Consignment contract in a supply chain with price, demand and yield randomness: A distributionally robust approach
研究一个供应商与电商平台在价格、需求和产量均不确定时签订的寄售合同，利用仅知一阶和二阶矩的分布鲁棒优化方法，推导供应商最优产量决策和最坏情况期望利润，并分析平台的内生寄售费率合同设计问题。
We investigate a supply chain consisting of a supplier and an e-commence platform who sign a consignment contract with uncertainty in price, demand, and yield. Due to the challenges of actually determining the joint distribution of random variables, we assume that only the partial distributional information is available for these three uncertainties. To address the issue of distributional ambiguity and to more accurately account for arbitrary correlations among these uncertainties, we introduce a moment-based distributionally robust optimization (DRO) approach that assumes only the first and second moments of these three uncertainties are known. Given an exogenous consignment rate, we derive the closed-form expression for the supplier’s optimal production decision and her worst-case expected profit. We study the impact of random price and random yield within the ambiguity set on the supplier’s production decision and the worst-case expected profit. From the e-commerce platform’s perspective, we further examine the contract design problem when the consignment rate is endogenous and analyze equilibrium solutions for both contracting parties. Our results show that the additional consideration of price or yield uncertainty within the ambiguity set does not always mitigate or enhance the degree of conservatism of the contracting parties, which is closely related to the correlation between any two types of uncertainty, as well as the degree of uncertainty itself.