Stochastic Optimization for Revenue Management

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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.