Mathematical Model of Location, Multi-Commodity and Multi-Period in Sustainable Closed-Loop Supply Chain Considering Risk and Demand and Quality Uncertainty (A case Study)

Document Type : Original Article


1 Ph.D Student, South Tehran Branch, Islamic Azad University.

2 Assistant Professor, South Tehran Branch, Islamic Azad University.

3 Associate Professor, South Tehran Branch, Islamic Azad University.


The main objective of sustainable supply chain is to balance the economic, environmental, and social goals that companies have to use closed-loop supply chains for cost reduction and increasing the efficiency of the supply chain. According to the research literature, considering the risk in supply chains, especially the return supply chain, is one of the topics that has been little studied. Therefore, the aim of this study is to locate the components of a three-objective, sustainable closed-loop, multi-commodity, and multi-period supply chain, considering uncertainty and market scenarios with a risk approach. Location in the sustainable closed-loop supply chain, considering the risk, and also paying attention to the quality of manufactured products and different scenarios of demand are among the innovations of this research. Due to the NP-Hard nature of the problem, the model is solved by the nondominated sorting genetic algorithm II (NSGA-II). Sensitivity analysis has been performed on the parameters of the problem, and the efficiency of the studied methods has been investigated. The average Pareto points obtained from the first objective function is 56789.9, the average Pareto points for the second objective function is 1828.8 and for the third objective function is 77365.32, and also the average solution time of the model is 15.9 seconds.


