Capacitated Trees, Capacitated Routing, and Associated Polyhedra
Name
OR-232-90.pdf
Size
3.47 MB
Format
Adobe PDF
Checksum (MD5)
4a58b9b94a13e406af4606bc9b195bc7
Author(s)
Araque, Jésus Rafael
Hall, Leslie A.
Magnanti, Thomas L.
Date Issued
November 1990
Publisher
Massachusetts Institute of Technology, Operations Research Center
Series/Report no.
Operations Research Center Working Paper;OR 232-90
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.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Persistent DSpace Link
