Title:
Topics in group methods for integer programming

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dc.contributor.advisor Cook, William J.
dc.contributor.author Chen, Kenneth en_US
dc.contributor.committeeMember Johnson, Ellis L.
dc.contributor.committeeMember Nemhauser, George L.
dc.contributor.committeeMember Parker, R. Gary
dc.contributor.committeeMember Tetali, Prasad
dc.contributor.department Mathematics en_US
dc.date.accessioned 2011-09-22T17:48:18Z
dc.date.available 2011-09-22T17:48:18Z
dc.date.issued 2011-06-15 en_US
dc.description.abstract In 2003, Gomory and Johnson gave two different three-slope T-space facet constructions, both of which shared a slope with the corresponding Gomory mixed-integer cut. We give a new three-slope facet which is independent of the GMIC and also give a four-slope T-space facet construction, which to our knowledge, is the first four-slope construction. We describe an enumerative framework for the discovery of T-space facets. Using an algorithm by Harvey for computing integer hulls in the plane, we give a heuristic for quickly computing lattice-free triangles. Given two rows of the tableau, we derive how to exactly calculate lattice-free triangles and quadrilaterals in the plane which can be used to derive facet-defining inequalities of the integer hull. We then present computational results using these derivations where non-basic integer variables are strengthened using Balas-Jeroslow lifting. en_US
dc.description.degree Ph.D. en_US
dc.identifier.uri http://hdl.handle.net/1853/41133
dc.publisher Georgia Institute of Technology en_US
dc.subject Lattice-free sets en_US
dc.subject T-space facets en_US
dc.subject Mixed-integer programming en_US
dc.subject.lcsh Integer programming
dc.title Topics in group methods for integer programming en_US
dc.type Text
dc.type.genre Dissertation
dspace.entity.type Publication
local.contributor.corporatename College of Sciences
local.contributor.corporatename School of Mathematics
relation.isOrgUnitOfPublication 85042be6-2d68-4e07-b384-e1f908fae48a
relation.isOrgUnitOfPublication 84e5d930-8c17-4e24-96cc-63f5ab63da69
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