In this work we give a complete description of the set covering polyhedron of circulant matrices $$C^k_{sk}$$ C s k k with $$s=2,3$$ s = 2 , 3 and $$k \ge 3 $$ k ≥ 3 by linear inequalities. In particular, we prove that every non boolean facet defining inequality is associated with a circulant...

In this work we give a complete description of the set covering polyhedron of circulant matrices <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$C^k_{sk}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msubsup> <mi>C</mi> <mrow> <mi>s</mi> <mi>k</mi> </mrow> <mi>k</mi> </msubsup> </math> </EquationSource> </InlineEquation> with <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$s=2,3$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>s</mi> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> </mrow> </math> </EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$k \ge 3 $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>k</mi> <mo>≥</mo> <mn>3</mn> </mrow> </math> </EquationSource> </InlineEquation> by linear inequalities. In particular, we prove that every non boolean facet defining inequality is...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

We study a special case of a structured mixed integer programming model that arises in a number of applications. For the most general case of the model, called PI, we have earlier analyzed the polyhedral structure (Miller et al. [2000a]), including identifying facet-defining valid inequalities....

We present and study a mixed integer programming model that arises as a substructure in many industrial applications. This model provides a relaxation of various capacitated production planning problems, more general fixed charge network flow problems, and other structured mixed integer...

In this paper we introduce a generalization of stable sets: stable multi-sets. A stable multi-set is an assignment of integers to the vertices of a graph, such that specified bounds on vertices and edges are not exceeded. In case all vertex and edge bounds equal one, stable multi-sets are...

In this paper we introduce a generalization of stable sets: stable multi-sets. A stable multi-set is an assignment of integers to the vertices of a graph, such that specified bounds on vertices and edges are not exceeded. In case all vertex and edge bounds equal one, stable multi-sets are...