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Risk in Revenue Management and Dynamic Pricing

School of Business, Queen's University, Kingston, Ontario, Canada K7L 3N6
School of Business, Queen's University, Kingston, Ontario, Canada K7L 3N6
School of Business, Queen's University, Kingston, Ontario, Canada K7L 3N6
ylevin{at}business.queensu.ca
jmcgill{at}business.queensu.ca
mnediak{at}business.queensu.ca

We present a new model for optimal dynamic pricing of perishable services or products that incorporates a simple risk measure permitting control of the probability that total revenues fall below a minimum acceptable level. The formulation assumes that sales must occur within a finite time period, that there is a finite—possibly large—set of available prices, and that demand follows a price-dependent, nonhomogeneous Poisson process. This model is particularly appropriate for applications in which attainment of a revenue target is an important consideration for managers; for example, in event management, in seasonal clearance of high-value items, or for business subunits operating under performance targets. We formulate the model as a continuous-time optimal control problem, obtain optimality conditions, explore structural properties of the solution, and report numerical results on problems of realistic size.

Subject classifications: inventory/production; perishable/aging items; marketing/pricing; uncertainty; dynamic programming/optimal control; applications; probability; stochastic model applications.
History: Received December 2005; revision received February 2007; accepted March 2007.