Valid inequalities and projecting the multicommodity extended formulation for uncapacitated fixed charge network flow problems

Multicommodity extended formulations of single source uncapacitated fixed charge network flow problems have significantly sharper linear programming relaxations than the standard flow formulations. However the tradeoff is the introduction of many new constraints and variables to accomodate a sink-or...

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Bibliographic Details
Published inEuropean journal of operational research Vol. 71; no. 1; pp. 95 - 109
Main Authors Rardin, Ronald L., Wolsey, Laurence A.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 26.11.1993
Elsevier
Elsevier Sequoia S.A
SeriesEuropean Journal of Operational Research
Subjects
Applied sciences
Exact sciences and technology
Extended formulations
Flows in networks. Combinatorial problems
Linear programming
Lot sizing
Network design
Operational research and scientific management
Operational research. Management science
Operations research
Production planning
Studies
Lot sizing
Network design
Extended formulations
Fixed charge problem
Network flow
Production control
Network
Inequality
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Summary:Multicommodity extended formulations of single source uncapacitated fixed charge network flow problems have significantly sharper linear programming relaxations than the standard flow formulations. However the tradeoff is the introduction of many new constraints and variables to accomodate a sink-oriented flow disaggregation. In this paper we introduce a new family of dicut collection inequalities and show that they completely describe the projection of the multicommodity formulation onto the original variables. A simple subclass is seen to include a variety of known inequalities for particular models, and combinatorial separation is examined for some special cases.
ISSN:0377-2217
1872-6860
DOI:10.1016/0377-2217(93)90263-M