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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. | Yugoslav Journal of Operations Research xx (2017), Number nn, zzz–zzz DOI: https://doi.org/10.2298/YJOR170918026S AN LP BASED APPROXIMATE DYNAMIC PROGRAMMING MODEL TO ADDRESS AIRLINE OVERBOOKING UNDER CANCELLATION, REFUND AND NO-SHOW Reza SOLEYMANIFAR Department of Industrial Engineering, University of Illinois at Urbana-Champaign Reza@Soleymanifar.com Received: September 2017 / Accepted: August 2018 Abstract: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. First we give a novel proof that the optimal objective function of this linear program is always an upper bound for the dynamic program. Secondly, we construct a decision rule based on this linear program and prove that it is asymptotically optimal under certain circumstances. Finally, using Monte Carlo simulation we demonstrate that, numerically, the result of the linear programming policy presented in this paper has a short distance to the upper bound of the optimal answer which makes it a fairly good approximate answer to the intractable dynamic program. Keywords: Revenue Management, Approximate Dynamic Programming, Overbooking, Cancellation, No-show, Refund. MSC: 90B85, 90C26. 1. INTRODUCTION The nature of the airline networks is more compatible with quantity control methods and therefore the frequency of papers published in this area is by far higher than that of pricing methods. Our Linear Program Policy , in comparReferred to as LPP from here on 2 Reza Soleymanifar / An LP based Approximate Dynamic Programming ison to dynamic programming is practically more important and faster due to its linear computational complexity. Dynamic programming formulations for real life problems suffer from .
