Document Type : Research Paper


1 Faculty member of ACECR, Development and Planning Institute, Tabriz, Iran.

2 Department of Industrial Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran.

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


The mathematical model of a multi-product multi-period multi-echelon closed-loop supply chain network design under uncertainty is designed in this paper. The designed network consists of raw material suppliers, plants, warehouses, distribution centers, and customer zones in forward chain and collection centers, repair centers, recovery/decomposition center, and disposal center in the reverse chain. The goal of the model is to determine the quantities of products and raw material transported between the supply chain entities in each period by considering different transportation mode, the number and locations of the potential facilities, the shortage of products in each period, and the inventory of products in warehouses and plants with considering discount and uncertainty parameters. The robust possibilistic optimization approach was used to control the uncertainty parameter. At the end to solve the proposed model, five meta-heuristic algorithms include genetic algorithm, bee colony algorithm, simulated annealing, imperial competitive algorithm, and particle swarm optimization are utilized. Finally, some numerical illustrations are provided to compare the proposed algorithms. The results show the genetic algorithm is an efficient algorithm for solving the designed model in this paper.


Main Subjects

[1]        Fazli-Khalaf, M., Mirzazadeh, A., & Pishvaee, M. S. (2017). A robust fuzzy stochastic programming model for the design of a reliable green closed-loop supply chain network. Human and ecological risk assessment: an international journal23(8), 2119-2149.
[2]        Ghahremani Nahr, J., Pasandideh, S. H. R., & Niaki, S. T. A. (2020). A robust optimization approach for multi-objective, multi-product, multi-period, closed-loop green supply chain network designs under uncertainty and discount. Journal of industrial and production engineering37(1), 1-22.
[3]        Jabbarzadeh, A., Haughton, M., & Khosrojerdi, A. (2018). Closed-loop supply chain network design under disruption risks: A robust approach with real world application. Computers & industrial engineering116, 178-191.
[4]        Mohtashami, Z., Aghsami, A., & Jolai, F. (2020). A green closed loop supply chain design using queuing system for reducing environmental impact and energy consumption. Journal of cleaner production242.
[5]        Prakash, S., Kumar, S., Soni, G., Jain, V., & Rathore, A. P. S. (2020). Closed-loop supply chain network design and modelling under risks and demand uncertainty: an integrated robust optimization approach. Annals of operations research290(1), 837-864.
[6]        Sadeghi, A., Mina, H., & Bahrami, N. (2020). A mixed integer linear programming model for designing a green closed-loop supply chain network considering location-routing problem. International journal of logistics systems and management36(2), 177-198.
[7]        Safaei, A. S., Roozbeh, A., & Paydar, M. M. (2017). A robust optimization model for the design of a cardboard closed-loop supply chain. Journal of cleaner production166, 1154-1168.
[8]        Govindan, K., Soleimani, H., & Kannan, D. (2015). Reverse logistics and closed-loop supply chain: A comprehensive review to explore the future. European journal of operational research240(3), 603-626.
[9]        Fleischmann, M., Beullens, P., BLOEMHOF‐RUWAARD, J. M., & Van Wassenhove, L. N. (2001). The impact of product recovery on logistics network design. Production and operations management10(2), 156-173.
[10]    Üster, H., Easwaran, G., Akçali, E., & 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.
[11]    Lee, D. H., & Dong, M. (2009). Dynamic network design for reverse logistics operations under uncertainty. Transportation research part E: logistics and transportation review45(1), 61-71.
[12]    Lee, J. E., Gen, M., & Rhee, K. G. (2009). Network model and optimization of reverse logistics by hybrid genetic algorithm. Computers & industrial engineering56(3), 951-964.
[13]    Kannan, G., Sasikumar, P., & Devika, K. (2010). A genetic algorithm approach for solving a closed loop supply chain model: A case of battery recycling. Applied mathematical modelling34(3), 655-670.
[14]    Khajavi, L. T., Seyed-Hosseini, S. M., & Makui, A. (2011). An integrated forward/reverse logistics network optimization model for multi-stage capacitated supply chain. iBusiness 3(2). DOI:10.4236/ib.2011.32030
[15]    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 economics135(1), 209-221.
[16]    Mahmoudi, H., Fazlollahtabar, H., & Mahdavi, I. (2013). Mathematical modeling for minimizing costs in a multilayer multi-product reverse supply chain. Industrial engineering & management2(2), 6.
[17]    Dönmez, İ. (2013). Design of reverse logistics network for waste batteries with an application in Turkey. Chemical engineering transactions. Retrieved from
[18]    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 modelling37(1-2), 328-344.
[19]    Özceylan, E., Paksoy, T., & 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 review61, 142-164.
