A robust bi-level programming model for designing a closed-loop supply chain considering government's collection policy

Document Type : Article


Department of Industrial Engineering, Faculty of Engineering and Technology, Alzahra University, Tehran, P.O. Box 199389373, Iran


This study aims in providing a new approach regarding design of a closed loop supply chain network through emphasizing on the impact of the environmental government policies based on a bi-level mixed integer linear programming model. Government is considered as a leader in the first level and tends to set a collection rate policy which leads to collect more used products in order to ensure a minimum distribution ratio to satisfy a minimum demands. In the second level, private sector is considered as a follower and tries to maximize its profit by designing its own closed loop supply chain network according to the government used products collection policy. A heuristic algorithm and an adaptive genetic algorithm based on enumeration method are proposed and their performances are evaluated through computational experiences. The comparison among numerical examples reveals that there is an obvious conflict between the government and CLSC goals. Moreover, it shows that this conflict should be considered and elaborated in uncertain environment by applying Min-Max regret scenario based robust optimization approach. The results show the necessity of using robust bi-level programming in closed loop supply chain network design under the governmental legislative decisions as a leader-follower configuration.


Main Subjects

1. Altmann, M. and Bogaschewsky, R. "An environmentally conscious robust closed-loop supply chain design", Journal of Business Economics, 84, pp. 613- 637 (2014).
2. Zeballos, L.J., Mendez, C.A., Barbosa-Povoa, A.P., and Novais, A.Q. "Multi-period design and planning of closed-loop supply chains with uncertain supply and demand", Computers & Chemical Engineering, 66, pp. 151-164 (2014).
3. Ma, R., Yao, L., Jin, M., Ren, P., Lv, Z. "Robust environmental closed-loop supply chain design under uncertainty", Chaos, Solitons & Fractals, 89, pp. 195- 202 (2015).
4. Talaei, M., Farhang Moghaddam, B., Pishvaee, M.S., Bozorgi-Amiri, A., and Gholamnejad, S. "A robust fuzzy optimization model for carbon-efficient closedloop supply chain network design problem: A numerical illustration in electronics industry", Journal of Cleaner Production, 113, pp. 662-673 (2015).
5. Giri, B.C. and Sharma, S. "Optimal production policy for a closed-loop hybrid system with uncertain demand and return under supply disruption", Journal of Cleaner Production, 112, pp. 2015-2028 (2016).
6. Keyvanshokooh, E., Ryan, S.M., and Kabir, E. "Hybrid robust and stochastic optimization for closed-loop supply chain network design using accelerated benders decomposition", European Journal of Operational Research, 249, pp.76-92 (2016).
7. Dutta, P., Das, D., Schultmann, F., and Frohling, M. "Design and planning of a closed-loop supply chain with three way recovery and buy-back offer", Journal of Cleaner Production, 135, pp. 604-619 (2016).
8. Zeballos, L.J. and Mendez, C.A. "Chapter 16 - managing risk in the design of product and closed-loop supply chain structure", In Computer Aided Chemical Engineering, Eds.: Mario R. Eden Mariano Martin and G. Chemmangattuvalappil Nishanth, 39, pp. 443-474 (2017).
9. Jeihoonian, M., Kazemi Zanjani, M., and Gendreau, M. "Closed-loop supply chain network design under uncertain quality status: case of durable products", International Journal of Production Economics, 183, pp. 470-486 (2017).
10. Huang, M., Yi, P., Guo, L., and Shi, T. "A modal interval based genetic algorithm for closed-loop supply chain network design under uncertainty", IFACPapersOnLine, 49, pp. 616-621 (2016).
11. Fareeduddin, M., Shokri, Z., Adnan, H., and Mujahid, N. "Multi-period planning of closed-loop supply chain with carbon policies under uncertainty", Transportation Research Part D: Transport and Environment, 51, pp. 146-172 (2017).
12. Safaei, A.S., Roozbeh, A., and Paydar, M.M. "A robust optimization model for the design of a cardboard closed-loop supply chain", Journal of Cleaner Production, 166, pp. 1154-1168 (2017).
