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A Monopolistic and Oligopolistic Stochastic Flow Revenue Management Model

Department of Management Science and Information Systems, Rutgers University, The State University of New Jersey, Newark, New Jersey 07102
Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208
xiaoweix{at}andromeda.rutgers.edu
hopp{at}northwestern.edu

This paper studies a one-shot inventory replenishment problem with dynamic pricing. The customer arrival rate is assumed to follow a geometric Brownian motion. Homogeneous customers have an isoelastic demand function and do not behave strategically. We find a closed-form optimal pricing policy, which utilizes current demand information. Under this pricing policy the inventory trajectory is deterministic, and a retailer sells all inventory. We show that dynamic pricing coordinated with the inventory decision achieves significantly higher profits than does static pricing. Furthermore, under oligopolistic competition we establish a weak perfect Bayesian equilibrium for the price and inventory replenishment game. We find the pricing equilibrium to be cooperative even in a noncooperative environment, but that inventory competition results in overstock and damages profits. Finally, we examine the trade-off between dynamic pricing and price precommitment and find that flexible pricing is still beneficial, provided competition is not too intense.

Subject classifications: differential games; dynamic pricing; geometric Brownian motion; martingales; revenue management.
History: Received June 2004; revision received October 2005; accepted November 2005.

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