Column generation algorithms for airline network revenue management problems

Abstract

At the heart of the airline revenue management problem (ARM) lies the seat allocation problem, which has the ultimate aim of finding the right combination of passengers that will result in maximum profit. Due to the dynamic nature of the problem, optimal seat allocations can change continuously over the reservation period. In addition, widely used bid-price booking control policy which necessitates the dual information is obliged to be updated as the demand and capacity values adjust over the reservation period. Thus, in order to make changes in an interactive basis, it is crucial to solve the seat allocation problem in a small amount of time. This study embodies column generation algorithms applied to ARM problems. Networkbased ARM problems are computationally hard to solve even if the airline network is small. However, in this study we challenged ourselves with large-scale airline networks. For computational efficiency, the network is divided into subnetworks by means of date and time information. The overall network is decomposed to origin destination pairs, so that each pair is treated as a single-leg problem. The resulting seat allocation models (static, dynamic and deterministic linear programming) having a non-linear objective function are linearized by means of the transformation technique proposed by Dantzig which embodies a transformation only by means of additional decision variables. Since column generation can not cope with problems extending row-wise, Dantzigs formulation is the perfect fit. After applying column generation, the numerical results for the models is demonstrated.