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BACKGROUND
The growth and success of the hospitality industry and its role in the global economy is enabled through the implementation of revenue management models and systems. Two types of events - cancellations and no-shows - impact the overbooking decision, with the difference being related simply to the timing of the events. A cancellation is defined as a reservation that is terminated by a customer at some point before the time of service (Phillips, 2004; Talluri and van Ryzin, 2005). With a cancellation, the business has an opportunity to replace the canceled reservation. Suppliers overbook in order to compensate for both cancellations and no-shows. In the absence of cancellations, the supplier does not need to update the booking limit or change it over time, but when cancellations are factored in, the situation becomes more complex. Specifically, the optimal booking limit for a supplier who allows bookings to cancel before departure will change over time. The supplier then needs to calculate a dynamic booking limit (Phillips, 2004; Talluri and van Ryzin, 2005). Various models for such calculation will be discussed in the following section.
Cancellations and cancellation policies
From the earliest days of commercial aviation in the United States, airlines have adopted the policy that a customer with a reservation could cancel at any time before departure without paying a penalty, and that a customer who had purchased a ticket for a flight would not be penalized if he or she failed to show up for that flight (Aydin et al , 2013). This policy raised a problem for airlines. In 1990, American Airlines estimated that 'about 15 per cent of seats on sold-out flights' would be empty if they had booked only up to capacity (Smith et al , 1992).
Since approximately 30-35 per cent of airline bookings in the 1990s were canceled before departure, the bookings management process at a passenger airline had to be able to update booking limits for cancellations. Many airlines, hotels and rental car companies have therefore instituted penalties for customers who cancel or do not show up. These penalties can range from 10 per cent or less of the price all the way to 100 per cent for a non-refundable airline ticket (Phillips, 2004; Talluri and van Ryzin, 2005)....