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Decomposition Algorithm for a Nonlinear Three-Index Transportation Problem

Author

Listed:
  • Vladimir Lobantsov

    (Department of Higher Mathematics, Physics and Computer Science, State University of Land Use Planning, 15 Kazakov St., Moscow 105064, Russia)

  • Alexander Tizik

    (Central Research Institute of Communications, 8, 1st Perova Polya Proezd, Moscow 111141, Russia)

  • Vladimir Tsurkov

    (Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 42 Vavilov St., Moscow 119333, Russia)

  • Ivan Matveev

    (Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 42 Vavilov St., Moscow 119333, Russia)

Abstract

A three-index transportation problem is considered, where the indices stand for supplier, consumer, and type of product. A quite broad statement is allowed, including additional points of production, consumption, and nonlinear transportation costs therein. The solution method is a further development of a universal approach proposed earlier by the authors, which is based on the decomposition of the original problem into a sequence of two-dimensional problems with the recalculation of the objective function coefficients. This paper demonstrates the customization of the method to a nonlinear three-index problem.

Suggested Citation

  • Vladimir Lobantsov & Alexander Tizik & Vladimir Tsurkov & Ivan Matveev, 2025. "Decomposition Algorithm for a Nonlinear Three-Index Transportation Problem," Mathematics, MDPI, vol. 13(6), pages 1-11, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:6:p:944-:d:1610930
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    References listed on IDEAS

    as
    1. Geetha, S. & Vartak, M. N., 1994. "The three-dimensional bottleneck assignment problem with capacity constraints," European Journal of Operational Research, Elsevier, vol. 73(3), pages 562-568, March.
    2. Morton Klein, 1967. "A Primal Method for Minimal Cost Flows with Applications to the Assignment and Transportation Problems," Management Science, INFORMS, vol. 14(3), pages 205-220, November.
    3. L. Kantorovitch, 1958. "On the Translocation of Masses," Management Science, INFORMS, vol. 5(1), pages 1-4, October.
    4. Junginger, Werner, 1993. "On representatives of multi-index transportation problems," European Journal of Operational Research, Elsevier, vol. 66(3), pages 353-371, May.
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