A Langrangian decomposition approach to weakly coupled dynamic optimization problems and its applications
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53010669-MIT.pdf
Description
Full printable version
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5.95 MB
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Author(s)
Hawkins, Jeffrey Thomas, 1977-
Advisor(s)
Dimitris Bertsimas.
Date Issued
2003
Publisher
Massachusetts Institute of Technology
Abstract
We present a Lagrangian based approach to decoupling weakly coupled dynamic optimization problems for both finite and infinite horizon problems. The main contributions of this dissertation are: (i) We develop methods for obtaining bounds on the optimal cost based on solving low dimensional dynamic programs; (ii) We utilize the resulting low dimensional dynamic programs and combine them using integer programming methods to find feasible policies for the overall problem; (iii) To illustrate the power of our methods we apply them to a large collection of dynamic optimization problems: multiarmed bandits, restless bandits, queueing networks, serial supply chains, linear control problems and on-line auctions, all with promising results. In particular, the resulting policies appear to be near optimal. (iv) We provide an indepth analysis of several aspects of on-line auctions, both from a buyer's and a seller's perspective. Specifically, for buyers we construct a model of on-line auctions using publicly available data and develop an algorithm for optimally bidding in multiple simultaneous auctions. For sellers we construct a model of on-line auctions using publicly available data and demonstrate how a seller can increase the final selling price using dynamic programming.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2003.
Includes bibliographical references (p. 187-192).
Subjects
Operations Research Center.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Sloan School of Management
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