2026-09-19T05:52:17Zhttps://dspace.mit.edu/server/oai/request

oai:dspace.mit.edu:1721.1/677682022-01-13T07:54:48Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022

Dimitris Bertsimas and David Gamarnik. Rikun, Alexander Anatolyevich Massachusetts Institute of Technology. Operations Research Center. Massachusetts Institute of Technology. Operations Research Center Sloan School of Management 2011-12-19T18:49:02Z 2011-12-19T18:49:02Z 2011 2011 http://hdl.handle.net/1721.1/67768 767527187 Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2011. Cataloged from PDF version of thesis. Includes bibliographical references (p. 105-111). This thesis investigates the application of robust optimization in the performance analysis of queueing and inventory systems. In the first part of the thesis, we propose a new approach for performance analysis of queueing systems based on robust optimization. We first derive explicit upper bounds on performance for tandem single class, multiclass single server, and single class multi-server queueing systems by solving appropriate robust optimization problems. We then show that these bounds derived by solving deterministic optimization problems translate to upper bounds on the expected steady-state performance for a variety of widely used performance measures such as waiting times and queue lengths. Additionally, these explicit bounds agree qualitatively with known results. In the second part of the thesis, we propose methods to compute (s,S) policies in supply chain networks using robust and stochastic optimization and compare their performance. Our algorithms handle general uncertainty sets, arbitrary network topologies, and flexible cost functions including the presence of fixed costs. The algorithms exhibit empirically practical running times. We contrast the performance of robust and stochastic (s,S) policies in a numerical study, and we find that the robust policy is comparable to the average performance of the stochastic policy, but has a considerably lower standard deviation across a variety of networks and realized demand distributions. Additionally, we identify regimes when the robust policy exhibits particular strengths even in average performance and tail behavior as compared with the stochastic policy. by Alexander Anatolyevich Rikun. Ph.D. 111 p. eng Massachusetts Institute of Technology 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. http://dspace.mit.edu/handle/1721.1/7582 Operations Research Center. Applications of robust optimization to queueing and inventory systems Thesis application/pdf Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="805928c7-8b6d-47c9-ae60-e675c3a086cd"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>Applications of robust optimization to queueing and inventory systems</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2011</PublicationDate> <Authors> <Author> <DisplayName>Rikun, Alexander Anatolyevich</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Operations Research Center.</Keyword> <Abstract>This thesis investigates the application of robust optimization in the performance analysis of queueing and inventory systems. In the first part of the thesis, we propose a new approach for performance analysis of queueing systems based on robust optimization. We first derive explicit upper bounds on performance for tandem single class, multiclass single server, and single class multi-server queueing systems by solving appropriate robust optimization problems. We then show that these bounds derived by solving deterministic optimization problems translate to upper bounds on the expected steady-state performance for a variety of widely used performance measures such as waiting times and queue lengths. Additionally, these explicit bounds agree qualitatively with known results. In the second part of the thesis, we propose methods to compute (s,S) policies in supply chain networks using robust and stochastic optimization and compare their performance. Our algorithms handle general uncertainty sets, arbitrary network topologies, and flexible cost functions including the presence of fixed costs. The algorithms exhibit empirically practical running times. We contrast the performance of robust and stochastic (s,S) policies in a numerical study, and we find that the robust policy is comparable to the average performance of the stochastic policy, but has a considerably lower standard deviation across a variety of networks and realized demand distributions. Additionally, we identify regimes when the robust policy exhibits particular strengths even in average performance and tail behavior as compared with the stochastic policy.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>