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The Convex Hull of Two Core Capacitated Network Design Problems

The network loading problem (NLP) is a specialized capacitated network design problem in which prescribed point-to-point demand between various pairs of nodes of a network must be met by installing (loading) a capacitated facility. We can load any number of units of the facility on each of the arcs at a specified arc dependent cost. The problem is to determine the number of facilities to be loaded on the arcs that will satisfy the given demand at minimum cost. This paper studies two core subproblems of the NLP. The first problem, motivated by a Lagrangian relaxation approach for solving the problem, considers a multiple commodity, single arc capacitated network design problem. The second problem is a three node network; this specialized network arises in larger networks if we aggregate nodes. In both cases, we develop families of facets and completely characterize the convex hull of feasible solutions to the integer programming formulation of the problems. These results in turn strengthen the formulation of the NLP.

Identiferoai:union.ndltd.org:MIT/oai:dspace.mit.edu:1721.1/5164
Date06 1900
CreatorsMagnanti, Thomas L., Mirchandani, Prakash, Vachani, Rita
PublisherMassachusetts Institute of Technology, Operations Research Center
Source SetsM.I.T. Theses and Dissertation
Languageen_US
Detected LanguageEnglish
TypeWorking Paper
Format1716245 bytes, application/pdf
RelationOperations Research Center Working Paper;OR 217-90

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