Planes are overbooked to avoid empty seats. Yet, there is a trade-off of increased upgradings, downgradings, and denied boardings. The patterns of reservations, cancellations, and no-shows are random. Thus, determining the best overbooking levels involves stochastic multistage optimal decision making and time series analysis. An overbooking model for a nonstop flight with two types of passengers is based on a statistical description of the booking process and two-dimensional stochastic dynamic programming. It produces, apparently for the first time, an optimal policy for a real case. The model has been validated and used at Scandinavian Airlines. The net potential revenue increase was about two million US dollars per year.
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Alstrup et al. (1989) studied this question.