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Lagrangean decomposition for the fixed charge multicommodity network design problem

Bektas, T., Crainic, T.G. and Gendron, B. (2008) Lagrangean decomposition for the fixed charge multicommodity network design problem , Southampton, UK University of Southampton (Discussion Papers in Centre for Operational Research, Management Science and Information Systems, CORMSIS-08-17).

Record type: Monograph (Discussion Paper)


Traditional Lagrangean relaxations for the multicommodity capacitated network design problem (MCNDP) involve dualizing either arc capacity or flow conservation constraints. The former (shortest-path relaxation) results in loosing the capacity structure whereas the latter (knapsack relaxation) does not maintain any information related to the network structure. Furthermore, both relaxations yield bounds that are at best equal to the value of the LP relaxation. This paper describes a new relaxation for the MCNDP, based on Lagrangean decomposition, which allows one to decompose the problem by nodes, and the subproblems partially preserve both the network and the capacity structure. This is, to the best of the authors' knowledge, the first relaxation for the MCNDP that theoretically yields better bounds than the LP relaxation.

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Published date: 2008


Local EPrints ID: 63014
PURE UUID: f0d0ea38-7a09-4161-956d-dc82cd7f20b3
ORCID for T. Bektas: ORCID iD

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Date deposited: 11 Mar 2009
Last modified: 17 Jul 2017 14:19

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Author: T. Bektas ORCID iD
Author: T.G. Crainic
Author: B. Gendron

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