A two-level pricing-inventory-routing problem in green Closed-loop supply chain: Bi-level programming and heuristic method

Document Type : Research Paper


1 Department of computer and industrial engineering, Birjand University of Technology,Birjand, Southern Khorasan, Iran

2 Department of Industrial Engineering, University of Kurdistan, Sanandaj, Iran

3 Department of Computer Science, Birjand University of Technology, Birjand, Southern Khorasan, Iran


In this paper, a bi-level mathematical formulation for a pricing-inventory-routing problem in the context of sustainable closed-loop supply chains is developed. The two levels are entitled as the upper level model and the lower level model. The upper level model (the leader model) tries to minimize greenhouse gas (GHG) emissions while the lower level model (the follower model) focuses on profit maximization. To solve the problem, an enumeration heuristic method based on knapsack problem and genetic algorithm (GA) is devised. The results show that the heuristic method is capable of obtaining high-quality solutions in reasonable CPU-times.


Main Subjects

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