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Overbooking is the practice of intentionally selling more rooms than are available in order to offset the effect of cancellations and no-shows. Studies estimate that although a hotel is fully booked, about 5-8% of the rooms are vacant on any given date. Poor overbooking decisions can prove to be very expensive for the hotel. In the short run, it is only a loss of room revenue, but over the long-term, casualties may include decreased customer loyalty, loss of hotel reputation, etc. American Airlines developed an optimization model that maximizes net revenues associated with overbooking decisions for the airline industry.
To illustrate the overbooking model developed by the American Airlines, let us consider a B757 jet flying from Chicago to Boston. The aircraft has about 180 seats. Based on the past travel pattern, it is observed that an average of 5% (or nine passengers) do not turn up at the time of boarding the flight. If the airlines book all seats for this leg, it is likely to fly with only 171 occupied seats. However it does not mean that it never flies with 172 or more (even 180) seats occupied. There is a lesser chance of the flight flying with 172 passengers, an even lesser chance of it flying with 175 and a miniscule chance of it flying with all 180 passengers. Therefore, if we book 181 passengers instead of 180, we are likely to end up with only 173 passengers (and almost always with lesser than 180 passengers). In an odd event of exactly 181 passengers reporting, the airline would need to bump one passenger. IATA has defined rules to compensate bumped passengers. If we can quantify all costs (including the cost of lost goodwill), the expected revenue would be the revenue from 181 passengers minus the expected cost of compensating the one additional passenger at that odd chance. Since the probability of exactly 181 passengers turning up is so low, the revenue from that additional passenger generally compensates more than the expected cost. For this example, the optimal number of passengers that can be booked would be 186 as illustrated in the figure below.
This model can be directly applied to the hotel industry as well. The driving force behind the model is the evaluation of the trade off between additional revenue accrued by selling an already-reserved room versus the downside from doing so. It has been found that net revenue increases with overbooking until the point where the downside from overbooking a room exceeds customer revenues. Beyond that point, the negative impact of overbooking increases rapidly because fewer and fewer customers appreciate being turned away.
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