A Comparison of Solution Methods for the Multi-Objective Closed Loop Supply Chains

Document Type : Research Paper


1 Department of Economy, Kharazmi University, Tehran, Iran.

2 Department of Civil Engineering, University of Memphis, Memphis, TN, USA

3 Department of Civil Engineering, University of Memphis, Memphis, TN, USA.

4 Department of Industrial Engineering, Yazd University, Yazd, Iran


Increased pressure on natural resources, rising production costs, and multiple disposal challenges resulted in a growing global demand for integrated closed sustainable supply chain networks. In this paper, a bi-objective mixed integer linear programming model is developed to minimize the overall cost and maximize the use of eco-friendly materials and clean technology. The paper evaluates the exact, heuristic, and metaheuristic methods in solving the proposed model in both small and large sizes. The sensitivity analysis was conducted on LP-metric method as it outperformed the other two exact methods in solving the small size problems. The evaluation of LP-metric, modified ε-constraint, and TH as the exact methods, and Lagrange relaxation algorithm as the heuristic method in terms of solution value and CPU time revealed the inability of exact methods in solving the large size problems. The best combination of effective parameters for meta-heuristic algorithms were determined using the Taguchi method. The evaluation of MOPSO, NSGA-II, SPEA-II, and MOEA/D as the metaheuristic methods by means of Number of Pareto Solutions (NPS), Mean Ideal Distance (MID), The Spread of Non-dominance Solutions (SNS), and CPU Time revealed the performance of these methods in solving the proposed model in a large size. The implementation of VIKOR technique identified the SPEA-II as the best method among the meta-heuristic methods. This study provides a holistic view regarding the importance of selecting an appropriate solution methodology based on the problem dimension to ensure obtaining the optimum and accurate solution within the reasonable processing time.


