Valid Inequalities and Facets of the Capacitated Plant Location Problem
Name
OR-149-86-.pdf
Size
2.48 MB
Format
Adobe PDF
Checksum (MD5)
89cd7611745f137ed4281d31f70fa363
Author(s)
Leung, Janny M. Y.
Magnanti, Thomas L.
Date Issued
May 1986
Publisher
Massachusetts Institute of Technology, Operations Research Center
Series/Report no.
Operations Research Center Working Paper;OR 149-86
Abstract
Recently, several successful applications of strong cutting plane methods to combinatorial optimization problems have renewed interest in cutting plane methods, and polyhedral characterizations, of integer programming problems.In this paper, we investigate the polyhedral structure of the capacitated plant location problem. Our purpose is to identify facets and valid inequalities for a wide range of capacitated fixed charge problems that contain this prototype problem as a substructure.The first part of the paper introduces a family of facets for a version of the capacitated plant location problem with constant capacity K for all plants. These facet inequalities depend on K and thus differ fundamentally from the valid inequalities for the uncapacitated version of the problem. We also introduce a second formulation for a model with indivisible customer demand and show that it is equivalent to a vertex packing problem on a derived graph. We identify facets and valid inequalities for this version of the problem by applying known results for the vertex packing polytope.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
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