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Algorithms and hardness results for the jump number problem, the joint replenishment problem, and the optimal clustering of frequency-constrained maintenance jobs

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dc.contributor.advisor Andreas S. Schulz. en_US
dc.contributor.author Telha Cornejo, Claudio (Claudio A.) en_US
dc.contributor.other Massachusetts Institute of Technology. Operations Research Center. en_US
dc.date.accessioned 2012-04-26T18:54:12Z
dc.date.available 2012-04-26T18:54:12Z
dc.date.copyright 2012 en_US
dc.date.issued 2012 en_US
dc.identifier.uri http://hdl.handle.net/1721.1/70446
dc.description Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2012. en_US
dc.description Cataloged from PDF version of thesis. en_US
dc.description Includes bibliographical references (p. 107-110). en_US
dc.description.abstract In the first part of this thesis we present a new, geometric interpretation of the jump number problem on 2-dimensional 2-colorable (2D2C) partial order. We show that the jump number of a 2D2C poset is equivalent to the maximum cardinality of an independent set in a properly defined collection of rectangles in the plane. We then model the geometric problem as a linear program. Even though the underlying polytope may not be integral, we show that one can always find an integral optimal solution. Inspired by this result and by previous work of A. Frank, T. Jordan and L. Vegh [13, 14, 15] on set-pairs, we derive an efficient combinatorial algorithm to find the maximum independent set and its dual, the minimum hitting set, in polynomial time. The combinatorial algorithm solves the jump number problem on convex posets (a subclass of 2D2C posets) significantly faster than current methods. If n is the number of nodes in the partial order, our algorithm runs in 0((n log n)2.5) time, while previous algorithms ran in at least 0(n9 ) time. In the second part, we present a novel connection between certain sequencing problems that involve the coordination of activities and the problem of factorizing integer numbers. We use this connection to derive hardness results for three different problems: -- The Joint Replenishment Problem with General Integer Policies. -- The Joint Replenishment Problem with Correction Factor. -- The Problem of Optimal Clustering of Frequency-Constrained Maintenance Jobs. Our hardness results do not follow from a standard type of reduction (e.g., we do not prove NP-hardness), and imply that no polynomial-time algorithm exists for the problems above, unless Integer Factorization is solvable in polynomial time.. en_US
dc.description.statementofresponsibility by Claudio Telha Cornejo. en_US
dc.format.extent 110 p. en_US
dc.language.iso eng en_US
dc.publisher Massachusetts Institute of Technology en_US
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. See provided URL for inquiries about permission. en_US
dc.rights.uri http://dspace.mit.edu/handle/1721.1/7582 en_US
dc.subject Operations Research Center. en_US
dc.title Algorithms and hardness results for the jump number problem, the joint replenishment problem, and the optimal clustering of frequency-constrained maintenance jobs en_US
dc.type Thesis en_US
dc.description.degree Ph.D. en_US
dc.contributor.department Massachusetts Institute of Technology. Operations Research Center. en_US
dc.identifier.oclc 785737191 en_US


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