13. Hassanzadeh Amin, S., Zhang, G., and Akhtar, P. "Effects of uncertainty on a tire closed-loop supply chain network", Expert Systems with Applications, 73, pp. 82-91 (2017).
14. Farrokh, M., Azar, A., Jandaghi, G., and Ahmadi, E. "A novel robust fuzzy stochastic programming for closed loop supply chain network design under hybrid uncertainty", Fuzzy Sets and Systems, 341, pp. 69-91 (2017).
15. Haddadsisakht, A. and Ryan, S.M. "Closed-loop supply chain network design with multiple transportation modes under stochastic demand and uncertain carbon tax", International Journal of Production Economics, 195, pp. 118-131 (2018).
16. Govindan, K., Soleimani, H., and Kannan, D. "Reverse logistics and closed-loop supply chain: A comprehensive review to explore the future", European Journal of Operational Research, 240(3), pp. 603-626 (2015).
17. Toffel, M.W. "Strategic management of product recovery", California Management Review, 46(2), pp. 120- 141 (2004).
18. European Parliament and council "Directive 2008/98/EC of the European parliament and of the council of 19 November 2008 on waste and repealing certain directives", (2008). ELI: http://data,europa.eu/eli/2008/98/oj.
19. Echefu, N. and Akpofure, E. "Environmental impact assessment in Nigeria: Regulatory background and procedural framework", UNEP EIA Training Resource Manual (2002).
20. Bracken, J. and McGill, J.T. "Mathematical programs with optimization problems in the constraints", Operations Research, 21(1), pp. 37-44 (1973).
21. Amouzegar, M.A. and Jacobsen, S.E. "A decision support system for regional hazardous waste management alternatives", Advances in Decision Sciences, 2(1), pp. 23-50 (1998).
22. Kulshreshtha, P. and Sarangi, S. ""No return, no refund": an analysis of deposit-refund systems", Journal of Economic Behavior & Organization, 46(4), pp. 379- 394 (2001).
23. Kara, B.Y. and Verter, V. "Designing a road network for hazardous materials transportation", Transportation Science, 38(2), pp. 188-196 (2004).
24. Sheu, J.-B., Chou, Y.-H., and Hu, C.-C. "An integrated logistics operational model for green-supply chain management", Transportation Research Part E: Logistics and Transportation Review, 41(4), pp. 287- 313 (2005).
25. Wojanowski, R., Verter, V., and Boyaci, T. "Retailcollection network design under deposit-refund", Computers & Operations Research, 34(2), pp. 324-345 (2007).
26. Erkut, E. and Gzara, F. "Solving the hazmat transport network design problem", Computers & Operations Research, 35(7), pp. 2234-2247 (2008).
27. de Figueiredo, J.N. and Mayerle, S.F. "Designing minimum-cost recycling collection networks with required throughput", Transportation Research Part E: Logistics and Transportation Review, 44(5), pp. 731- 752 (2008).
28. Mitra, S. and Webster, S. "Competition in remanufacturing and the effects of government subsidies", International Journal of Production Economics, 111(2), pp. 287-298 (2008).
29. Plambeck, E. and Wang, Q. "Effects of e-waste regulation on new product introduction", Management Science, 55(3), pp. 333-347 (2009).
30. Aksen, D., Aras, N., and Karaarslan, A.G. "Design and analysis of government subsidized collection systems for incentive-dependent returns", International Journal of Production Economics, 119(2), pp. 308-327 (2009).
31. Sheu, J.-B. and Chen, Y.J. "Impact of government financial intervention on competition among green supply chains", International Journal of Production Economics, 138(1), pp. 201-213 (2012).
32. Wang, W., Zhang, Y., Zhang, K., Bai, T., and Shang, J. "Reward-penalty mechanism for closed-loop supply chains under responsibility-sharing and different power structures", International Journal of Production Economics, 170, pp. 178-190 (2015).
33. Rezapour, S., Farahani, R.Z., Fahimnia, B., Govindan, K., and Mansouri, Y. "Competitive closed-loop supply chain network design with price-dependent demands", Journal of Cleaner Production, 93, pp. 251-272 (2015).
34. Moore, J.T. and Bard, J.F. "The mixed integer linear bilevel programming problem", Operations Research, 38(5), pp. 911-921 (1990).