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Capacitated Trees, Capacitated Routing, and Associated Polyhedra

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Show simple item record Araque, Jésus Rafael en_US Hall, Leslie A. en_US Magnanti, Thomas L. en_US 2004-05-28T19:27:25Z 2004-05-28T19:27:25Z 1990-11 en_US
dc.description.abstract We study the polyhedral structure of two related core combinatorial problems: the subtree cardinalityconstrained minimal spanning tree problem and the identical customer vehicle routing problem. For each of these problems, and for a forest relaxation of the minimal spanning tree problem, we introduce a number of new valid inequalities and specify conditions for ensuring when these inequalities are facets for the associated integer polyhedra. The inequalities are defined by one of several underlying support graphs: (i) a multistar, a "star" with a clique replacing the central vertex; (ii) a clique cluster, a collection of cliques intersecting at a single vertex, or more generally at a central" clique; and (iii) a ladybug, consisting of a multistar as a head and a clique as a body. We also consider packing (generalized subtour elimination) constraints, as well as several variants of our basic inequalities, such as partial multistars, whose satellite vertices need not be connected to all of the central vertices. Our development highlights the relationship between the capacitated tree and capacitated forest polytopes and a so-called path-partitioning polytope,and shows how to use monotone polytopes and a set of simple exchange arguments to prove that valid inequalities are facets. en_US
dc.format.extent 1744 bytes
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dc.language.iso en_US en_US
dc.publisher Massachusetts Institute of Technology, Operations Research Center en_US
dc.relation.ispartofseries Operations Research Center Working Paper;OR 232-90 en_US
dc.title Capacitated Trees, Capacitated Routing, and Associated Polyhedra en_US
dc.type Working Paper en_US

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