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Multi-Commodity Network Flows

Author

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  • T. C. Hu

    (IBM Research Center, Yorktown Heights, New york)

Abstract

A network is a set of nodes N ı connected by arcs with nonnegative arc capacities b ıj which indicates the maximum amount of flow that can pass through the arc from N ı to N j . Given all b ıj , there is a maximum flow from N ı to N j using all arcs. Under the assumption that b ıj = b jı , the present paper generalizes the max-flow min-cut theorem of Ford and Fulkerson to the problem of finding the maximum simultaneous flows of two commodities and gives an algorithm similar to the labelling method for constructing the two flows.

Suggested Citation

  • T. C. Hu, 1963. "Multi-Commodity Network Flows," Operations Research, INFORMS, vol. 11(3), pages 344-360, June.
    • Handle: RePEc:inm:oropre:v:11:y:1963:i:3:p:344-360
    DOI: 10.1287/opre.11.3.344
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    Citations

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    Cited by:

    1. Pengfei Zhang & Neng Fan, 2017. "Analysis of budget for interdiction on multicommodity network flows," Journal of Global Optimization, Springer, vol. 67(3), pages 495-525, March.
    2. Natalia Vanetik, 2012. "On the fractionality of the path packing problem," Journal of Combinatorial Optimization, Springer, vol. 24(4), pages 526-539, November.
    3. Lin, Yi-Kuei, 2007. "Generate upper boundary vectors meeting the demand and budget for a p-commodity network with unreliable nodes," European Journal of Operational Research, Elsevier, vol. 183(1), pages 253-262, November.
    4. A. Ouorou & P. Mahey & J.-Ph. Vial, 2000. "A Survey of Algorithms for Convex Multicommodity Flow Problems," Management Science, INFORMS, vol. 46(1), pages 126-147, January.
    5. Yeh, Wei-Chang, 2008. "A simple minimal path method for estimating the weighted multi-commodity multistate unreliable networks reliability," Reliability Engineering and System Safety, Elsevier, vol. 93(1), pages 125-136.
    6. Hiroshi Hirai, 2014. "The Maximum Multiflow Problems with Bounded Fractionality," Mathematics of Operations Research, INFORMS, vol. 39(1), pages 60-104, February.
    7. Fred Glover & Gary Kochenberger & Moses Ma & Yu Du, 2022. "Quantum Bridge Analytics II: QUBO-Plus, network optimization and combinatorial chaining for asset exchange," Annals of Operations Research, Springer, vol. 314(1), pages 185-212, July.
    8. Elke Eisenschmidt & Utz-Uwe Haus, 2013. "A polynomial time approximation algorithm for the two-commodity splittable flow problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(3), pages 381-391, June.
    9. Sedeno-Noda, A. & Gonzalez-Martin, C. & Gutierrez, J., 2005. "The biobjective undirected two-commodity minimum cost flow problem," European Journal of Operational Research, Elsevier, vol. 164(1), pages 89-103, July.
    10. Lin, Yi-Kuei, 2007. "On a multicommodity stochastic-flow network with unreliable nodes subject to budget constraint," European Journal of Operational Research, Elsevier, vol. 176(1), pages 347-360, January.
    11. Myung, Young-Soo & Kim, Hyun-joon, 2004. "A cutting plane algorithm for computing k-edge survivability of a network," European Journal of Operational Research, Elsevier, vol. 156(3), pages 579-589, August.
    12. Bertrand Guenin, 2002. "Integral Polyhedra Related to Even-Cycle and Even-Cut Matroids," Mathematics of Operations Research, INFORMS, vol. 27(4), pages 693-710, November.
    13. Ali Kakhbod & S. Tabatabaei Yazdi, 2010. "On describing the routing capacity regions of networks," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(1), pages 95-106, August.
    14. Fred Glover & Gary Kochenberger & Moses Ma & Yu Du, 2020. "Quantum Bridge Analytics II: QUBO-Plus, network optimization and combinatorial chaining for asset exchange," 4OR, Springer, vol. 18(4), pages 387-417, December.
    15. Lin, Yi-Kuei, 2007. "Performance evaluation for the logistics system in case that capacity weight varies from arcs and types of commodity," International Journal of Production Economics, Elsevier, vol. 107(2), pages 572-580, June.
    16. Lin, Yi-Kuei, 2006. "A simple algorithm to generate all (d,B)-MCs of a multicommodity stochastic-flow network," Reliability Engineering and System Safety, Elsevier, vol. 91(8), pages 923-929.
    17. 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.
    18. Lin, Yi-Kuei, 2007. "Reliability of a computer network in case capacity weight varying with arcs, nodes and types of commodity," Reliability Engineering and System Safety, Elsevier, vol. 92(5), pages 646-652.
    19. Lin, Yi-Kuei, 2010. "A stochastic model to study the system capacity for supply chains in terms of minimal cuts," International Journal of Production Economics, Elsevier, vol. 124(1), pages 181-187, March.

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