The underlying Markov decision process in the single-leg airline yield-management problem
The underlying Markov decision process in the single-leg airline yield-management problem
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DOI：
10.1287/trsc.33.2.136
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发表时间：
1999-05-01
影响因子：
4.6
通讯作者：
Stidham, S Jr
中科院分区：
文献类型：
--
作者：
Lautenbacher, CJ;Stidham, S Jr
我们引入术语动态和静态，分别确定单航段航空公司收益管理问题的流行方法：那些允许不同票价等级的客户同时预订（动态），以及那些假设不同票价等级的需求以预定顺序分别到达（静态）。我们提出了一个连贯的框架，通过底层的动态程序共同连接这些看似不同的模型。我们开发了一个离散时间马尔可夫决策过程制定镜像Janakiram等人。sci. 33，147 - 167（1999），以解决单航段问题，而不取消、超额预订或打折。借用的结果，从预订控制文献，我们证明了相关的最优值函数的最优性，随后，预订限制政策的最优。然后，我们将同样的技术应用于单腿文献中更有影响力的论文，立即统一静态和动态模型，并建立产量管理和控制问题之间的联系。最后，我们提出了一个综合配方，产生的静态和动态模型的特殊情况。
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 framework 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.