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Dynamic programming decomposition for choice-based revenue management with flexible products

机译：动态编程分解，以灵活的产品实现基于选择的收益管理

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We reconsider the stochastic dynamic program of revenue management with flexible products and customer choice behavior as proposed by Gallego et al. [Gallego G, Iyengar G. Phillips RL. Dubey A (2004) Managing flexible products on a network. Working paper. Columbia University, New York]. In the scientific literature on revenue management, as well as in practice, the prevailing strategy to operationalize dynamic programs is to decompose the network by resources and solve the resulting one-dimensional problems. However, to date, these dynamic programming decomposition approaches have not been applicable to problems with flexible products, because sold flexible products must be included in the dynamic program's state space and do not correspond directly to resources. In this paper, we contribute to the existing research by presenting a general approach to operationalizing revenue management with flexible products and customer choice in a dynamic programming environment. In particular, we reformulate the original dynamic program by means of Fourier-Motzkin elimination to obtain an equivalent dynamic program with a standard resource-based state space. This reformulation allows the application of dynamic programming decomposition approaches. Numerical experiments show that the new approach has a superior revenue performance and that its average revenues are close to the upper bound on the optimal expected revenue from the choice-based deterministic linear program (CDLP). Moreover, our reformulation improves the revenues by up to 8% compared to an extended variant of a standard choice-based approach that immediately assigns flexible products after their sale.
机译：我们根据Gallego等人的建议，重新考虑了具有灵活产品和客户选择行为的随机动态收益管理程序。 [Gallego G，Iyengar G. Phillips RL。 Dubey A（2004）在网络上管理灵活的产品。工作文件。纽约哥伦比亚大学]。在有关收入管理的科学文献中以及在实践中，用于运行动态程序的主要策略是通过资源分解网络并解决由此产生的一维问题。但是，迄今为止，这些动态编程分解方法尚未应用于柔性产品的问题，因为已售出的柔性产品必须包含在动态程序的状态空间中，并且不直接与资源相对应。在本文中，我们通过提出一种在动态编程环境中使用灵活的产品和客户选择来实施收入管理的通用方法，为现有研究做出了贡献。特别是，我们通过傅立叶-莫兹金消除法对原始动态程序进行了重新构造，以获得具有标准基于资源的状态空间的等效动态程序。这种重新制定允许动态编程分解方法的应用。数值实验表明，该新方法具有出色的收益性能，其平均收益已接近基于选择的确定性线性程序（CDLP）的最佳预期收益的上限。此外，与基于标准选择方法的扩展变体相比，我们的重新制定将收入提高了8％，该扩展方法是在销售后立即分配灵活的产品。

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