Models and Methods for Multiple Resource Constrained Job Scheduling under Uncertainty

Persistent Link:
http://hdl.handle.net/10150/193630
Title:
Models and Methods for Multiple Resource Constrained Job Scheduling under Uncertainty
Author:
Keller, Brian
Issue Date:
2009
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:
We consider a scheduling problem where each job requires multiple classes of resources, which we refer to as the multiple resource constrained scheduling problem(MRCSP). Potential applications include team scheduling problems that arise in service industries such as consulting and operating room scheduling. We focus on two general cases of the problem. The first case considers uncertainty of processing times, due dates, and resource availabilities consumption, which we denote as the stochastic MRCSP with uncertain parameters (SMRCSP-U). The second case considers uncertainty in the number of jobs to schedule, which arises in consulting and defense contracting when companies bid on future contracts but may or may not win the bid. We call this problem the stochastic MRCSP with job bidding (SMRCSP-JB).We first provide formulations of each problem under the framework of two-stage stochastic programming with recourse. We then develop solution methodologies for both problems. For the SMRCSP-U, we develop an exact solution method based on the L-shaped method for problems with a moderate number of scenarios. Several algorithmic enhancements are added to improve efficiency. Then, we embed the L-shaped method within a sampling-based solution method for problems with a large number of scenarios. We modify a sequential sampling procedure to allowfor approximate solution of integer programs and prove desired properties. The sampling-based method is applicable to two-stage stochastic integer programs with integer first-stage variables. Finally, we compare the solution methodologies on a set of test problems.For SMRCSP-JB, we utilize the disjunctive decomposition (D2 ) algorithm for stochastic integer programs with mixed-binary subproblems. We develop several enhancements to the D2 algorithm. First, we explore the use of a cut generation problem restricted to a subspace of the variables, which yields significant computational savings. Then, we examine generating alternative disjunctive cuts based on the generalized upper bound (GUB) constraints that appear in the second-stage of the SMRCSP-JB. We establish convergence of all D2 variants and present computational results on a set of instances of SMRCSP-JB.
Type:
text; Electronic Dissertation
Keywords:
disjunctive decomposition; sampling; stochastic integer programming; stochastic scheduling
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Systems & Industrial Engineering; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Bayraksan, Guzin
Committee Chair:
Bayraksan, Guzin

Full metadata record

DC FieldValue Language
dc.language.isoENen_US
dc.titleModels and Methods for Multiple Resource Constrained Job Scheduling under Uncertaintyen_US
dc.creatorKeller, Brianen_US
dc.contributor.authorKeller, Brianen_US
dc.date.issued2009en_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.abstractWe consider a scheduling problem where each job requires multiple classes of resources, which we refer to as the multiple resource constrained scheduling problem(MRCSP). Potential applications include team scheduling problems that arise in service industries such as consulting and operating room scheduling. We focus on two general cases of the problem. The first case considers uncertainty of processing times, due dates, and resource availabilities consumption, which we denote as the stochastic MRCSP with uncertain parameters (SMRCSP-U). The second case considers uncertainty in the number of jobs to schedule, which arises in consulting and defense contracting when companies bid on future contracts but may or may not win the bid. We call this problem the stochastic MRCSP with job bidding (SMRCSP-JB).We first provide formulations of each problem under the framework of two-stage stochastic programming with recourse. We then develop solution methodologies for both problems. For the SMRCSP-U, we develop an exact solution method based on the L-shaped method for problems with a moderate number of scenarios. Several algorithmic enhancements are added to improve efficiency. Then, we embed the L-shaped method within a sampling-based solution method for problems with a large number of scenarios. We modify a sequential sampling procedure to allowfor approximate solution of integer programs and prove desired properties. The sampling-based method is applicable to two-stage stochastic integer programs with integer first-stage variables. Finally, we compare the solution methodologies on a set of test problems.For SMRCSP-JB, we utilize the disjunctive decomposition (D2 ) algorithm for stochastic integer programs with mixed-binary subproblems. We develop several enhancements to the D2 algorithm. First, we explore the use of a cut generation problem restricted to a subspace of the variables, which yields significant computational savings. Then, we examine generating alternative disjunctive cuts based on the generalized upper bound (GUB) constraints that appear in the second-stage of the SMRCSP-JB. We establish convergence of all D2 variants and present computational results on a set of instances of SMRCSP-JB.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectdisjunctive decompositionen_US
dc.subjectsamplingen_US
dc.subjectstochastic integer programmingen_US
dc.subjectstochastic schedulingen_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineSystems & Industrial Engineeringen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorBayraksan, Guzinen_US
dc.contributor.chairBayraksan, Guzinen_US
dc.contributor.committeememberHead, Larryen_US
dc.contributor.committeememberKucukyavuz, Simgeen_US
dc.contributor.committeememberBaker, Kenen_US
dc.identifier.proquest10536en_US
dc.identifier.oclc659752268en_US
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