An LP based approximate dynamic programming model to address airline overbooking under cancellation, refund and no show

In this paper we simultaneously address four constraints relevant to airline revenue management problem: Flight cancellation, customer no-shows, overbooking and refunding. We develop a linear program closely related to the dynamic program formulation of the problem which we later use to approximate the optimal decision rule for rejecting or accepting customers. We give a novel proof that the optimal objective function of this linear program is always an upper bound for the dynamic program.