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Discrete Cost Multicommodity Network Optimization Problems and Exact Solution Methods

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  • Michel Minoux

Abstract

We first introduce a generic model for discrete cost multicommodity network optimization, together with several variants relevant to telecommunication networks such as: the case where discrete node cost functions (accounting for switching equipment) have to be included in the objective; the case where survivability constraints with respect to single-link and/or single-node failure have to be taken into account. An overview of existing exact solution methods is presented, both for special cases (such as the so-called single-facility and two-facility network loading problems) and for the general case where arbitrary step-increasing link cost-functions are considered. The basic discrete cost multicommodity flow problem (DCMCF) as well as its variant with survivability constraints (DCSMCF) are addressed. Several possible directions for improvement or future investigations are mentioned in the concluding section. Copyright Kluwer Academic Publishers 2001

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  • Michel Minoux, 2001. "Discrete Cost Multicommodity Network Optimization Problems and Exact Solution Methods," Annals of Operations Research, Springer, vol. 106(1), pages 19-46, September.
    • Handle: RePEc:spr:annopr:v:106:y:2001:i:1:p:19-46:10.1023/a:1014554606793
    DOI: 10.1023/A:1014554606793
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    Cited by:

    1. Knippel, Arnaud & Lardeux, Benoit, 2007. "The multi-layered network design problem," European Journal of Operational Research, Elsevier, vol. 183(1), pages 87-99, November.
    2. Masoud Yaghini & Mohammad Karimi & Mohadeseh Rahbar & Mohammad Hassan Sharifitabar, 2015. "A Cutting-Plane Neighborhood Structure for Fixed-Charge Capacitated Multicommodity Network Design Problem," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 48-58, February.
    3. Lixin Tang & Wei Jiang & Georgios Saharidis, 2013. "An improved Benders decomposition algorithm for the logistics facility location problem with capacity expansions," Annals of Operations Research, Springer, vol. 210(1), pages 165-190, November.
    4. Georgios Saharidis & Marianthi Ierapetritou, 2013. "Speed-up Benders decomposition using maximum density cut (MDC) generation," Annals of Operations Research, Springer, vol. 210(1), pages 101-123, November.
    5. Khodakaram Salimifard & Sara Bigharaz, 2022. "The multicommodity network flow problem: state of the art classification, applications, and solution methods," Operational Research, Springer, vol. 22(1), pages 1-47, March.

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