Main Subjects

  1. Ahmad, W. N. K. W., Rezaei, J., Tavasszy, L. A., & de Brito, M. P. (2016). Commitment to and preparedness for sustainable supply chain management in the oil and gas industry. Journal of environmental management, 180, 202-213.
  2. Ahmad, W. N. K. W., Rezaei, J., Tavasszy, L. A., & de Brito, M. P. (2016). Commitment to and preparedness for sustainable supply chain management in the oil and gas industry. Journal of environmental management, 180, 202-213.
  3. Taghizadedh Yazdi., M., Salmani Zarchi, (2019). Presenting a comprehensive multi-objective model of supply chain of multi-level-multi-product green closed loop with the classic approach of weighted total: Pareto front production (Case study: Shahpar Mumtaz Shoes Company). Industrial Management Perspective, 36, 107-137 (In Persian)
  4. Aqlan, F., & Lam, S. S. (2016). Supply chain optimization under risk and uncertainty: A case study for high-end server manufacturing. Computers & Industrial Engineering, 93, 78-87.
  5. Aras, N., Aksen, D., & Tanu─čur, A. G. (2008). Locating collection centers for incentive-dependent returns under a pick-up policy with capacitated vehicles. European Journal of Operational Research, 191(3), 1223-1240.
  6. Soleimani, H., & Govindan, K. (2014). Reverse logistics network design and planning utilizing conditional value at risk. European Journal of Operational Research, 237(2), 487-497.
  7. Baptista, S., Barbosa-Póvoa, A. P., Escudero, L. F., Gomes, M. I., & Pizarro, C. (2019). On risk management of a two-stage stochastic mixed 0–1 model for the closed-loop supply chain design problem. European Journal of Operational Research, 274(1), 91-107.
  8. Chan, F. T., Jha, A., & Tiwari, M. K. (2016). Bi-objective optimization of three echelon supply chain involving truck selection and loading using NSGA-II with heuristics algorithm. Applied Soft Computing, 38, 978-987.
  9. Cheraghalipour, A., Paydar, M. M., & Hajiaghaei-Keshteli, M. (2018). A bi-objective optimization for citrus closed-loop supply chain using Pareto-based algorithms. Applied Soft Computing, 69, 33-59.
  10. Jia, F., Zhang, T., & Chen, L. (2020). Sustainable supply chain Finance: Towards a research agenda. Journal of Cleaner Production, 243,
  11. Das, K., & Chowdhury, A. H. (2012). Designing a reverse logistics network for optimal collection, recovery and quality-based product-mix planning.International Journal of Production Economics, 135(1), 209-221.
  12. 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 computation, 6(2), 182-197.
  13. Dehghan, E., Nikabadi, M. S., Amiri, M., & Jabbarzadeh, A. (2018). Hybrid robust, stochastic and possibilistic programming for closed-loop supply chain network design. Computers & Industrial Engineering, 123, 220-231.
  14. Manupati, V. K., Schoenherr, T., Ramkumar, M., Wagner, S. M., Pabba, S. K., & Inder Raj Singh, R. (2020). A blockchain-based approach for a multi-echelon sustainable supply chain. International Journal of Production Research, 58(7), 2222-2241.
  15. Modica, P. D., Altinay, L., Farmaki, A., Gursoy, D., & Zenga, M. (2020). Consumer perceptions towards sustainable supply chain practices in the hospitality industry. Current Issues in Tourism, 23(3), 358-375.
  16. Ene, S., & Öztürk, N. (2014). Open loop reverse supply chain network design. Procedia-Social and Behavioral Sciences, 109, 1110-1115.
  17. Farrokh, M., Azar, A., Jandaghi, G., & Ahmadi, E. (2018). A novel robust fuzzy stochastic programming for closed loop supply chain network design under hybrid uncertainty. Fuzzy Sets and Systems, 341, 69-91.
  18. Rahimi, M., & Ghezavati, V. (2018). Sustainable multi-period reverse logistics network design and planning under uncertainty utilizing conditional value at risk (CVaR) for recycling construction and demolition waste. Journal of Cleaner Production, 172, 1567-1581
  19. Flygansvær, B., Dahlstrom, R., & Nygaard, A. (2018). Exploring the pursuit of sustainability in reverse supply chains for electronics.Journal of Cleaner Production, 189, 472-484.
  20. Yun, Y., Chuluunsukh, A., & Gen, M. (2020). Sustainable Closed-Loop Supply Chain Design Problem: A Hybrid Genetic Algorithm Approach. Mathematics, 8(1), 84.
  21. Masoudipour, E., Amirian, H., & Sahraeian, R. (2017). A novel closed-loop supply chain based on the quality of returned products. Journal of cleaner production, 151, 344-355.
  22. Reyhani Yamchi, H., Jabarzadeh, Y., Ghaffarinasab, N., Kumar, V., & Garza-Reyes, J. A. (2020). A multi-objective linear optimization model for designing sustainable closed-loop agricultural supply chain.
  23. Jeihoonian, M., Zanjani, M. K., & Gendreau, M. (2017). Closed-loop supply chain network design under uncertain quality status: Case of durable products. International Journal of Production Economics, 183, 470-486.
  24. Kim, J., Do Chung, B., Kang, Y., & Jeong, B. (2018). Robust optimization model for closed-loop supply chain planning under reverse logistics flow and demand uncertainty. Journal of cleaner production, 196, 1314-1328.
  25. Goh, M., & Meng, F. (2009). A stochastic model for supply chain risk management using conditional value at risk. In Managing Supply Chain Risk and Vulnerability (pp. 141-157). Springer, London.
