Article ID: | iaor20104504 |
Volume: | 177 |
Issue: | 1 |
Start Page Number: | 91 |
End Page Number: | 114 |
Publication Date: | Jun 2010 |
Journal: | Annals of Operations Research |
Authors: | Homem-de-Mello Tito, Chen Lijian |
Keywords: | yield management, programming: probabilistic |
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.