A note on the optimal pricing and production decisions with price-driven substitution

Abstract

Recently, Kim and Bell (2011) developed a revenue managemnent pricing model with price-driven substitution. The authors considered production decisions under unlimited production capacity and investigated the impact of price-driven substitution on a firm's pricing and production decisions. The authors modeled the consumer demands for each market segment as linear additive demand function based on exogenous variables, where demand substitution occurred as a function of price differences between the two products. In this article, we extend this work to examine the impact of a production capacity constraint on the firm's joint pricing and inventory decisions. Based on this extended model, we investigate the impact of price-driven substitution on a firm's pricing and production decisions where there is a limit on total capacity. We show how revenue managers should adjust prices and production levels to take into account price-driven substitution under a capacity constraint setting. Both deterministic and stochastic models are developed, and the impact of price-driven substitution and a capacity constraint on the optimal prices, production levels, and revenues is illustrated.