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The mixed-integer bilinear programming problem with extensions to zero-one quadratic programs

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dc.contributor.authorAdams, Warren Philipen
dc.contributor.committeechairSherali, Hanifen
dc.contributor.committeememberFrair, Lester C.en
dc.contributor.committeememberGhandforoush, F.en
dc.contributor.committeememberMoore, L.J.en
dc.contributor.committeememberNachlas, Joel A.en
dc.contributor.departmentIndustrial Engineering and Operations Researchen
dc.date.accessioned2017-01-30T21:23:59Zen
dc.date.available2017-01-30T21:23:59Zen
dc.date.issued1985en
dc.description.abstractThis research effort is concerned with a class of mathematical programming problems referred to as Mixed-Integer Bilinear Programming Problems. This class of problems, which arises in production, location-allocation, and distribution-application contexts, may be considered as a discrete version of the well-known Bilinear Programming Problem in that one set of decision variables is restricted to be binary valued. The structure of this problem is studied, and special cases wherein it is readily solvable are identified. For the more general case, a new linearization technique is introduced and demonstrated to lead to a tighter linear programming relaxation than obtained through available linearization methods. Based on this linearization, a composite Lagrangian relaxation-implicit enumeration-cutting plane algorithm is developed. Extensive computational experience is provided to test the efficiency of various algorithmic strategies and the effects of problem data on the computational effort of the proposed algorithm. The solution strategy developed for the Mixed-Integer Bilinear Programming Problem may be applied, with suitable modifications,. to other classes of mathematical programming problems: in particular, to the Zero-One Quadratic Programming Problem. In what may be considered as an extension to the work performed on the Mixed-Integer Bilinear Programming Problem, a solution strategy based on an equivalent linear reformulation is developed for the Zero-One Quadratic Programming Problem. The strategy is essentially an implicit enumeration algorithm which employs Lagrangian relaxation, Benders' cutting planes, and local explorations. Computational experience for this problem class is provided to justify the worth of the proposed linear reformulation and algorithm.en
dc.description.degreePh. D.en
dc.format.extentvii, 85 leavesen
dc.format.mimetypeapplication/pdfen
dc.identifier.urihttp://hdl.handle.net/10919/74711en
dc.language.isoen_USen
dc.publisherVirginia Polytechnic Institute and State Universityen
dc.relation.isformatofOCLC# 12928200en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1985.A325en
dc.subject.lcshInteger programmingen
dc.subject.lcshLinear programmingen
dc.subject.lcshQuadratic programmingen
dc.titleThe mixed-integer bilinear programming problem with extensions to zero-one quadratic programsen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineIndustrial Engineering and Operations Researchen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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