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Re-Solving Stochastic Programming Models for Airline Revenue Management

Lijian Chen (chen.855***at***osu.edu)
Tito Homem-de-Mello (tito***at***northwestern.edu)

Abstract: We study some mathematical programming formulations for the origin-destination model in airline revenue management. In particular, we focus on the traditional probabilistic model proposed in the literature. The approach we study consists of solving a sequence of two-stage stochastic programs with simple recourse, which can be viewed as an approximation to a multi- stage stochastic programming formulation to the seat allocation problem. Our theoretical results show that the proposed approximation is robust, in the sense that solving more successive two-stage programs can never worsen the expected revenue obtained with the corresponding allocation policy. Although intuitive, such a property is known not to hold for the traditional deterministic linear programming model found in the literature. We also show that this property does not hold for some bid-price policies. In addition, we propose a heuristic method to choose the re-solving points, rather than re-solving at equally-spaced times as customary. Numerical results are presented to illustrate the effectiveness of the proposed approach.

Keywords: stochastic programming, revenue management, multi-stage models

Category 1: Applications -- OR and Management Sciences

Category 2: Stochastic Programming

Citation: Working paper 04-012, Dept. of Industrial Engineering and Management Sciences, Northwestern University

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Entry Submitted: 12/21/2004
Entry Accepted: 12/21/2004
Entry Last Modified: 11/27/2006

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