Optimal Pricing and Replenishment in a Single-Product Inventory System with Brownian Demand

We study an inventory system that supplies price-sensitive demand modeled by Brownian motion. The optimal pricing and inventory replenishment decisions under both long-run average and discounted objectives are derived, and related to or contrasted with previously known results. In addition, we emphasize the interplay between pricing and replenishment decisions, and the ways in which they react to the demand uncertainty. We show that the joint optimization of both decisions may result in significant profit improvement compared to the traditional method of making decisions separately or sequentially. We also show that multiple price changes result in only a limited profit improvement over the optimal single price.