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Fixed charge multicommodity network design using p-partition facets

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  • Agarwal, Y.K.
  • Aneja, Y.P.

Abstract

We are given an undirected network G[V, E] and a set of traffic demands. To install a potential edge e ∈ E we incur a cost Fe to provide a positive capacity ae. The objective is to select edges, at minimum cost, so as to permit a feasible multicommodity flow of all traffic. We study structure of the projection polytope of this problem, in the space of binary variables associated with fixed-charges, by relating facets of a p node problem (p=2,3, or 4), defined over a multi-graph obtained by a p-partition of V, to the facets of the original problem. Inspired from the well-known “cover” inequalities of the Knapsack Problem, we develop the notion of p-partition cover inequalities. We present necessary and sufficient conditions for such inequalities to be facet defining for p = 3 and 4. A simple heuristic approach for separating and adding such violated inequalities is presented, and implemented for p values up to 10. We report optimal solutions for problems with 30 nodes, 60 edges, and fully dense demand matrices within a few minutes of cpu time for most instances. Some results for dense graph problems are also reported.

Suggested Citation

  • Agarwal, Y.K. & Aneja, Y.P., 2017. "Fixed charge multicommodity network design using p-partition facets," European Journal of Operational Research, Elsevier, vol. 258(1), pages 124-135.
  • Handle: RePEc:eee:ejores:v:258:y:2017:i:1:p:124-135
    DOI: 10.1016/j.ejor.2016.09.015
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    References listed on IDEAS

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    1. T. L. Magnanti & R. T. Wong, 1984. "Network Design and Transportation Planning: Models and Algorithms," Transportation Science, INFORMS, vol. 18(1), pages 1-55, February.
    2. Yogesh Agarwal & Yash Aneja, 2012. "Fixed-Charge Transportation Problem: Facets of the Projection Polyhedron," Operations Research, INFORMS, vol. 60(3), pages 638-654, June.
    3. Herrmann, J. W. & Ioannou, G. & Minis, I. & Proth, J. M., 1996. "A dual ascent approach to the fixed-charge capacitated network design problem," European Journal of Operational Research, Elsevier, vol. 95(3), pages 476-490, December.
    4. Quentin Botton & Bernard Fortz & Luis Gouveia & Michael Poss, 2013. "Benders Decomposition for the Hop-Constrained Survivable Network Design Problem," INFORMS Journal on Computing, INFORMS, vol. 25(1), pages 13-26, February.
    5. A. Balakrishnan & T. L. Magnanti & R. T. Wong, 1989. "A Dual-Ascent Procedure for Large-Scale Uncapacitated Network Design," Operations Research, INFORMS, vol. 37(5), pages 716-740, October.
    6. Gendron, Bernard, 2002. "A note on "a dual-ascent approach to the fixed-charge capacitated network design problem"," European Journal of Operational Research, Elsevier, vol. 138(3), pages 671-675, May.
    7. BIENSTOCK, Daniel & CHOPRA, Sunil & GÜNLÜK, Oktay & TSAI, Chih-Yang, 1998. "Minimum cost capacity installation for multicommodity network flows," LIDAM Reprints CORE 1391, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Agarwal, Y.K. & Aneja, Y.P. & Jayaswal, Sachin, 2022. "Directed fixed charge multicommodity network design: A cutting plane approach using polar duality," European Journal of Operational Research, Elsevier, vol. 299(1), pages 118-136.
    2. Wu, Tao & Xiao, Fan & Zhang, Canrong & Zhang, Defu & Liang, Zhe, 2019. "Regression and extrapolation guided optimization for production–distribution with ship–buy–exchange options," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 129(C), pages 15-37.

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