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An efficient generalized network-simplex-based algorithm for manufacturing network flows

Author

Listed:
  • Prahalad Venkateshan

    (AmTrust Bank)

  • Kamlesh Mathur

    (Case Western Reserve University)

  • Ronald H. Ballou

    (Case Western Reserve University)

Abstract

Fang and Qi (Optim. Methods Softw. 18:143–165, 2003) introduced a new generalized network flow model called manufacturing network flow model for manufacturing process modeling. A key distinguishing feature of such models is the assembling of component raw-materials, in a given proportion, into an end-product. This assembling operation cannot be modeled using usual generalized networks (which allow gains and losses in flows), or using multi-commodity networks (which allow flows of multiple commodity types on a single arc). The authors developed a network-simplex-based algorithm to solve a minimum cost flow problem formulated on such a generalized network and indicated systems of linear equations that need to be solved during the course of the network-simplex-based solution procedure. In this paper, it is first shown how various steps of the network-simplex-based solution procedure can be performed efficiently using appropriate data structures. Further, it is also shown how the resulting system of linear equations can be solved directly on the generalized network.

Suggested Citation

  • Prahalad Venkateshan & Kamlesh Mathur & Ronald H. Ballou, 2008. "An efficient generalized network-simplex-based algorithm for manufacturing network flows," Journal of Combinatorial Optimization, Springer, vol. 15(4), pages 315-341, May.
    • Handle: RePEc:spr:jcomop:v:15:y:2008:i:4:d:10.1007_s10878-007-9080-6
    DOI: 10.1007/s10878-007-9080-6
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    References listed on IDEAS

    as
    1. Haiyan Lu & Enyu Yao & Liqun Qi, 2006. "Some further results on minimum distribution cost flow problems," Journal of Combinatorial Optimization, Springer, vol. 11(4), pages 351-371, June.
    2. A. M. Geoffrion & G. W. Graves, 1974. "Multicommodity Distribution System Design by Benders Decomposition," Management Science, INFORMS, vol. 20(5), pages 822-844, January.
    3. Ellis L. Johnson, 1966. "Networks and Basic Solutions," Operations Research, INFORMS, vol. 14(4), pages 619-623, August.
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    Cited by:

    1. Michael Holzhauser & Sven O. Krumke & Clemens Thielen, 2017. "Maximum flows in generalized processing networks," Journal of Combinatorial Optimization, Springer, vol. 33(4), pages 1226-1256, May.
    2. Mohammad Ali Raayatpanah & Salman Khodayifar & Thomas Weise & Panos Pardalos, 2022. "A novel approach to subgraph selection with multiple weights on arcs," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 242-268, August.
    3. David R. Morrison & Jason J. Sauppe & Sheldon H. Jacobson, 2013. "A Network Simplex Algorithm for the Equal Flow Problem on a Generalized Network," INFORMS Journal on Computing, INFORMS, vol. 25(1), pages 2-12, February.
    4. ÇalIskan, Cenk, 2011. "A specialized network simplex algorithm for the constrained maximum flow problem," European Journal of Operational Research, Elsevier, vol. 210(2), pages 137-147, April.

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