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A Suggested Computation for Maximal Multi-Commodity Network Flows

Author

Listed:
  • L. R. Ford, Jr.

    (The RAND Corporation, Santa Monica, California)

  • D. R. Fulkerson

    (The RAND Corporation, Santa Monica, California)

Abstract

A simplex computation for an arc-chain formulation of the maximal multi-commodity network flow problem is proposed. Since the number of variables in this formulation is too large to be dealt with explicitly, the computation treats non-basic variables implicitly by replacing the usual method of determining a vector to enter the basis with several applications of a combinatorial algorithm for finding a shortest chain joining a pair of points in a network.

Suggested Citation

  • L. R. Ford, Jr. & D. R. Fulkerson, 1958. "A Suggested Computation for Maximal Multi-Commodity Network Flows," Management Science, INFORMS, vol. 5(1), pages 97-101, October.
    • Handle: RePEc:inm:ormnsc:v:5:y:1958:i:1:p:97-101
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    File URL: http://dx.doi.org/10.1287/mnsc.5.1.97
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    Cited by:

    1. Patriksson, Michael, 2008. "A survey on the continuous nonlinear resource allocation problem," European Journal of Operational Research, Elsevier, vol. 185(1), pages 1-46, February.
    2. Desaulniers, G. & Desrosiers, J. & Dumas, Y. & Marc, S. & Rioux, B. & Solomon, M. M. & Soumis, F., 1997. "Crew pairing at Air France," European Journal of Operational Research, Elsevier, vol. 97(2), pages 245-259, March.
    3. Gamst, Mette & Neergaard Jensen, Peter & Pisinger, David & Plum, Christian, 2010. "Two- and three-index formulations of the minimum cost multicommodity k-splittable flow problem," European Journal of Operational Research, Elsevier, vol. 202(1), pages 82-89, April.
    4. Attila Bernáth & Tamás Király & Erika Kovács & Gergely Mádi-Nagy & Gyula Pap & Júlia Pap & Jácint Szabó & László Végh, 2013. "Algorithms for multiplayer multicommodity flow problems," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(4), pages 699-712, December.
    5. Pages, Adela & Nabona, Narcis, 2007. "A heuristic for the long-term electricity generation planning problem using the Bloom and Gallant formulation," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1245-1264, September.
    6. Zhu, Wenbin & Huang, Weili & Lim, Andrew, 2012. "A prototype column generation strategy for the multiple container loading problem," European Journal of Operational Research, Elsevier, vol. 223(1), pages 27-39.
    7. Spliet, Remy & Desaulniers, Guy, 2015. "The discrete time window assignment vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 244(2), pages 379-391.
    8. Delorme, Maxence & Iori, Manuel & Martello, Silvano, 2016. "Bin packing and cutting stock problems: Mathematical models and exact algorithms," European Journal of Operational Research, Elsevier, vol. 255(1), pages 1-20.
    9. repec:spr:mathme:v:87:y:2018:i:1:d:10.1007_s00186-017-0610-4 is not listed on IDEAS

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