An exploration of stochastic decomposition algorithms for stochastic linear programs with recourse.

Persistent Link:
http://hdl.handle.net/10150/186667
Title:
An exploration of stochastic decomposition algorithms for stochastic linear programs with recourse.
Author:
Lowe, Wing Wah.
Issue Date:
1994
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
Stochastic linear programs are linear programs in which some of the problem data are random variables. The particular kind of programs that we study belong to the recourse model. Under this model, some decisions are postponed until better information becomes available (e.g., an outcome of a random variable is realized), while other decisions must be made 'here and now.' For example, in a telecommunication network planning problem, decisions regarding the addition of network capacity have to be made before knowing customer demand (i.e., 'here and now'). Once the demand is realized, efficient usage of the network can then be determined. This work explores algorithms for the solution of such programs: stochastic linear programs with recourse. The algorithms investigated can be described as decomposition based cutting plane methods in which the cuts are estimated from random samples. Moreover, the algorithms all use the incremental sampling plan inherent to the Stochastic Decomposition (SD) algorithm developed by Higle and Sen in 1991. Our study includes both two stage and multistage programs. For the solution of two stage programs, we present the Conditional Stochastic Decomposition (CSD) algorithm, a multicut version of the SD algorithm. CSD is most suitable for situations in which data are difficult to obtain and may be computationally intense. Because of this potential intensity, we explore algorithms which require less computational effort than CSD. These algorithms combine features of both CSD and SD and are referred to as hybrid algorithms. Following our exploration of these algorithms for two stage problems, we next explore an extension of the SD algorithm that can be used for multistage problems with stagewise independent random variables. For the sake of notational brevity, our technical development is centered around the three stage case, although the extension to multistage problems is straightforward. Under mild conditions, convergence results similar to those found in the two stage algorithms hold. Multistage stochastic decomposition is currently a largely uncharted area. Our research represents the first major effort in this direction.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Dissertations, Academic.; Operations research.; System theory.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Systems and Industrial Engineering; Graduate College
Degree Grantor:
University of Arizona
Committee Chair:
Higle, Julia L.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleAn exploration of stochastic decomposition algorithms for stochastic linear programs with recourse.en_US
dc.creatorLowe, Wing Wah.en_US
dc.contributor.authorLowe, Wing Wah.en_US
dc.date.issued1994en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractStochastic linear programs are linear programs in which some of the problem data are random variables. The particular kind of programs that we study belong to the recourse model. Under this model, some decisions are postponed until better information becomes available (e.g., an outcome of a random variable is realized), while other decisions must be made 'here and now.' For example, in a telecommunication network planning problem, decisions regarding the addition of network capacity have to be made before knowing customer demand (i.e., 'here and now'). Once the demand is realized, efficient usage of the network can then be determined. This work explores algorithms for the solution of such programs: stochastic linear programs with recourse. The algorithms investigated can be described as decomposition based cutting plane methods in which the cuts are estimated from random samples. Moreover, the algorithms all use the incremental sampling plan inherent to the Stochastic Decomposition (SD) algorithm developed by Higle and Sen in 1991. Our study includes both two stage and multistage programs. For the solution of two stage programs, we present the Conditional Stochastic Decomposition (CSD) algorithm, a multicut version of the SD algorithm. CSD is most suitable for situations in which data are difficult to obtain and may be computationally intense. Because of this potential intensity, we explore algorithms which require less computational effort than CSD. These algorithms combine features of both CSD and SD and are referred to as hybrid algorithms. Following our exploration of these algorithms for two stage problems, we next explore an extension of the SD algorithm that can be used for multistage problems with stagewise independent random variables. For the sake of notational brevity, our technical development is centered around the three stage case, although the extension to multistage problems is straightforward. Under mild conditions, convergence results similar to those found in the two stage algorithms hold. Multistage stochastic decomposition is currently a largely uncharted area. Our research represents the first major effort in this direction.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectDissertations, Academic.en_US
dc.subjectOperations research.en_US
dc.subjectSystem theory.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineSystems and Industrial Engineeringen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.chairHigle, Julia L.en_US
dc.contributor.committeememberDuckstein, Lucienen_US
dc.contributor.committeememberSen, Suvrajeeten_US
dc.identifier.proquest9426301en_US
dc.identifier.oclc722893012en_US
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