Capacity Uncertainty in Airline Revenue Management: Models, Algorithms, and Computations

Abstract

Most airline revenue optimization models assume capacity to be fixed by fleet assignment, and thus treat it as deterministic. However, empirical data show that on 40% of flights, capacity is updated at least once within the booking horizon. Capacity updates can be caused by fleet-assignment reoptimizations or by short-term operational problems. This paper proposes a first model to integrate the resulting capacity uncertainty in the leg-based airline revenue management process. While assuming deterministic demand, the proposed model includes stochastic scenarios to represent potential capacity updates. To derive optimal inventory controls, we provide both a mixed-integer program and a combinatorial solution approach, and discuss efficient ways of optimizing the special case of a single capacity update. We also explore effects of denied boarding cost and the model’s relationship to the static overbooking problem. We numerically evaluate the model on empirically calibrated demand instances and benchmark it on the established deterministic approach and an upper bound based on perfect hindsight. In addition, we show that the combinatorial solution approach reduces the computational effort. Finally, we compare the static overbooking approach derived from the capacity uncertainty model to existing approaches based on the expected marginal seat revenue (EMSR).