Pareto-optimal contracts for a supply chain with satisficing objectives

We analyse a decentralized supply chain consisting of a supplier and a retailer, each with a satisficing objective, that is, to maximize the probability of achieving a predetermined target profit. The supply chain is examined under two types of commonly used contracts: linear tariff contracts (including wholesale price contracts as special cases) and buy-back contracts. First, we identify the Pareto-optimal contract(s) for each contractual form. In particular, it is shown that there is a unique wholesale price that is Pareto optimal for both contractual types. Second, we evaluate the performance of the Pareto-optimal contracts. In contrast to the well-known results for a supply chain with the traditional expected profit objectives, we show that wholesale price contracts can coordinate the supply chain whereas buy-back contracts cannot. This provides an additional justification for the popularity of wholesale price contracts besides their simplicities and lower administration costs.