Stochastic Optimization for Revenue Management

该项目将侧重于解决收入管理领域某些问题的方法。特别是，它将集中在技术的发展，以确定如何动态管理的可用性，多种类型的产品，包括从一个共同的资源池销售给多个类别的客户。所提出的方法涉及两个不同领域的技术集成：马尔可夫决策过程和基于蒙特卡洛的随机优化。 其关键思想是利用这两种工具的优势，通过使用基于蒙特卡洛的技术来获得初始静态解，然后使用精确但计算密集的马尔可夫决策过程方法来动态地优化解。 最近，大量的注意力已经投入到易腐物品的库存控制。在许多情况下，产品必须在制造产品的资源“消失”之前出售。“典型的例子是航空公司，酒店和汽车租赁行业;然而，类似的想法也适用于其他情况。解决这些问题的研究领域被称为收入管理。 该项目旨在分析收益管理的一个重要方面-即数学方法的发展，以确定在每个给定的时间点向不同类别的客户销售的各种物品的数量。这对工业界和消费者都很重要，因为这种方法有助于确保供求适当匹配。即使有强大的计算机，这样的问题也可能是棘手的，因为涉及的变量非常多。 为了克服这一障碍，该项目将开发将不同数学领域的技术融合在一起的方法，以有效地解决各种收入管理问题。 由于定量方法是收益管理的基础，因此无论从理论上还是实践上，都将为该领域的持续发展提供支持。本项目的主要益处如下：（1）本研究将为收益管理领域的学术界和实务界做出贡献。 (2)这种技术的成功实施将有助于建立这样一种方法，作为解决类似问题的可行替代工具。 (3)参与的学生将被引入新的应用领域，并将学习新的数学技术，这将拓宽他们的知识，并提高他们对运筹学的认识，作为提高真实的系统性能的关键因素。

This project will focus on methods to solve certain problems in the area of revenue management. In particular, it will center on the development of techniques to determine how to dynamically manage the availability of multiple types of products comprised from a common pool of resources for sale to multiple classes of customers. The proposed methods involve the integration of techniques from two different fields: Markov decision processes and Monte Carlo-based stochastic optimization. The key idea is to exploit the strengths of both tools by using a Monte Carlo-based technique to obtain an initial static solution, and then using the exact, but computationally-intensive, Markov-decision-process approach to dynamically refine the solution. Recently, a great deal of attention has been devoted to the control of inventories of perishable items. In a number of settings, products must be sold before the resources, from which the products are made, "perish." Typical examples are the airline, hotel, and rental car industries; however, similar ideas have application to other contexts as well. The area of study that addresses these issues is called revenue management. This project aims to analyze an important aspect of revenue management - namely, the development of mathematical approaches to determine the quantities of various items to sell to different classes of customers at each given point in time. This is significant to both industry and consumers, since such methods help ensure an appropriate match of supply and demand. Even with powerful computers, such problems can be intractable, because of the extremely large number of variables involved. To overcome this obstacle, this project will develop methods that blend together techniques from separate mathematical fields to efficiently solve various revenue management problems. Since quantitative methods form the cornerstone of revenue management efforts, this will support the continued growth of the field from both practical and theoretical standpoints.The major benefits of this project are as follows: (1) This research will contribute to the field of revenue management, both for academics as well as for practitioners. (2) The successful implementation of this technique will help establish such an approach as a viable alternative tool for similar problems. (3) The students involved will be introduced to new application areas and will learn new mathematical techniques that will broaden their knowledge, and improve their perception of operations research as a key ingredient to improve the performance of real systems.