Multicommodity network flows: The impact of formulation on decomposition
 Kim L. Jones,
 Irvin J. Lustig,
 Judith M. Farvolden,
 Warren B. Powell
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This paper investigates the impact of problem formulation on Dantzig—Wolfe decomposition for the multicommodity network flow problem. These problems are formulated in three ways: origindestination specific, destination specific, and product specific. The pathbased origindestination specific formulation is equivalent to the treebased destination specific formulation by a simple transformation. Supersupply and superdemand nodes are appended to the treebased product specific formulation to create an equivalent pathbased product specific formulation. We show that solving the pathbased problem formulations by decomposition results in substantially fewer master problem iterations and lower CPU times than by using decomposition on the equivalent treebased formulations. Computational results on a series of multicommodity network flow problems are presented.
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 Title
 Multicommodity network flows: The impact of formulation on decomposition
 Journal

Mathematical Programming
Volume 62, Issue 13 , pp 95117
 Cover Date
 19930201
 DOI
 10.1007/BF01585162
 Print ISSN
 00255610
 Online ISSN
 14364646
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Industry Sectors
 Authors

 Kim L. Jones ^{(1)}
 Irvin J. Lustig ^{(1)}
 Judith M. Farvolden ^{(3)}
 Warren B. Powell ^{(1)}
 Author Affiliations

 1. Department of Civil Engineering and Operations Research, Program in Statistics and Operations Research, Princeton University, Princeton, NJ, USA
 3. Department of Industrial Engineering, University of Toronto, Ont., Canada