Development of closed-loop supply chain mathematical model (cost-benefit-environmental effects) under uncertainty conditions by approach of genetic algorithm

Document Type : Research Paper


1 Department of Industrial Management, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran.

2 Department of Management, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran.

3 Department of Management, Sanandaj Branch, Islamic Azad University, Sanandaj, Iran.

4 Department of Industrial Engineering, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran.



In the current world, the debate on the reinstatement and reuse of consumer prod-ucts has become particularly important. Since the supply chain of the closed loop is not only a forward flow but also a reverse one; therefore, companies creating integ-rity between direct and reverse supply chain are successful. The purpose of this study is to develop a new mathematical model for closed loop supply chain net-work. In the real world the demand and the maximum capacity offered by the sup-plier are uncertain which in this model; the fuzzy theory discussion was used to cover the uncertainty of the mentioned variables. The objective functions of the model include minimizing costs, increasing revenues of recycling products, increas-ing cost saving from recycling and environmental impacts. According to the NP-hard, an efficient algorithm was suggested based on the genetic Meta heuristic algo-rithm to solve it. Twelve numerical problems were defined and solved using the NSGA-II algorithm to validate the model


Main Subjects

[1] Al-Salem, M., Diabat, A., Dalalah, D., & Alrefaei, M., A closed-loop supply chain management problem: Reformulation and piecewise linearization. Journal of Manufacturing Systems, 2016, 40, 1-8.
[2] Amin, S. H., & Baki, F., A facility location model for global closed-loop supply chain network designs. Applied Mathematical Modeling, 2017,  41, 316-330. https://
[3] Amin, S. H., & Zhang, G., A multi-objective facility location model for closed-loop supply chain network under uncertain demand and return. Applied Mathematical Modeling , 2013, 37(6), 4165-4176.
[4] Chen, Y. T., Chan, F. T., Chung, S. H., & Park, W. Y., Optimization of product refurbishment in closed-loop supply chain using multi-period model integrated with fuzzy controller under uncertainties. Robotics and Computer-Integrated Manufacturing, 2018, 50, 1-12. https://DOI: 10.1016/j.rcim.2017.05.005
[5] Dai, Z., & Zheng, X., Design of close-loop supply chain network under uncertainty using hybrid genetic algorithm: A fuzzy and chance-constrained programming model. Computers & Industrial Engineering, 2015, 88, 444-457.
[6] Farrokh, M., Azar, A., Jandaghi, G., & Ahmadi, E., A novel robust fuzzy stochastic programming for closed loop supply chain network design under hybrid uncertainty. Fuzzy Sets and Systems, 2018, 341, 69-91. https://DOI: 10.1016/j.fss.2017.03.019
[7] Fathollahi-Fard, A. M., Hajiaghaei-Keshteli, M., A stochastic multi-objective model for a closed-loop supply chain with environmental considerations. Applied Soft Computing, 2018, 69, 232-249.             https:// DOI: 10.1016/j.asoc.2018.04.055
[8] Haupt, R. L., Haupt, S. E., Practical genetic algorithms, New York: Wiley, 1998, (Vol. 2).
[9] Izadikhah, M., Azadi, M., Shokri Kahi, V., Farzipoor Saen, R., Developing a new chance constrained NDEA model to measure the performance of humanitarian supply chains, International Journal of Production Research, 2019, 57 (3), P. 662-682, Doi: 10.1080/00207543.2018.1480840
[10] Izadikhah, M., A fuzzy goal programming based procedure for machine tool selection, Journal of Intelligent & Fuzzy Systems, 2015, 28 (1), P. 361-372, Doi: 10.3233/IFS-141311
[11] Jayant, A., Gupta, P., & Garg, S. K., Simulation modelling and analysis of network design for closed-loop supply chain: a case study of battery industry. Procedia Engineering, 2014, 97(1672), 2213-2221.
[12] Kadambala, D. K., Subramanian, N., Tiwari, M. K., Abdulrahman, M., & Liu, C., Closed loop supply chain networks: Designs for energy and time value efficiency. International Journal of Production Economics, 2017, 183, 382-393.
[13] Kafa, N., Hani, Y., & El Mhamedi, A., An integrated sustainable partner selection approach with closed-loop supply chain network configuration. IFAC-PapersOnLine, 2015, 48(3), 1840-1845.
