{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/29599"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/29599","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"A Langrangian decomposition approach to weakly coupled dynamic optimization problems and its applications","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Hawkins, Jeffrey Thomas, 1977-"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. 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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. 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(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."],"dc:description.degree":["Ph.D."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/1721.1/29599"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. 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