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Some further results on minimum distribution cost flow problems

Author

Listed:
  • Haiyan Lu

    (Zhejiang University
    Southern Yangtze University)

  • Enyu Yao

    (Zhejiang University)

  • Liqun Qi

    (Hong Kong Polytechnic University)

Abstract

Manufacturing network flow (MNF) is a generalized network model that can model more complicated manufacturing scenarios, such as the synthesis of different materials to one product and/or the distilling of one material to many different products. Minimum distribution cost flow problem (MDCF) is a simplified version of MNF optimization problems, in which a general supplier wants to proportionally distribute certain amount of a particular product from a source node to several retailers at different destinations through a distribution network. A network simplex algorithm has been outlined in recent years for solving a special case of MDCF. In this paper, we characterize the network structure of the bases of the MDCF problem and develop a primal simplex algorithm that exploits the network structure of the problem. These results are extensions of those of the ordinary network flow problems. In conclusion, some related interesting problems are proposed for future research.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:11:y:2006:i:4:d:10.1007_s10878-006-8211-9
    DOI: 10.1007/s10878-006-8211-9
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    References listed on IDEAS

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    1. Calvete, Herminia I., 2003. "Network simplex algorithm for the general equal flow problem," European Journal of Operational Research, Elsevier, vol. 150(3), pages 585-600, November.
    2. Ravindra K. Ahuja & James B. Orlin & Giovanni M. Sechi & Paola Zuddas, 1999. "Algorithms for the Simple Equal Flow Problem," Management Science, INFORMS, vol. 45(10), pages 1440-1455, October.
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    Cited by:

    1. Gengjun Gao & Yuxuan Che & Jian Shen, 0. "Path optimization for joint distribution of medical consumables under hospital SPD supply chain mode," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-18.
    2. 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.
    3. 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.
    4. 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.
    5. Gengjun Gao & Yuxuan Che & Jian Shen, 2021. "Path optimization for joint distribution of medical consumables under hospital SPD supply chain mode," Journal of Combinatorial Optimization, Springer, vol. 42(4), pages 866-883, November.
    6. 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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