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Using the properties of the normal distribution, the objective of the probabilistic/risk overbooking model is to find the AU that will keep DB to some airline-specified target level, in the event that the flight is fully booked (BKD = AU), with a specified level of confidence. The AU for a future flight departure given CAP and estimates of NSR and STD with an airline-specified objective (for example) of keeping DB = 0 with 95% confidence is: The probabilistic model thus incorporates the uncertainty or variability in the distribution of no-show rates for the future flight departure. If recent observations of no-show rates suggest a larger STD, the denominator of the model will become larger and the optimal AU will be lower, due to increased uncertainty about no-shows. On the other hand, a lower STD will lead to a higher AU, due to lower uncertainty about future no-shows. The probabilistic/risk model for overbooking lends itself to a variety of extensions that allow the airline greater flexibility in determining its own overbooking policy. The airline might wish to reduce the required level of confidence of exceeding the DB target, in order to overbook more aggressively. The Z-factor in the models denominator will decrease, causing an increase in AU. The airline can also decide to increase its DB tolerance to account for the likelihood that it will be able to find passengers willing to become voluntary denied boardings, at little or no cost to the airline. In essence, the effective capacity of the flight increases by the number of voluntary denied boardings (VOLDB) that the airline believes it can solicit at the time of departure, should it be necessary. The models numerator becomes (CAP VOLDB), increasing AU. It is also possible for the airline to include forecasted empty first-class or business-class cabin seats as being available for upgrading passengers from economy class, should more show up than the economy-class physical capacity. Again, this action increases the effective capacity of the flight.




96 Fundamentals of Pricing and Revenue Management A major extension of the probabilistic/risk overbooking approach is the cost-based overbooking model, which not only incorporates the uncertainty of future flight no-show behavior, but explicitly accounts for the actual costs associated with denied boardings and



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