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2012 Asymptotically optimal dynamic pricing for network revenue management
Rami Atar, Martin I. Reiman
Stoch. Syst. 2(2): 232-276 (2012). DOI: 10.1214/12-SSY062

Abstract

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.

Citation

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Rami Atar. Martin I. Reiman. "Asymptotically optimal dynamic pricing for network revenue management." Stoch. Syst. 2 (2) 232 - 276, 2012. https://doi.org/10.1214/12-SSY062

Information

Published: 2012
First available in Project Euclid: 24 February 2014

zbMATH: 1293.91069
MathSciNet: MR3354768
Digital Object Identifier: 10.1214/12-SSY062

Subjects:
Primary: 60F17, 93E20

Rights: Copyright © 2012 INFORMS Applied Probability Society

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Vol.2 • No. 2 • 2012
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