[14] Kaya, O., & Urek, B., A mixed integer nonlinear programming model and heuristic solutions for location, inventory and pricing decisions in a closed loop supply chain. Computers & Operations Research, 2016, 65, 93-103. https:// doi>10.1016/j.cor.2015.07.005
[15] Özceylan, E., Paksoy, T., & Bektaş, T., 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, 2014, 61, 142-164. https:// DOI: 10.1016/j.tre.2013.11.001
[16] Özceylan, E., & Paksoy, T., A mixed integer programming model for a closed-loop supply-chain network . International Journal of Production Research, 2013, 51(3), 718-734.
[17] Paksoy, T., Bektaş, T., & Özceylan, E., Operational and environmental performance measures in a multi-product closed-loop supply chain. Transportation Research Part E: Logistics and Transportation Review, 2011, 47(4), 532-546. https:// DOI: 10.1016/j.tre.2010.12.001
[18] Paydar, M. M., Babaveisi, V., & Safaei, A. S., An engine oil closed-loop supply chain design considering collection risk. Computers & Chemical Engineering, 2017, 104, 38-55.
[19] Pishvaee, M. S., Razmi, J., & Torabi, S. A., Robust possibility programming for socially responsible supply chain network design: A new approach. Fuzzy sets and systems, 2012, 206, 1-20.
[20] Ramezani, M., Kimiagari, A. M., Karimi, B., & Hejazi, T. H., Closed-loop supply chain network design under a fuzzy environment. Knowledge-Based Systems, 2014, 59, 108-120.
[21] Ruimin, M. A., Lifei, Y. A. O., Maozhu, J. I. N., Peiyu, R. E. N., & Zhihan, L. V., Robust environmental closed-loop supply chain design under uncertainty, 2016, 89,19.
[22] Sabri E.H., Beamon B.M., A multi objective approach to simultaneous strategicand operational, 2000, 28, 581-598   https:// (99)00080-8
[23] Subulan, K., Taşan, A. S., & Baykasoğlu, A., Designing an environmentally conscious tire closed-loop supply chain network with multiple recovery options using interactive fuzzy goal programming. Applied Mathematical Modeling,2015, 39(9), 2661-2702. https://
[24] Tahmasebi, H.A., Raheb, M, Jafari, S., Presented and solved a green optimization model in the closed-loop supply chain with the aim of increasing profit and reducing environmental problems, taking into account the warranty period of the product. Journal of Investigating Operations in its Applications, 2018,  15(3), 27-44. https:// doi.
[25] Talaei, M., Moghaddam, B. F., Pishvaee, M. S., Bozorgi-Amiri, A., & Gholamnejad, S., A robust fuzzy optimization model for carbon-efficient closed-loop supply chain network design problem: a numerical illustration in electronics industry. Journal of Cleaner Production, 2016, 113, 662-673.                        
  https://DOI: 10.1016/j.jclepro.2015.10.074
[26] Tao, Z. G., Guang, Z. Y., Hao, S., & Song, H. J., Multi-period closed-loop supply chain network equilibrium with carbon emission constraints. Resources, Conservation and Recycling, 2015, 104, 354-365. https://DOI: 10.1016/j.resconrec.2015.07.016
[27] Tiwari, A., Chang, P. C., Tiwari, M. K., & Kandhway, R., A Hybrid Territory Defined evolutionary algorithm approach for closed loop green supply chain network design. Computers & Industrial Engineering, 2016, 99, 432-447. https://
[28] Xie, L., & Ma, J., Study the complexity and control of the recycling-supply chain of China's color TVs market based on the government subsidy. Communications in Nonlinear Science and Numerical Simulation, 2016, 38, 102-116.
[29] Zeballos, L. J., Méndez, C. A., & Barbosa-Povoa, A. P., Integrating decisions of product and closed-loop supply chain design under uncertain return flows . Computers & Chemical Engineering, 2018, 112, 211-238. https:// DOI: 10.1016/j.compchemeng.2018.02.011 
[30] Zohal, M., & Soleimani, H., Developing an ant colony approach for green closed-loop supply chain network design: a case study in gold industry. Journal of Cleaner Production, 2016, 133, 314-337.
[31] Zohori, S., Karimi, B, Mihami, R., Controlling the inventory of corrupt commodities in the closed loop supply chain, taking into account random demand. Journal of Industrial Engineering, 2016, 50(3), 429-439. https:// DOI:  10.22059/JIENG.2016.63162
Volume 6, Issue 2
April 2021
Pages 245-262
  • Receive Date: 09 March 2019
  • Revise Date: 24 May 2019
  • Accept Date: 31 May 2019
  • First Publish Date: 01 April 2021