Overbooking is perhaps the oldest revenue management (RM) practice that is still of great importance and widely used in the airline and other hospitality industries today; however, overbooking practiced at most airlines is merely a part of the capacity management process that is fairly static in nature and takes place whenever re-optimization of a flight takes place.
Most static methods are essentially keeping overbooking separate from seat control. More specifically, airlines must first calculate overbooking levels using expected bookings, cancellations, and no-shows, which are then used to establish the number of seats an airline would allow itself to sell (the so-called virtual capacity). After that, some optimization algorithm such as dynamic programming (DP) is used to calculate bid prices (or one of the EMSR heuristics is used to calculate nested booking limits) on this augmented number of seats known as virtual capacity ([4]).
Some dynamic methods allow integration of overbooking into optimization, for example, by including cancellations, no-shows and overbooking in a singleleg DP model as Subramanian et al. ([5]) have done. This discrete-time based model is so comprehensive that there has been renewed research interest recently from both inside ([1, 2]) and outside ([6]) of PROS. With such an integrated DP model, at least in theory, the overbooking problem essentially disappears since the overbooking level is dynamically captured in the bid prices when cancellations, no-shows, and overbooking costs are included in the model.