A Dynamic Pricing Model for Coordinated Sales and Operations

Abstract

Recent years have seen advances in research and management practice in the area of pricing, and particularly in dynamic pricing and revenue management. At the same time, researchers and managers have made dramatic improvements in operations and supply chain management. The interactions between pricing and operations/supply chain performance, however, are not as well understood. In this paper, we examine this linkage by developing a deterministic, finite-horizon dynamic programming model that captures a price/demand effect as well as a stockpiling/consumption effect – price and market stockpile influence demand, demand influences consumption, and consumption influences the market stockpile. The decision variable is the unit sales price in each period. Through the market stockpile, pricing decisions in a given period explicitly depend on decisions in prior periods. Traditional operations models typically assume exogenous demand, thereby ignoring some of the market dynamics. Herein, we model endogenous demand, and we develop analytical insights into the nature of optimal prices and promotions. We develop conditions under which the optimal prices converge to a constant. In other words, price promotion is suboptimal. We also analytically and numerically illustrate cases where the optimal prices vary over time. In particular, we show that price dynamics may be driven by both (a) revenue effects, due to nonlinear market responses to prices and/or inventory, and (b) cost effects, due to economies of scale in operations. The paper concludes with a discussion of directions for future research.

Keywords: Dynamic pricing, Marketing-operations interface, Revenue management