Asymmetric Pricing and Replenishment Controls for Substitutable Products

We study settings in which a firm offering substitutable products may face restrictions in its ability to either replenish or adjust the prices of some of its products, resulting in asymmetries in the pricing and replenishment controls available for each product. Specifically, we first consider a firm selling two substitutable products, a seasonal and a regular product, which differ in how their inventories are managed over a finite selling horizon. The seasonal product has an initial inventory with no further replenishment opportunities and is dynamically priced throughout the selling horizon, whereas the regular product has a static price but can be replenished periodically subject to a limited capacity. We characterize the firm's optimal replenishment decision for the regular product as well as the dynamic pricing and initial quantity selection decisions for the seasonal product. Through the insights gained by the optimal policy structure, we also develop a simple‐to‐implement and effective heuristic policy. In addition, we investigate profit implications of markdown policies and study how potential differences in quality perceptions between the products impact the optimal policy. Lastly, we consider further types of asymmetries resulting in pricing with partial replenishment or replenishment with partial pricing and provide insights on the value of additional pricing and replenishment flexibilities. Our study helps broaden our understanding of joint pricing and replenishment decisions for substitutable products under circumstances where these decisions may not all be available for all products.