stochastic search method, population-based algorithm, convergence with probability one,

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Airline revenue management is concerned with identifying the maximum revenue seat allocation policies. Since a major loss in revenue results from cancellations and no-shows, overbooking has received a significant attention in the literature over the years. In this study, we propose new static and dynamic single-leg overbooking models. In the static case we introduce two models; the first one aims to determine the overbooking limit and the second one is about finding the overbooking limit and the booking limits to allocate the virtual capacity among multiple fare classes. Since the second static model is hard to solve, we also introduce computationally tractable models that give upper and lower bounds on its optimal expected net revenue. In the dynamic case, we propose a dynamic programming model, which is based on two streams of events. The first stream corresponds to the arrival of booking requests and the second one corresponds to the cancellations. We conduct simulation experiments to illustrate the effectiveness of the proposed models.Keywords: Revenue management; airline; overbooking; cancellation; static model; dynamic model; dynamic programming; simulation 1. Introduction. Historically, airline industry plays the steering role in revenue management. This can be attributed to the quick responses of the airline executives, who have realized the importance of controlling the reservation process in order to increase their gains over a fiscal year. The main problem, then and now, in airline revenue management is to determine how to reserve the seats for the requests coming from the passengers. Naturally, the objective of this problem is to maximize the total revenue. We refer to (Talluri and van Ryzin, 2005, Section 1.2) for a historical account of the role of airline industry in revenue management.

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