Single-dimensional leg-level dynamic programming with booking-time dependent cancellation probabilities for revenue management

In this paper, an optimisation method is introduced that accounts for cancellations. We do so by estimating the opportunity cost of a booking between the time of booking and the expected time of cancellation. The formulation involves an estimate of the value of the state of the system at the time of cancellation (which is in the future), found through novel heuristics we introduce. The fare that is used to determine whether a product is available for sale, is adjusted by the risk the airline faces. We introduce an example which shows that there may be cases where it is optimal to reject a higher-priced product if the risk of cancellation is high, while accepting a lower-priced product. Simulations show increases in revenues against a traditional formulations that does not explicitly models cancellations. We show our method is robust against choice of heuristic, misjudgement of cancellation probability and forecasting errors.