Do the buyback contracts of undistributed stocks coordinate the supply chain?

Abstract

The concept of supply chain coordination implies that it is possible to obtain an optimal result for both independent chain participants and supply chain due to participants’ coordinated actions. This paper examines the question whether a buyback contract will be coordinating or not. The authors argue that a coordinating buyback contract should have the following substantive properties: practical feasibility, collective and individual rationality. The paper off ers a mathematical defi nition of a coordinating buyback contract which highlights these properties. Entering into buyback contract process is considered as a two-step game of two players (a supplier and retailer) on the assumption that the players are risk neutral and make decisions with full information available, the market price is fixed, and the product demand is a random variable. The authors demonstrate that the buyback contract does not coordinate the chain, however, there has been obtained a non-empty set of eff ective contracts depending on the buyback price. For such contracts, the defi nition of “conditional coordination” is given to introduce the property of a supplier’s partial rationality; its existence was proved. The findings reveal that the choice of buyback price affects the allocation of profits between chain participants so the decision on its choice must be cooperative. To substantiate the nature of cooperative choice of conditionally coordinating contracts, the asymmetric Nash solution is considered. All results were obtained both in general terms and under the assumption that the product demand has uniform distribution. For the latter case, the conditionally coordinating contract parameters were found and it was justified that the conclusion of such a contract is possible only when a supplier has greater bargain power than a retailer.