouse-based design model for reverse logistics, J. Oper. Res. Soc. Vol. 57 (6). PP. 615–629.

Selim, H. Ozkarahan, I. (2008), A supply chain distribution network design model: an interactive fuzzy goal programming-based solution approach, Int. J. Adv. Manuf. Technol. 36 , 401–418.

Torabi, S.A., Hassini, E., (2008), An interactive possibilistic programming approach for multiple objective supply chain master planning. Fuzzy Sets andSystems, Vol. 159, PP. 193–214.

Tsiakis P, Papageorgiou LG. (2008). Optimal production allocation and distribution supply chain networks. International Journal of Production Economics.111:468–83.

Uster, H.,Easwaran,G.,ElifAkcali, E.,SilaCetinkaya,S., (2007), Bendersdecomposition with alternativemultiplecutsforamulti-productclosed-loopsupplychain networkdesignmodel.NavalResearchLogistics. Vol. 54. PP.890–907.

Wang, H.F., Hsu, H.W., (2010), A closed-loop logistic model with a spanning-tree based genetic algorithm, Comput. Oper. Res. Vol. 37 .PP. 376–389.

Zimmermann, H. J. (1996),  Fuzzy set theory and its applications. 3rd. Ed. Kluwer Academic Pub, Boston.

Zohal, M., Soleimani, H., (2016), Developing an ant colony approach for green closed-loop supply chain network design: a case study in gold industry , Journal of Cleaner Production, Vol.133.PP. 314e337