The Underlying Markov Decision Process in the Single-Leg Airline Yield-Management Problem

Conrad J. Lautenbacher and Shaler Stidham
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Conrad J. Lautenbacher: NationsBank, NC1-001-04-16, 101 North Tryon Street, Charlotte, North Carolina 28255
Shaler Stidham: Department of Operations Research, CB 3180, Smith Building, University of North Carolina, Chapel Hill, North Carolina 27599-3180

Transportation Science, 1999, vol. 33, issue 2, 136-146

Abstract: We introduce the terms dynamic and static, respectively, to identify the prevailing approaches to the single-leg airline yield-management problem: those allowing customers of different fare classes to book concomitantly (dynamic), and those assuming that the demands for the different fare classes arrive separately in a predetermined order (static). We present a coherent frame-work linking these seemingly disparate models through the underlying dynamic program common to both. We develop a discrete-time Markov decision process formulation mirroring that of Janakiram et al. Transp. Sci. 33 , 147–167 (1999) to solve the single-leg problem without cancellations, overbooking, or discounting. Borrowing a result from the queueing-control literature, we prove the concavity of the associated optimal value functions and, subsequently, the optimality of a booking limit policy. We then apply this same technique to the more influential papers from the single-leg literature, at once unifying the static and dynamic models and establishing the connection between the yield-management and queueing-control problems. Finally, we propose an omnibus formulation that yields the static and dynamic models as special cases.

Date: 1999
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