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Asymptotically optimal dynamic pricing for network revenue management

Author(s): Rami Atar | Martin I. Reiman

Journal: Stochastic Systems
ISSN 1946-5238

Volume: 2;
Issue: 2;
Start page: 232;
Date: 2012;
Original page

Keywords: Revenue management | dynamic pricing | the Gallego and Van Ryzin model | fluid optimization problem | diffusion control problem | asymptotic optimality | Brownian bridge | bridge policy

A dynamic pricing problem that arises in are venue 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 Tthe 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 ofa 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.
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