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.
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Supported by the National Science Foundation under grant DMI-0115385.
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Chen, L., Homem-de-Mello, T. Re-solving stochastic programming models for airline revenue management. Ann Oper Res 177, 91–114 (2010). https://doi.org/10.1007/s10479-009-0603-7
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DOI: https://doi.org/10.1007/s10479-009-0603-7