       [1]        Meade, L., Sarkis, J., and Presley, A. (2007). The theory and practice of reverse logistics. International Journal of Logistics Systems and Management3(1), 56-84.
       [2]        Üster, H., Easwaran, G., Akçali, E., and Çetinkaya, S. (2007). Benders decomposition with alternative multiple cuts for a multi‐product closed‐loop supply chain network design model. Naval Research Logistics (NRL)54(8), 890-907.
       [3]        Toma, P., Massari, S., and Miglietta, P. P. (2016). Natural resource use efficiency and economic productivity. Life Cycle Approaches to Sustainable Regional Development; Massari, S., Sonnemann, G., Balkau, F., Eds, 143-148.
       [4]        Guide Jr, V. D. R., Teunter, R. H., and Van Wassenhove, L. N. (2003). Matching demand and supply to maximize profits from remanufacturing. Manufacturing and Service Operations Management5(4), 303-316.
       [5]        Zhang, K., and Feng, S. (2014, October). Research on revenue sharing coordination contract in automobile closed-loop supply chain. In Proceedings of 2014 IEEE International Conference on Service Operations and Logistics, and Informatics (pp. 298-302). IEEE.
       [6]        Vahdani, B., Tavakkoli-Moghaddam, R., Modarres, M., and Baboli, A. (2012). Reliable design of a forward/reverse logistics network under uncertainty: a robust-M/M/c queuing model. Transportation Research Part E: Logistics and Transportation Review48(6), 1152-1168.
       [7]        Yun, Y., Chuluunsukh, A., and Gen, M. (2020). Sustainable Closed-Loop Supply Chain Design Problem: A Hybrid Genetic Algorithm Approach. Mathematics, 8(1), 84.
       [8]        Ghasemzadeh, Z., Sadeghieh, A., and Shishebori, D. (2021). A stochastic multi-objective closed-loop global supply chain concerning waste management: a case study of the tire industry. Environment, Development and Sustainability23(4), 5794-5821.
       [9]        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 and Industrial Engineering51(2), 309-320.
     [10]      Wang, H. F., and Hsu, H. W. (2010). A closed-loop logistic model with a spanning-tree based genetic algorithm. Computers and operations research37(2), 376-389.
     [11]      Chen, Y. T., Chan, F. T. S., and Chung, S. H. (2015). An integrated closed-loop supply chain model with location allocation problem and product recycling decisions. International Journal of Production Research53(10), 3120-3140.
     [12]      Jabbarzadeh, A., Haughton, M., and Khosrojerdi, A. (2018). Closed-loop supply chain network design under disruption risks: A robust approach with real world application. Computers and Industrial Engineering116, 178-191.
     [13]      Shishebori, D., Yousefi Babadi, A., and Noormohammadzadeh, Z. (2018). A Lagrangian relaxation approach to fuzzy robust multi-objective facility location network design problem. Scientia Iranica25(3), 1750-1767.
     [14]      Özceylan, E., Demirel, N., Çetinkaya, C., and Demirel, E. (2017). A closed-loop supply chain network design for automotive industry in Turkey. Computers and industrial engineering113, 727-745.
     [15]      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 Review47(4), 532-546.
     [16]      Shishebori, D., Karimi-Nasab, M., and Snyder, L. V. (2017). A two-phase heuristic algorithm for designing reliable capacitated logistics networks under disruptions. European Journal of Industrial Engineering11(4), 425-468.
     [17]      Devika, K., Jafarian, A., and Nourbakhsh, V. (2014). Designing a sustainable closed-loop supply chain network based on triple bottom line approach: A comparison of metaheuristics hybridization techniques. European Journal of Operational Research235(3), 594-615.
     [18]      Talaei, M., Moghaddam, B. F., Pishvaee, M. S., Bozorgi-Amiri, A., and Gholamnejad, S. (2016). A robust fuzzy optimization model for carbon-efficient closed-loop supply chain network design problem: a numerical illustration in electronics industry. Journal of Cleaner Production113, 662-673.
     [19]      Fahimnia, B., Sarkis, J., and Eshragh, A. (2015). A tradeoff model for green supply chain planning: A leanness-versus-greenness analysis. Omega54, 173-190.
     [20]      Kannan, D., Diabat, A., Alrefaei, M., Govindan, K., and Yong, G. (2012). A carbon footprint based reverse logistics network design model. Resources, conservation and recycling67, 75-79.
     [21]      Ramudhin, A., Chaabane, A., Kharoune, M., and Paquet, M. (2008, December). Carbon market sensitive green supply chain network design. In 2008 IEEE International Conference on Industrial Engineering and Engineering Management (pp. 1093-1097). IEEE.
     [22]      Garg, K., Kannan, D., Diabat, A., and Jha, P. C. (2015). A multi-criteria optimization approach to manage environmental issues in closed loop supply chain network design. Journal of Cleaner Production100, 297-314.
     [23]      Abdolazimi, O., Esfandarani, M. S., Salehi, M., and Shishebori, D. (2020a). Robust design of a multi-objective closed-loop supply chain by integrating on-time delivery, cost, and environmental aspects, case study of a Tire Factory. Journal of Cleaner Production, 121566.
     [24]      Liao, Y., Kaviyani-Charati, M., Hajiaghaei-Keshteli, M., and Diabat, A. (2020). Designing a closed-loop supply chain network for citrus fruits crates considering environmental and economic issues. Journal of Manufacturing Systems55, 199-220.
     [25]      Papen, P., and Amin, S. H. (2019). Network configuration of a bottled water closed-loop supply chain with green supplier selection. Journal of Remanufacturing9(2), 109-127.
