Multiperiod airline overbooking with a single fare class

Consider a multiperiod airline overbooking problem that relates to a single-leg flight and a single service class. Passengers may cancel their reservations at any time, including being no-shows at flight-time. At that time, the airline bumps passengers in excess of flight capacity and pays a penalty for so doing. We give conditions on the fares, refunds, and distributions of passenger demand for reservations and cancellations in each period, and on the bumping penalty function, that ensure that a booking-limit policy is optimal, i.e., in each period the airline accepts reservation requests up to a booking limit if the number of initial reservations is less than that booking limit, and declines reservation requests otherwise. The optimal booking limits are easily computed. We give conditions under which the optimal booking limits are monotone in the time to flight departure. The model is applied to the discount allocation problem in which lower fare classes book prior to higher fare classes.