Dynamic Programming Decomposition Methods For Capacity Allocation And Network Revenue Management Problems
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Dynamic Programming Decomposition Methods for Capacity Allocation and Network Revenue Management Problems
In this thesis, we develop decomposition-based approximate dynamic programming methods for problems in capacity allocation and network revenue management. Noting that the dynamic programming formulation of these problems suffers from the "curse of dimensionality", we demonstrate that a set of single-dimensional dynamic problems can be employed to provide approximate solutions to the original dynamic program. We show that the proposed approximations have two important characteristics: First, they provide relatively tight performance bounds on the optimal value of the stochastic optimization problem under consideration. Second, they give rise to policies that on average perform significantly better than a variety of benchmark methods found in the literature. We begin by focusing on network revenue management problems. We assume a profit maximizing airline operating a network of flight legs and processing itinerary requests arriving randomly over time. We consider several variants of the basic model and for each show that the dynamic programming formulation can be decomposed by flight legs into a set of single-leg revenue management problems. Furthermore, we demonstrate that the appropriate decomposition method gives rise to an upper bound on the optimal total expected revenue and that this upper bound is tighter than the upper bound provided by a deterministic linear program known from the literature. Finally, computational experiments show that the pol- icy based on the suggested value function approximation performs significantly better than a set of standard benchmark methods. In addition to network revenue management applications, we also consider a capacity allocation problem with a fixed amount of daily processing capacity. Here, the decision maker tries to minimize the cost of scheduling a set of jobs arriving randomly over time to be processed within a given planning horizon. The scheduling (holding) cost of a given job depends on its priority level and the length of its scheduled waiting period. In this setting, the decomposition approach that we suggest decomposes the problem by booking days. In particular, we replace the original dynamic program with a sequence of single-dimensional dynamic programs, each of which is concerned with capacity limitations on one particular booking day only. We show that our approach provides tight lower bounds on the minimum total expected holding cost. Furthermore, it gives rise to a scheduling policy that on average performs better than a variety of benchmark methods known from the literature.
Revenue Management and Pricing Analytics
“There is no strategic investment that has a higher return than investing in good pricing, and the text by Gallego and Topaloghu provides the best technical treatment of pricing strategy and tactics available.” Preston McAfee, the J. Stanley Johnson Professor, California Institute of Technology and Chief Economist and Corp VP, Microsoft. “The book by Gallego and Topaloglu provides a fresh, up-to-date and in depth treatment of revenue management and pricing. It fills an important gap as it covers not only traditional revenue management topics also new and important topics such as revenue management under customer choice as well as pricing under competition and online learning. The book can be used for different audiences that range from advanced undergraduate students to masters and PhD students. It provides an in-depth treatment covering recent state of the art topics in an interesting and innovative way. I highly recommend it." Professor Georgia Perakis, the William F. Pounds Professor of Operations Research and Operations Management at the Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts. “This book is an important and timely addition to the pricing analytics literature by two authors who have made major contributions to the field. It covers traditional revenue management as well as assortment optimization and dynamic pricing. The comprehensive treatment of choice models in each application is particularly welcome. It is mathematically rigorous but accessible to students at the advanced undergraduate or graduate levels with a rich set of exercises at the end of each chapter. This book is highly recommended for Masters or PhD level courses on the topic and is a necessity for researchers with an interest in the field.” Robert L. Phillips, Director of Pricing Research at Amazon “At last, a serious and comprehensive treatment of modern revenue management and assortment optimization integrated with choice modeling. In this book, Gallego and Topaloglu provide the underlying model derivations together with a wide range of applications and examples; all of these facets will better equip students for handling real-world problems. For mathematically inclined researchers and practitioners, it will doubtless prove to be thought-provoking and an invaluable reference.” Richard Ratliff, Research Scientist at Sabre “This book, written by two of the leading researchers in the area, brings together in one place most of the recent research on revenue management and pricing analytics. New industries (ride sharing, cloud computing, restaurants) and new developments in the airline and hotel industries make this book very timely and relevant, and will serve as a critical reference for researchers.” Professor Kalyan Talluri, the Munjal Chair in Global Business and Operations, Imperial College, London, UK.
Applications in Statistical Computing
This volume presents a selection of research papers on various topics at the interface of statistics and computer science. Emphasis is put on the practical applications of statistical methods in various disciplines, using machine learning and other computational methods. The book covers fields of research including the design of experiments, computational statistics, music data analysis, statistical process control, biometrics, industrial engineering, and econometrics. Gathering innovative, high-quality and scientifically relevant contributions, the volume was published in honor of Claus Weihs, Professor of Computational Statistics at TU Dortmund University, on the occasion of his 66th birthday.