Separable approximations for joint capacity control and overbooking decisions in network revenue management

We develop a network revenue management model to jointly make capacity control and overbooking decisions. Our approach is based on the observation that if the penalty cost of denying boarding to the reservations at the departure time were given by a separable function, then the dynamic programming formulation of the network revenue management problem would decompose by the itineraries and it could be solved by focusing on one itinerary at a time. Motivated by this observation, we use an iterative and simulation-based method to build separable approximations to the penalty cost that we incur at the departure time. Computational experiments compare our model with two benchmark strategies that are based on a deterministic linear programming formulation. The profits obtained by our model improve over those obtained by the benchmark strategies by about 3 per cent on the average, which is a significant figure in the network revenue management setting. For the test problems with tight leg capacities, the profit improvements can be as high as 13 per cent.