Pricing

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

Hong Chen∗ Sauder School of Business, University of British Columbia, Canada Owen Q. Wu† Sauder School of Business, University of British Columbia, Canada David D. Yao‡ IEOR Dept., Columbia University, New York, USA Current version: May 2006

Abstract 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. Keywords: Joint pricing-replenishment decision, price sensitive demand, Brownian model.

Part of this work was done while the author was affiliated with Cheung Kong Graduate School of Business, China. Supported in part by University Graduate Fellowship from the University of British Columbia. ‡ Supported in part by NSF grant DMI-0085124. Part of this author’s research was undertaken while at the Dept of Systems Engineering and Engineering Management, Chinese University of Hong Kong, and supported by HK/RGC Grant CUHK4173/03E.

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Introduction

In recent years, substantially more research has been done on joint inventory and pricing strategies. The focus has been on establishing the optimality of structural inventory and pricing policies. One of the key determinants of the complexity and generality of these models is the assumption about the demand processes. Various demand models have been proposed...