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Advances in Solving the Multicommodity-Flow Problem

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  • Richard D. McBride

    (Marshall School of Business, University of Southern California, Los Angeles, California 90089-1421)

Abstract

The multicommodity-flow problem arises in a wide variety of important applications. Many communications, logistics, manufacturing, and transportation problems can be formulated as large multicommodity-flow problems. During the last few years researchers have made steady advances in solving extremely large multicommodity-flow problems. This improvement has been due both to algorithmic and to hardware advances. At present the primal simplex method using the basis-partitioning approach gives excellent solution times even on modest hardware. These results imply that we can now efficiently solve the extremely large multicommodity-flow models found in industry. The extreme-point solution can also be quickly reoptimized to meet the additional requirements often imposed upon the continuous solution. Currently practitioners are using EMNET, a primal basis-partitioning algorithm, to solve extremely large logistics problems with more than 600,000 constraints and 7,000,000 variables in the food industry.

Suggested Citation

  • Richard D. McBride, 1998. "Advances in Solving the Multicommodity-Flow Problem," Interfaces, INFORMS, vol. 28(2), pages 32-41, April.
    • Handle: RePEc:inm:orinte:v:28:y:1998:i:2:p:32-41
    DOI: 10.1287/inte.28.2.32
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    References listed on IDEAS

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    1. Jeff L. Kennington, 1978. "A Survey of Linear Cost Multicommodity Network Flows," Operations Research, INFORMS, vol. 26(2), pages 209-236, April.
    2. Judith M. Farvolden & Warren B. Powell & Irvin J. Lustig, 1993. "A Primal Partitioning Solution for the Arc-Chain Formulation of a Multicommodity Network Flow Problem," Operations Research, INFORMS, vol. 41(4), pages 669-693, August.
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    Cited by:

    1. Dewil, R. & Vansteenwegen, P. & Cattrysse, D. & Van Oudheusden, D., 2015. "A minimum cost network flow model for the maximum covering and patrol routing problem," European Journal of Operational Research, Elsevier, vol. 247(1), pages 27-36.
    2. Jose L. Walteros & Andrés L. Medaglia & Germán Riaño, 2015. "Hybrid Algorithm for Route Design on Bus Rapid Transit Systems," Transportation Science, INFORMS, vol. 49(1), pages 66-84, February.
    3. Yipeng Zhang & Yunbing Gao & Bingbo Gao & Yuchun Pan & Mingyang Yan, 2015. "An Efficient Graph-based Method for Long-term Land-use Change Statistics," Sustainability, MDPI, vol. 8(1), pages 1-14, December.
    4. Ming Fan & Jan Stallaert & Andrew B. Whinston, 2003. "Decentralized Mechanism Design for Supply Chain Organizations Using an Auction Market," Information Systems Research, INFORMS, vol. 14(1), pages 1-22, March.
    5. Garg, Manish & Smith, J. Cole, 2008. "Models and algorithms for the design of survivable multicommodity flow networks with general failure scenarios," Omega, Elsevier, vol. 36(6), pages 1057-1071, December.
    6. 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.
    7. Slava Sery & Vince Presti & Donald E. Shobrys, 2001. "Optimization Models for Restructuring BASF North America's Distribution System," Interfaces, INFORMS, vol. 31(3), pages 55-65, June.
    8. Richard D. McBride & John W. Mamer, 2004. "Implementing an LU Factorization for the Embedded Network Simplex Algorithm," INFORMS Journal on Computing, INFORMS, vol. 16(2), pages 109-119, May.
    9. Jeffery L. Kennington & Karen R. Lewis, 2004. "Generalized Networks: The Theory of Preprocessing and an Empirical Analysis," INFORMS Journal on Computing, INFORMS, vol. 16(2), pages 162-173, May.
    10. Antonio Frangioni, 2005. "About Lagrangian Methods in Integer Optimization," Annals of Operations Research, Springer, vol. 139(1), pages 163-193, October.
    11. K L Poh & K W Choo & C G Wong, 2005. "A heuristic approach to the multi-period multi-commodity transportation problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(6), pages 708-718, June.

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