[20]    Soleimani, H., & Govindan, K. (2014). Reverse logistics network design and planning utilizing conditional value at risk. European journal of operational research237(2), 487-497.
[21]    Rezaee, A., Dehghanian, F., Fahimnia, B., & Beamon, B. (2017). Green supply chain network design with stochastic demand and carbon price. Annals of operations research250(2), 463-485.
[22]    Alavi, S., Azad, N., Heydar, M., & Davoudpour, H. (2016). Integrated production, inventory, and location-allocation decisions in designing supply chain networks. International journal of information systems and supply chain management (IJISSCM)9(4), 22-42.
[23]    Nobil, A. H., & Taleizadeh, A. A. (2016). Analysing a fuzzy integrated inventory-production-distribution planning problem with maximum NPV of cash flows in a closed-loop supply chain. International Journal of Inventory Research3(1), 31-48.
[24]    Talaei, M., Moghaddam, B. F., Pishvaee, M. S., Bozorgi-Amiri, A., & 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.
[25]    Zhalechian, M., Tavakkoli-Moghaddam, R., Zahiri, B., & Mohammadi, M. (2016). Sustainable design of a closed-loop location-routing-inventory supply chain network under mixed uncertainty. Transportation research part E: logistics and transportation review89, 182-214.
[26]    Ciccullo, F., Pero, M., Caridi, M., Gosling, J., & Purvis, L. (2018). Integrating the environmental and social sustainability pillars into the lean and agile supply chain management paradigms: A literature review and future research directions. Journal of cleaner production172, 2336-2350.
[27]    Das, K. (2018). Integrating lean systems in the design of a sustainable supply chain model. International Journal of Production Economics198, 177-190.
[28]    Haddadsisakht, A., & Ryan, S. M. (2018). Closed-loop supply chain network design with multiple transportation modes under stochastic demand and uncertain carbon tax. International journal of production economics195, 118-131.
[29]    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 systems341, 69-91.
[30]    Darbari, J. D., Kannan, D., Agarwal, V., & Jha, P. C. (2019). Fuzzy criteria programming approach for optimising the TBL performance of closed loop supply chain network design problem. Annals of operations research273(1-2), 693-738.
[31]    Ghahremani-Nahr, J., Kian, R., & Sabet, E. (2019). A robust fuzzy mathematical programming model for the closed-loop supply chain network design and a whale optimization solution algorithm. Expert systems with applications116, 454-471.
[32]    Samuel, C. N., Venkatadri, U., Diallo, C., & Khatab, A. (2020). Robust closed-loop supply chain design with presorting, return quality and carbon emission considerations. Journal of Cleaner Production247.
[33]    Gholizadeh, H., Tajdin, A., & Javadian, N. (2020). A closed-loop supply chain robust optimization for disposable appliances. Neural computing and applications32(8), 3967-3985.
[34]    Pishvaee, M. S., Rabbani, M., & Torabi, S. A. (2011). A robust optimization approach to closed-loop supply chain network design under uncertainty. Applied mathematical modelling35(2), 637-649.
[35]    Pishvaee, M. S., & Torabi, S. A. (2010). A possibilistic programming approach for closed-loop supply chain network design under uncertainty. Fuzzy sets and systems161(20), 2668-2683.
[36]    Altiparmak, F., Gen, M., Lin, L., & Karaoglan, I. (2009). A steady-state genetic algorithm for multi-product supply chain network design. Computers & industrial engineering56(2), 521-537.
[37]    Kim, K. W., Gen, M., & Yamazaki, G. (2003). Hybrid genetic algorithm with fuzzy logic for resource-constrained project scheduling. Applied soft computing2(3), 174-188.
[38]    Zegordi, S. H., Abadi, I. K., & Nia, M. B. (2010). A novel genetic algorithm for solving production and transportation scheduling in a two-stage supply chain. Computers & industrial engineering58(3), 373-381.
[39]    Hu, C., & Li, S. (2009). Two-phase interactive satisfying method of fuzzy multiple objective optimization with linguistic preference. International journal of information technology & decision making8(03), 427-443.
[40]    Hamzadayi, A., & Yildiz, G. (2012). A genetic algorithm based approach for simultaneously balancing and sequencing of mixed-model U-lines with parallel workstations and zoning constraints. Computers & industrial engineering62(1), 206-215.
[41]    Chitra, C., & Subbaraj, P. (2012). A nondominated sorting genetic algorithm solution for shortest path routing problem in computer networks. Expert systems with applications39(1), 1518-1525.
[42]    Atashpaz-Gargari, E., & Lucas, C. (2007, September). Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition. 2007 IEEE congress on evolutionary computation (pp. 4661-4667). IEEE.
[43]    Eberhart, R., & Kennedy, J. (1995, October). A new optimizer using particle swarm theory. Proceedings of the sixth international symposium on micro machine and human Science (pp. 39-43). IEEE.
[44]    Nakrani, S., & Tovey, C. (2004). On honey bees and dynamic server allocation in internet hosting centers. Adaptive behavior12(3-4), 223-240.
[45]    Lin, L., Gen, M., & Wang, X. (2009). Integrated multistage logistics network design by using hybrid evolutionary algorithm. Computers & industrial engineering56(3), 854-873.