Supply Chain Coordination with Multiple Shipments: The Optimal Inventory Subsidizing Contracts

We study a supply chain involving a supplier-retailer relationship. When production lead-time is long and the selling season is short, the retailer has to place an order ahead of the season, which resembles the classical Newsvendor model. However, we consider the situation when the supplier agrees to deliver the order in multiple shipments in the season, and then the retailer needs to determine the quantity and/or timing of each shipment. Under a centralized setting, we derive the optimal quantity and/or timing decisions of the retailer. Under a decentralized setting, incentive misalignment arises from ineffective allocation of inventory costs between the parties, in addition to the well-known double marginalization effect. Hence, we devise an incentive contract, which involves a risk-sharing mechanism at the end of the season and an inventory subsidizing scheme for the entire season; in practice, the inventory subsidizing scheme can be implemented in different ways, such as a direct subsidizing scheme or a delayed-payment scheme. The proposed contract can achieve channel coordination and Pareto optimality. Furthermore, we can show that the inventory subsidizing scheme plays a key role in channel coordination because without the inventory subsidizing scheme, the loss of supply chain efficiency is almost always significant.