Search results for "Vertex enumeration problem"

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Polyhedral results for a vehicle routing problem

1991

Abstract The Vehicle Routing Problem is a well known, and hard, combinatorial problem, whose polyhedral structure has deserved little attention. In this paper we consider the particular case in which all the demands are equal (since in the general case the associated polytope may be empty). From a known formulation of the problem we obtain the dimension of the corresponding polytope and we study the facetial properties of every inequality in it.

Discrete mathematicsFacet (geometry)Information Systems and ManagementGeneral Computer ScienceDimension (graph theory)Structure (category theory)PolytopeManagement Science and Operations ResearchIndustrial and Manufacturing EngineeringCombinatoricsModeling and SimulationVehicle routing problemRouting (electronic design automation)Integer programmingVertex enumeration problemMathematicsEuropean Journal of Operational Research
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The Linear Ordering Polytope

2010

So far we developed a general integer programming approach for solving the LOP. It was based on the canonical IP formulation with equations and 3-dicycle inequalities which was then strengthened by generating mod-k-inequalities as cutting planes. In this chapter we will add further ingredients by looking for problem- specific inequalities. To this end we will study the convex hull of feasible solutions of the LOP: the so-called linear ordering polytope.

CombinatoricsConvex hullLinear programmingBirkhoff polytopeComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONConvex polytopeCross-polytopeMathematicsofComputing_NUMERICALANALYSISUniform k 21 polytopeEhrhart polynomialVertex enumeration problemMathematics
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