Asymptotically Optimal Dynamic Pricing for Network Revenue Management

A dynamic pricing problem that arises in a revenue management context is considered, involving several resources and several demand classes, each of which uses a particular subset of the resources. The arrival rates of demand are determined by prices, which can be dynamically controlled. When a demand arrives, it pays the posted price for its class and consumes a quantity of each resource commensurate with its class. The time horizon is finite: at time T the demands cease, and a terminal reward (possibly negative) is received that depends on the unsold capacity of each resource. The problem is to choose a dynamic pricing policy to maximize the expected total reward. When viewed in diffusion scale, the problem gives rise to a diffusion control problem whose solution is a Brownian bridge on the time interval [0, T ]. We prove diffusion-scale asymptotic optimality of a dynamic pricing policy that mimics the behavior of the Brownian bridge. The 'target point' of the Brownian bridge is obtained as the solution of a finite dimensional optimization problem whose structure depends on the terminal reward. We show that, in an airline revenue management problem with no-shows and overbooking, under a realistic assumption on the resource usage of the classes, this finite dimensional optimization problem reduces to a set of newsvendor problems, one for each resource. AMS 2000 subject classifications: 60F17, 93E20 Keywords: Revenue management, dynamic pricing, the Gallego and Van Ryzin model, fluid optimization problem, diffusion control problem, asymptotic optimality, Brownian bridge, bridge policy Research supported in part by BSF (Grant 2008466), ISF (Grant 1349/08) and the Technion's fund for promotion of research