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

Document Type: Article


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

2 Department of Industrial Engineering, Faculty of Engineering and Technology, Shahed University, Tehran, P.O. Box 319118651, 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.


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