Show simple item record

dc.contributor.advisorAndreas S. Schulz.en_US
dc.contributor.authorMittal, Shashi, Ph. D. Massachusetts Institute of Technologyen_US
dc.contributor.otherMassachusetts Institute of Technology. Operations Research Center.en_US
dc.date.accessioned2012-01-30T15:22:20Z
dc.date.available2012-01-30T15:22:20Z
dc.date.copyright2011en_US
dc.date.issued2011en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/68701
dc.descriptionThesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2011.en_US
dc.descriptionThis electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.en_US
dc.descriptionCataloged from student submitted PDF version of thesis.en_US
dc.descriptionIncludes bibliographical references (p. 101-107).en_US
dc.description.abstractThis 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.statementofresponsibilityby Shashi Mittal.en_US
dc.format.extent107 p.en_US
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsM.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.urihttp://dspace.mit.edu/handle/1721.1/7582en_US
dc.subjectOperations Research Center.en_US
dc.titleAlgorithms for discrete, non-linear and robust optimization problems with applications in scheduling and service operationsen_US
dc.typeThesisen_US
dc.description.degreePh.D.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Operations Research Center
dc.contributor.departmentSloan School of Management
dc.identifier.oclc773935349en_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record