Optimal Pricing and Replenishment in a Single-Product Inventory System

We study an inventory system that supplies price-sensitive demand modeled by Brownian motion, focusing on the optimal pricing and inventory replenishment decisions, under both long-run average and discounted objectives. Analytical solutions are obtained in all cases, and related to or contrasted against previously known results. In addition, we bring out the interplay between the pricing and the replenishment decisions, and the way they react to demand uncertainty. We show that the joint optimization of both decisions may result in significant profit improvement over the traditional way of making the decisions separately or sequentially. We also show that multiple price changes will only result in a limited profit improvement over a single price.