Pareto quantity flexibility contracts for a supply chain under multiple objectives

We analyse a decentralized supply chain consisting of a supplier and a retailer. The terms of trade between the two agents are specified by a quantity flexibility (QF) contract. We first identify the Pareto QF contracts for the supply chain where each agent adopts a satisficing objective, that is, to maximize the probability of achieving his/her predetermined target profit. It is shown that to coordinate such a supply chain, QF contracts have to degenerate into wholesale price (WP) contracts. This provides an additional justification for the popularity of WP contracts besides their simplicities and lower administration costs. Next, we consider the supply chain where each agent adopts multiple objectives, namely the satisficing objective and the objective of expected profit maximization (EPM). It is shown that there always exist QF contracts that coordinate the supply chain under the objective of EPM and are simultaneously Pareto optimal for the satisficing objective.