Coordination of Supply Chain with One Supplier and Two Competing Risk-Averse Retailers under an Option Contract

Abstract

This paper studies an option contract for coordinating a supply chain comprising one risk-neutral supplier and two risk-averse retailers engaged in promotion competition in the selling season. For a given option contract, in decentralized case, each risk-averse retailer decides the optimal order quantity and the promotion policy by maximizing the conditional value-at-risk of profit. Based on the retailers’ decision, the supplier derives the optimal production policy by maximizing expected profit. In centralized case, the optimal decision of the supply chain system is obtained. Based on the decentralized and centralized decision, we find the coordination conditions of the supply chain system, which can optimize the supply chain system profit and make the profits of the supply chain members achieve Pareto optimum. As for the subchain, we also find the coordination conditions, which generalize the results of the supply chain with one supplier and one retailer. Our analysis and numerical experiments show that there exists a unique Nash equilibrium between two retailers, and the optimal order quantity of each retailer increases (decreases) with its own (competitor’s) promotion level.