Continuous knapsack sets with divisible capacities

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dc.citation.epage20en_US
dc.citation.issueNumber1-2en_US
dc.citation.spage1en_US
dc.citation.volumeNumber156en_US
dc.contributor.authorWolsey, L. A.en_US
dc.contributor.authorYaman, H.en_US
dc.date.accessioned2018-04-12T10:57:36Z
dc.date.available2018-04-12T10:57:36Z
dc.date.issued2016en_US
dc.departmentDepartment of Industrial Engineeringen_US
dc.description.abstractWe study two continuous knapsack sets (Formula presented.) and (Formula presented.) with (Formula presented.) integer, one unbounded continuous and (Formula presented.) bounded continuous variables in either (Formula presented.) or (Formula presented.) form. When the coefficients of the integer variables are integer and divisible, we show in both cases that the convex hull is the intersection of the bound constraints and (Formula presented.) polyhedra arising as the convex hulls of continuous knapsack sets with a single unbounded continuous variable. The latter convex hulls are completely described by an exponential family of partition inequalities and a polynomial size extended formulation is known in the (Formula presented.) case. We also provide an extended formulation for the (Formula presented.) case. It follows that, given a specific objective function, optimization over both (Formula presented.) and (Formula presented.) can be carried out by solving (Formula presented.) polynomial size linear programs. A further consequence of these results is that the coefficients of the continuous variables all take the values 0 or 1 (after scaling) in any non-trivial facet-defining inequality of the convex hull of such sets.en_US
dc.description.provenanceMade available in DSpace on 2018-04-12T10:57:36Z (GMT). No. of bitstreams: 1 bilkent-research-paper.pdf: 179475 bytes, checksum: ea0bedeb05ac9ccfb983c327e155f0c2 (MD5) Previous issue date: 2016en
dc.identifier.doi10.1007/s10107-015-0868-3en_US
dc.identifier.eissn1436-4646
dc.identifier.issn0025-5610
dc.identifier.urihttp://hdl.handle.net/11693/36928
dc.language.isoEnglishen_US
dc.publisherSpringeren_US
dc.relation.isversionofhttp://dx.doi.org/10.1007/s10107-015-0868-3en_US
dc.source.titleMathematical Programmingen_US
dc.subjectContinuous knapsack seten_US
dc.subjectConvex hullen_US
dc.subjectDivisible capacitiesen_US
dc.subjectPartition inequalitiesen_US
dc.subjectSplittable flow arc seten_US
dc.subjectLinear programmingen_US
dc.subjectContinuous knapsack seten_US
dc.subjectConvex hullen_US
dc.subjectDivisible capacitiesen_US
dc.subjectPartition inequalitiesen_US
dc.subjectSplittable flowsen_US
dc.subjectComputational geometryen_US
dc.titleContinuous knapsack sets with divisible capacitiesen_US
dc.typeArticleen_US

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