  26. Huang, L., Murong, L., & Wang, W. (2020). Green closed-loop supply chain network design considering cost control and CO2 emission. Modern Supply Chain Research and Applications.
  27. Mota, B., Gomes, M. I., Carvalho, A., & Barbosa-Povoa, A. P. (2018). Sustainable supply chains: An integrated modeling approach under uncertainty. Omega, 77, 32-57.
  28. Radfar, A, Mohammaditabar, D, (2019), Two-objective optimization of the inventory management problem by the vendor in a green multilevel supply chain, Industrial Management Perspective, 35, 109-134 (In Persian)
  29. Paydar, M. M., Babaveisi, V., & Safaei, A. S. (2017). An engine oil closed-loop supply chain design considering collection risk. Computers & Chemical Engineering, 104, 38-55.
  30. Pedram, A., Yusoff, N. B., Udoncy, O. E., Mahat, A. B., Pedram, P., & Babalola, A. (2017). Integrated forward and reverse supply chain: A tire case study. Waste Management, 60, 460-470.
  31. Phuc, P. N. K., Vincent, F. Y., & Tsao, Y. C. (2017). Optimizing fuzzy reverse supply chain for end-of-life vehicles. Computers & Industrial Engineering, 113, 757-765.
  32. Rockafellar, R. T., & Uryasev, S. (2000). Optimization of conditional value-at-risk. Journal of risk, 2, 21-42.
  33. Rockafellar, R. T., & Uryasev, S. (2002). Conditional value-at-risk for general loss distributions. Journal of banking & finance, 26(7), 1443-1471.
  34. Saedinia, R., Vahdani, B., Etebari, F., & Nadjafi, B. A. (2019). Robust gasoline closed loop supply chain design with redistricting, service sharing and intra-district service transfer. Transportation Research Part E: Logistics and Transportation Review, 123, 121-141.
  35. Rabbani, M., Hosseini-Mokhallesun, S. A. A., Ordibazar, A. H., & Farrokhi-Asl, H. (2020). A hybrid robust possibilistic approach for a sustainable supply chain location-allocation network design. International Journal of Systems Science: Operations & Logistics, 7(1), 60-75.
  36. Salimi, F., & Vahdani, B. (2018). Designing a bio-fuel network considering links reliability and risk-pooling effect in bio-refineries.Reliability Engineering & System Safety, 174, 96-107.
  37. Asgari, Nasrin, Ehsan Nikbakhsh, Alex Hill, and Reza Zanjirani Farahani. Supply chain management 1982–2015: a review. IMA Journal of Management Mathematics, 27(3), 353-379.
  38. Sawik, T. (2011). Supplier selection in make-to-order environment with risks. Mathematical and Computer Modelling, 53(9-10), 1670-1679.
  39. Singh, S. R., & Saxena, N. (2013). A closed loop supply chain system with flexible manufacturing and reverse logistics operation under shortages for deteriorating items. Procedia Technology, 10, 330-339.
  40. Sobotka, A., Sagan, J., Baranowska, M., & Mazur, E. (2017). Management of reverse logistics supply chains in construction projects. Procedia engineering, 208, 151-159.
  41. Qian, X., Chan, F. T., Zhang, J., Yin, M., & Zhang, Q. (2020). Channel coordination of a two-echelon sustainable supply chain with a fair-minded retailer under cap-and-trade regulation. Journal of Cleaner Production, 244,
  42. Vahdani, B., & Ahmadzadeh, E. (2019). Designing a realistic ICT closed loop supply chain network with integrated decisions under uncertain demand and lead time. Knowledge-Based Systems.
  43. Vahdani, B., Razmi, J., & Tavakkoli-Moghaddam, R. (2012). Fuzzy possibilistic modeling for closed loop recycling collection networks. Environmental Modeling & Assessment, 17(6), 623-637.
  44. Zhou, Y. J., Chen, X. H., & Wang, Z. R. (2008). Optimal ordering quantities for multi-products with stochastic demand: Return-CVaR model. International Journal of Production Economics, 112(2), 782-795.
  45. Zhao, X., Xia, X., Wang, L., & Yu, G. (2018 ). Risk-Averse Facility Location for Green Closed-Loop Supply Chain Networks Design under Uncertainty. Sustainability, 10(11), 4072.
  46. Wu, Z., Kwong, C. K., Aydin, R., & Tang, J. (2017). A cooperative negotiation embedded NSGA-II for solving an integrated product family and supply chain design problem with remanufacturing consideration. Applied Soft Computing, 57, 19-34.
  47. Xu, X., Meng, Z., & Shen, R. (2013). A tri-level programming model based on Conditional Value-at-Risk for three-stage supply chain management. Computers & Industrial Engineering, 66(2), 470-475.
  48. Xu, Z., Elomri, A., Pokharel, S., Zhang, Q., Ming, X. G., & Liu, W. (2017). Global reverse supply chain design for solid waste recycling under uncertainties and carbon emission constraint. Waste management, 64, 358-370.
  49. Yi, J. H., Deb, S., Dong, J., Alavi, A. H., & Wang, G. G. (2018). An improved NSGA-III Algorithm with adaptive mutation operator for big data optimization problems. Future Generation Computer Systems, 88, 571-585.
  50. Yu, H., & Solvang, W. D. (2018). Incorporating flexible capacity in the planning of a multi-product multi-echelon sustainable reverse logistics network under uncertainty. Journal of cleaner production, 198, 285-303.
  51. Heidari, J., Memarian, A., Bozorgi Amiri, (2019). A, Coordination of environmental quality decisions and product quality of products in a two-tier green supply chain. The Journal of Industrial Management Perspective, 33, 87-114. (In Persian)