     [26]      Validi, S., Bhattacharya, A., and Byrne, P. J. (2015). A solution method for a two-layer sustainable supply chain distribution model. Computers and Operations Research54, 204-217.
     [27]      Niu, B., Tan, L., Liu, J., Liu, J., Yi, W., and Wang, H. (2019). Cooperative bacterial foraging optimization method for multi-objective multi-echelon supply chain optimization problem. Swarm and Evolutionary Computation49, 87-101.
     [28]      Khalifehzadeh, S., Seifbarghy, M., and Naderi, B. (2015). A four-echelon supply chain network design with shortage: Mathematical modeling and solution methods. Journal of Manufacturing Systems35, 164-175.
     [29]      Bottani, E., Murino, T., Schiavo, M., and Akkerman, R. (2019). Resilient food supply chain design: Modelling framework and metaheuristic solution approach. Computers and Industrial Engineering135, 177-198.
     [30]      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 Applications39(8), 6782-6791.
     [31]      Amin, S. H., & Zhang, G. (2013). A multi-objective facility location model for closed-loop supply chain network under uncertain demand and return. Applied Mathematical Modelling37(6), 4165-4176.
     [32]      Alshamsi, A., & Diabat, A. (2018). Large-scale reverse supply chain network design: An accelerated Benders decomposition algorithm. Computers & Industrial Engineering124, 545-559.
     [33]      Santibanez-Gonzalez, E. D., & Diabat, A. (2013). Solving a reverse supply chain design problem by improved Benders decomposition schemes. Computers & Industrial Engineering66(4), 889-898.
     [34]      Alshamsi, A., & Diabat, A. (2017). A Genetic Algorithm for Reverse Logistics network design: A case study from the GCC. Journal of Cleaner Production151, 652-669.
     [35]      Diabat, A., Battaïa, O., & Nazzal, D. (2015). An improved Lagrangian relaxation-based heuristic for a joint location-inventory problem. Computers & Operations Research61, 170-178.
     [36]      Ruan, J., & Xu, Z. (2011). Environmental friendly automated line for recovering the cabinet of waste refrigerator. Waste management31(11), 2319-2326.
     [37]      Kemp, R., & Volpi, M. (2008). The diffusion of clean technologies: a review with suggestions for future diffusion analysis. Journal of Cleaner Production16(1), S14-S21.
     [38]      Taylor, D. H. (Ed.). (1997). Global cases in logistics and supply chain management. Cengage Learning EMEA.
     [39]      Esmaili, M., Amjady, N., & Shayanfar, H. A. (2011). Multi-objective congestion management by modified augmented ε-constraint method. Applied Energy88(3), 755-766.
     [40]      Torabi, S. A., & Hassini, E. (2008). An interactive possibilistic programming approach for multiple objective supply chain master planning. Fuzzy sets and systems159(2), 193-214.
     [41]      Cuevas, E., Gálvez, J., & Avalos, O. (2020). Introduction to Optimization and Metaheuristic Methods. In Recent Metaheuristics Algorithms for Parameter Identification (pp. 1-8). Springer, Cham.
     [42]      Srinivas, N., & Deb, K. (1994). Muiltiobjective optimization using nondominated sorting in genetic algorithms. Evolutionary computation2(3), 221-248.
     [43]      Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. A. M. T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE transactions on evolutionary computation6(2), 182-197.
     [44]      Zhang, Q., & Li, H. (2007). MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Transactions on evolutionary computation11(6), 712-731.
     [45]      Abdolazimi, O., Esfandarani, M. S., & Shishebori, D. (2020b). Design of a supply chain network for determining the optimal number of items at the inventory groups based on ABC analysis: a comparison of exact and meta-heuristic methods. Neural Computing and Applications, 1-16.
     [46]      Opricovic, S., & Tzeng, G. H. (2007). Extended VIKOR method in comparison with outranking methods. European journal of operational research178(2), 514-529.
     [47]      Coello, C. A. C., Pulido, G. T., & Lechuga, M. S. (2004). Handling multiple objectives with particle swarm optimization. IEEE Transactions on evolutionary computation8(3), 256-279.
     [48]      Ortiz-Rodriguez, J.M., Martinez-Blanco, M.R., VegaCarrillo, H.R., “ARTIFICIAL NEURALNETWORKS APPLICATION”, Chapter 24, Intech, 2011.
     [49]      Peterson, G. E., Clair, D. S., Aylward, S. R., & Bond, W. E. (1995). Using Taguchi's method of experimental design to control errors in layered perceptrons. IEEE transactions on neural networks6(4), 949-961.
     [50]      Yang, S. M., & Lee, G. S. (1999). Neural network design by using Taguchi method.
     [51]      Sukthomya, W., & Tannock, J. (2005). The optimisation of neural network parameters using Taguchi’s design of experiments approach: an application in manufacturing process modelling. Neural Computing & Applications14(4), 337-344.
     [52]      Tortum, A., Yayla, N., Çelik, C., & Gökdağ, M. (2007). The investigation of model selection criteria in artificial neural networks by the Taguchi method. Physica A: Statistical Mechanics and its Applications, 386(1), 446-468.
     [53]      Porkar, S., Mahdavi, I., Vishkaei, B. M., & Hematian, M. (2018). Green supply chain flow analysis with multi-attribute demand in a multi-period product development environment. Operational Research, 1-31.
     [54]      Shakhsi-Niaei, M., & Esfandarani, M. S. (2019). Multi-objective deterministic and robust models for selecting optimal pipe materials in water distribution system planning under cost, health, and environmental perspectives. Journal of cleaner production207, 951-960.