Coordinating Inventory and Pricing Decisions Under Total Minimum Commitment Contracts

A total minimum commitment contract is a supply contract under which a firm commits to buying a minimum quantity of a product from its supplier during the contract duration (e.g., one year). Such contracts are widely used in industries, because they provide the buyer with flexibility in terms of the timing and size of each individual order and the supplier with a guaranteed total order volume. Previous studies on such contracts are primarily concerned with the firm's inventory decisions, but none of them has considered the coordination of inventory and pricing decisions. In this paper, we fill this gap by studying dynamic inventory and pricing problems under a commitment contract. Under a general demand model with backlogging and zero lead time, we prove that the optimal policy is a committed-inventory-position-dependent base-stock list-price policy and characterize its structural properties. We also conduct an extensive numerical study to derive further managerial insights. In particular, we find that dynamic pricing can substantially improve the firm's profitability and enables it to select contracts with large committed quantities and price discount rates, and ignoring the commitment in joint pricing and ordering decisions can result in substantial profit loss. Finally, we partly extend our results to a lost-sales model and a backlogging model with positive lead times