Stochastic Optimization for Revenue Management

本项目将侧重于解决收入管理领域某些问题的方法。特别是，它将集中于开发技术，以确定如何动态管理从公共资源池中组成的多种类型产品的可用性，以向多类客户销售。所提出的方法集成了两个不同领域的技术：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，使用基于蒙特卡罗的技术来获得初始静态解，然后使用精确的、但计算密集型的马尔可夫决策过程方法来动态改进解。近年来，易腐物品的库存控制问题引起了人们的极大关注。在许多情况下，产品必须在制造产品的资源“消亡”之前出售。典型的例子是航空公司、酒店和租车行业；然而，类似的想法也适用于其他环境。解决这些问题的研究领域称为收入管理。该项目旨在分析收入管理的一个重要方面--即发展数学方法，以确定在每个给定时间点向不同类别客户出售的各种物品的数量。这对行业和消费者都很重要，因为这些方法有助于确保适当的供需匹配。即使有强大的计算机，这样的问题也可能很难解决，因为涉及的变量非常多。为了克服这一障碍，该项目将开发将来自不同数学领域的技术混合在一起的方法，以有效地解决各种收入管理问题。由于量化方法是收入管理工作的基石，这将从实践和理论的角度支持该领域的持续发展。本项目的主要好处如下：(1)这项研究将对收入管理领域做出贡献，无论是对学术界还是实践者都是如此。(2)这项技术的成功实施将有助于建立这样一种方法，将其作为解决类似问题的可行替代工具。(3)学生将被介绍到新的应用领域，并将学习新的数学技术，这些技术将拓宽他们的知识，并提高他们对运筹学作为提高实际系统性能的关键成分的认识。

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.