In many application areas such as airlines and hotels a large number of bookings are typically cancelled. Explicitly taking into account cancellations creates an opportunity for increasing revenue. Motivated by this we propose a revenue management model based on Talluri and van Ryzin (2004) that takes cancellations into account in addition to customer choice behaviour. Moreover, we consider overbooking limits as these are influenced by cancellations. We model the problem as a Markov decision process and propose three dynamic programming formulations to solve the problem, each appropriate in a different setting. We show that in certain settings the problem can be solved exactly using a tractable solution method. For other settings we propose tractable heuristics, since the problem faces the curse of dimensionality. Numerical results show that the heuristics perform almost as good as the exact solution. However, the model without cancellations can lead to a revenue loss of up to 20 percent. Lastly we provide a parameter estimation method based on Newman et al. (2014). This estimation method is fast and provides good parameter estimates. The combination of the model, the tractable and well-performing solution methods, and the parameter estimation method ensures that the model can efficiently be applied in practice. 
Revenue management under customer choice behaviour with cancellations and overbooking