Polyhedra Study of Mixed Integer Programs With Variable Upper Bounds

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Shebalov, Sergey

Contributors dc:contributor

• Diego Klabjan

• Operations Research

Language dc:language

eng

Identifier

(MiAaPQ)AAI3153425

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86845