Robust contract design and coordination under consignment contracts with revenue sharing

We study a classical supply chain consisting of a supplier and a retailer in which the former can sell the product through the latter under a consignment contract with revenue sharing. In this case, the supplier faces both uncertain yield (supply) and demand. In practice, it is difficult to precisely elicit the joint probability distribution of random demand and yield. Therefore, we investigate how to match demand with supply for supply chain when only partial distribution parameters, such as the first-two moments, are known. We use a distributionally robust approach to solve this challenge within the framework of a stylized two-stage Stackelberg game model. Under centralized and decentralized settings, a simple closed-form expression of the optimal robust production quantity that can properly match supply and demand can be completely characterized. Then, by comparing the performance of the two settings, we show that a supply chain double-marginalization issue exists. As such, we propose a subsidy mechanism based on a revenue-sharing contract to improve supply chain performance, and also prove the existence of a Pareto-improvement set, which can plausibly overcome the low efficiency of the supply chain. Our numerical studies further observe the impact of demand and yield uncertainty on the double-marginalization effect, the Pareto-improvement set, and both contract parties' expected profit loss. We also extend our model to consider the case of endogenizing pricing and asymmetric demand information.