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Algorithms for discrete, non-linear and robust optimization problems with applications in scheduling and service operations

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dc.contributor.advisor Andreas S. Schulz. en_US Mittal, Shashi, Ph. D. Massachusetts Institute of Technology en_US
dc.contributor.other Massachusetts Institute of Technology. Operations Research Center. en_US 2012-01-30T15:22:20Z 2012-01-30T15:22:20Z 2011 en_US 2011 en_US
dc.description Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2011. en_US
dc.description This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. en_US
dc.description Cataloged from student submitted PDF version of thesis. en_US
dc.description Includes bibliographical references (p. 101-107). en_US
dc.description.abstract This thesis presents efficient algorithms that give optimal or near-optimal solutions for problems with non-linear objective functions that arise in discrete, continuous and robust optimization. First, we present a general framework for designing approximation schemes for combinatorial optimization problems in which the objective function is a combination of more than one function. Examples of such problems include those in which the objective function is a product or ratio of two or more linear functions, parallel machine scheduling problems with the makespan objective, robust versions of weighted multi-objective optimization problems, and assortment optimization problems with logit choice models. For many of these problems, we give the first fully polynomial time approximation scheme using our framework. Next, we present approximation schemes for optimizing a rather general class of non-linear functions of low rank over a polytope. In contrast to existing results in the literature, our approximation scheme does not require the assumption of quasi-concavity of the objective function. For the special case of minimizing a quasi-concave function of low-rank, we give an alternative algorithm which always returns a solution which is an extreme point of the polytope. This algorithm can also be used for combinatorial optimization problems where the objective is to minimize a quasi-concave function of low rank. We also give complexity-theoretic results with regards to the inapproximability of minimizing a concave function over a polytope. Finally, we consider the problem of appointment scheduling in a robust optimization framework. The appointment scheduling problem arises in many service operations, for example health care. For each job, we are given its minimum and maximum possible execution times. The objective is to find an appointment schedule for which the cost in the worst case scenario of the realization of the processing times of the jobs is minimized. We present a global balancing heuristic, which gives an easy to compute closed form optimal schedule when the underage costs of the jobs are non-decreasing. In addition, for the case where we have the flexibility of changing the order of execution of the jobs, we give simple heuristics to find a near-optimal sequence of the jobs. en_US
dc.description.statementofresponsibility by Shashi Mittal. en_US
dc.format.extent 107 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 en_US
dc.subject Operations Research Center. en_US
dc.title Algorithms for discrete, non-linear and robust optimization problems with applications in scheduling and service operations en_US
dc.type Thesis en_US Ph.D. en_US
dc.contributor.department Massachusetts Institute of Technology. Operations Research Center. en_US
dc.identifier.oclc 773935349 en_US

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