A Bi-Level Programming Model for Closed-Loop Supply Chain Network Design with Competition between two chains in Uncertain Environment: A Benders Decomposition Solution

Abstract

In this paper the closed-loop supply chain network design problem is modeled and solved in a competitive and uncertain environment. The competition between two supply chains is on the price of products in forward channel and the price of returns (incentives) on the reverse channel. Demand is price sensitive and the amount of returned products is also linearly dependent on the incentives. Fuzzy set theory is used to cope with uncertainty. The proposed bi-level model is proved to be concave then we turn it to a single level model which is also proved to be a concave one. Afterwards, the single level model is solved using the Benders Decomposition approach. Finally, computational results are presented based on data inspired from real case. Results show that the proposed algorithm is converged in reasonable iterations. Increasing the price elasticity coefficient (intensifying competition) leads to less profit and Increasing the rival’s price elasticity coefficient leads to more profits for the existing chain.

Keywords

• supply chain
• competition
• bi-level model
• closed-loop supply chain
• benders decomposition