Airline Network Revenue Management with Buy-up

The emergence of budget airlines, the advent of new sales channels, the disappearance of traditional fare-class fences, and other on-going changes in the airline industry pose serious challenges to traditional revenue management models, which make some rigid and unrealistic assumptions. One of these is that passengers who do not get the fare they want book and travel on other airlines or do not travel at all. In reality many are not necessarily lost to the airline but buy up, i.e., buy a more expensive ticket. In this paper, we model network revenue management which incorporates buy-up using dynamic programming (DP). The resulting DP model is unlikely to be solved optimally due to the curse of dimensionality and hence is solved approximately by various simpler models such as deterministic linear programming (DLP), probabilistic nonlinear programming (PNLP), randomized linear programming (RLP), and approximate dynamic programming. Policies based on partitioned booking limits and bid prices in conjunction with some of the above approximate models are proposed to control capacity. We show that the partitioned booking limit policies for several models are asymptotically optimal. The bid-price policy is also shown to be asymptotically optimal provided that correct bid prices are used. We establish some analytical results to estimate expected network revenue gradients based on the RLP. Numerical results show that a significant increase in revenue is obtainable for all five booking schemes on four test examples even when the buy-up probability is relatively small.