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An overbooking model for a fixed nonstop flight with two types of passengers is presented. The model takes cancellations, and reservations prior to departure into consideration as well as ‘no-shows’ (passengers who fail to arrive for flights without notice), denied boardings and downgrading of passengers. The model treats the airline booking process as a Markovian nonhomogeneous sequential decision process. The model is solved by two dimensional stochastic dynamic programming. Computational experiences and numerical results from a real-life case, including different types of sensivity analysis, are presented.