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The Group-Theoretic Structure in the Fixed-Charge Transportation Problem

Author

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  • J. L. Kennington

    (Southern Methodist University, Dallas, Texas)

  • V. E. Unger

    (Georgia Institute of Technology, Atlanta, Georgia)

Abstract

The multiparametric integer programming problem for the right-hand side is to minimize c ′ t subject to At = b ( y ), t ≧ 0, t = 0 (mod 1), where b ( y ) can be expressed in the form b ( y ) = b̄ + F ( y ), where F is a matrix of constant coefficients, and y is an integer vector parameter. The group problem associated with any integer programming problem may be viewed as a multiparametric integer programming problem. The purpose of this paper is to show that the group problem associated with the fixed-charge transportation problem can be viewed as a multiparametric integer programming problem having a totally unimodular constraint matrix.

Suggested Citation

  • J. L. Kennington & V. E. Unger, 1973. "The Group-Theoretic Structure in the Fixed-Charge Transportation Problem," Operations Research, INFORMS, vol. 21(5), pages 1142-1153, October.
    • Handle: RePEc:inm:oropre:v:21:y:1973:i:5:p:1142-1153
    DOI: 10.1287/opre.21.5.1142
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    Cited by:

    1. Jawahar, N. & Balaji, A.N., 2009. "A genetic algorithm for the two-stage supply chain distribution problem associated with a fixed charge," European Journal of Operational Research, Elsevier, vol. 194(2), pages 496-537, April.

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