A game theoretic approach for two echelon supply chains with continuous depletion

Abstract

In a recent paper by Esmaeili et al. (2009) [5] a seller-buyer supply chain management problem was considered from both non-cooperative and cooperative game perspectives. The buyer and seller models were based on a discrete depletion inventory strategy. In this paper, we modify these models based on a continuous depletion for the seller and continuous purchasing for the buyer. The continuous depletion strategy is not only more common in large industries such as the heavy equipment industry, but can lead to considerable savings for both the buyer and seller in the supply chain. Furthermore, previous approaches for solving the cooperative game do not result in valid solutions. In this paper an improved approach is proposed, which not only obtains valid Pareto efficient solutions but also ensures cooperative stability. Finally, proof of pseudo concavity for the buyer’s objective in all possible cases is elaborated.