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3 Dynamic Overbooking www.pros.com 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. Some commonly implemented overbooking methods in practice include, but are not limited to, the following: • The "naive" approach [1, 2] sets the virtual capacity as the ratio of the physical capacity and the showup rate in an attempt to ensure that at departure the number of expected show-ups would exactly equal the physical capacity. • Revenue-based overbooking [1, 2], which seeks the optimal static overbooking level that maximizes the total expected revenue net of expected denied boarding cost. • Cost-based overbooking, which determines the optimal static overbooking level based on minimizing the sum of spillage cost (penalty due to denied boarding) and spoilage cost (revenue loss due to flying with empty seats). • Science-level-based overbooking, which determines the optimal overbooking level based on a pre-specified tolerance on number of expected denied boardings. • Net demand [3], which uses gross demand reduced by forecasted cancellations as demand input into the optimization routine so cancellations are not explicitly modeled. 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. Overview

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