Risk Minimizing Price-Rebate-Return Contracts in Supply Chains With Ordering and Pricing Decisions: A Multimethodological Analysis

In recent years, we have witnessed the wide implementation of many sophisticated supply contracts in the industry, such as the price, rebate, and return (P2R) contract. The P2R contract is offered by the manufacturer to the retailer. In this paper, a practice-based approach is adopted in which we first report the use of P2R contracts in the real world from industrial interviews. Based on the meanings of risk as revealed from the interviews, we proceed to construct analytical models and derive the minimum risk coordinating P2R (PMR*) contract, which yields the minimum level of risk for the manufacturer and coordinates the supply chain. We analytically show that the manufacturer's expected profit is increasing with the return price and the rebate value under the PMR* contract. We reveal that different risk measurements may lead to different PMR* contracts. In particular, when the price-dependent demand distribution takes the additive form, we interestingly find that the manufacturer can become riskfree in coordinating the supply chain with the PMR* contract; however, it is not the case for the multiplicative case. Furthermore, we observe that the demand distribution's shape affects the setting of the PMR* contract. Managerial implications are also discussed.