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.

中文翻译：

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具有订购和定价决策的供应链中价格-回扣-退货合同的风险最小化：多方法分析

近年来，我们见证了行业内许多复杂的供应合同的广泛实施，如价格、返利和退货（P2R）合同。P2R 合同由制造商提供给零售商。在本文中，我们采用了一种基于实践的方法，我们首先通过行业访谈报告了现实世界中 P2R 合同的使用。根据访谈揭示的风险含义，我们继续构建分析模型并推导出最小风险协调 P2R (PMR*) 合同，该合同为制造商提供最低风险水平并协调供应链。我们分析表明，制造商的预期利润随着 PMR* 合同下的退货价格和返利价值而增加。我们揭示了不同的风险度量可能会导致不同的 PMR* 合同。特别是，当依赖价格的需求分布采用可加形式时，我们有趣地发现，制造商在协调供应链与 PMR* 合同时可以变得无风险；但是，乘法情况并非如此。此外，我们观察到需求分布的形状会影响 PMR* 合约的设置。还讨论了管理影响。s 形状影响 PMR* 合约的设置。还讨论了管理影响。s 形状影响 PMR* 合约的设置。还讨论了管理影响。