Stochastic Orders in Risk-Based Overbooking

In this article, we propose a risk-based overbooking model, in which an overbooking limit is chosen such that an expected profit is maximized. We derive an optimality condition, when a show demand given a total number of reservations follows a binomial distribution. We also determine a directional change of the optimal overbooking limit with respect to various model parameters, such as a show-up probability, a per-unit revenue and a per-unit oversale cost. Finally, we show that the optimal expected profit decreases, if the show-up probability increases.