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Title:Polyhedra Study of Mixed Integer Programs With Variable Upper Bounds
Author(s):Shebalov, Sergey
Doctoral Committee Chair(s):Diego Klabjan
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Operations Research
Abstract:We investigate the convex hull of the set defined by a single constraint with continues and binary variables and in addition, variable upper bound constraints are present. We introduce the flow cover inequality, which is valid for a projection. We also give conditions under which this inequality is facet defining. We use sequence independent lifting to obtain valid inequalities for the entire set. In general, computing the lifting function is NP-hard, but under an additional restriction on the cover we obtain a closed form. In the second part of the thesis we first elaborate on general sequence dependent lifting for this set and present a dynamic program for calculating lifting coefficients. Then we consider projections of this set to knapsack cover and to the single binary variable polytope. We present the result of sequence independent lifting of the knapsack cover inequality and obtain lifting some coefficients for sequence dependent lifting with for specific sequences. We generate two new families of facet defining inequalities for the single binary variable polytope and prove that combined with the trivial inequalities they give a full description of this polytope. Finally, we give an optimization problem for the lifting coefficients.
Issue Date:2004
Type:Text
Language:English
Description:112 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2004.
URI:http://hdl.handle.net/2142/86845
Other Identifier(s):(MiAaPQ)AAI3153425
Date Available in IDEALS:2015-09-28
Date Deposited:2004


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