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A mofified gub algorithm for solving linear minimax problems

Author

Listed:
  • Takahito Kuno
  • Kouji Mori
  • Hiroshi Konno

Abstract

This article is concerned with the minimization of the maximal value of a set of linear functions subject to linear constraints. It is well known that this problem can be transformed into a standard linear programming problem by introducing an additional variable. In case index sets of nonzero coefficients of the variables contained in each function are mutually exclusive, the constraints of the associated LP problem exhibit the almost‐GUB structure. We devised a technique which reduces the number of arithmetic operations by exploiting this special structure. Computational results are also presented, which indicates that our method is more efficient than the ordinary revised simplex method.

Suggested Citation

  • Takahito Kuno & Kouji Mori & Hiroshi Konno, 1989. "A mofified gub algorithm for solving linear minimax problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(3), pages 311-320, June.
    • Handle: RePEc:wly:navres:v:36:y:1989:i:3:p:311-320
    DOI: 10.1002/1520-6750(198906)36:33.0.CO;2-L
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    References listed on IDEAS

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    1. R. K. Ahuja, 1986. "Algorithms for the minimax transportation problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 33(4), pages 725-739, November.
    2. Seymour Kaplan, 1974. "Application of Programs with Maximin Objective Functions to Problems of Optimal Resource Allocation," Operations Research, INFORMS, vol. 22(4), pages 802-807, August.
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    Cited by:

    1. Hanan Luss, 1999. "On Equitable Resource Allocation Problems: A Lexicographic Minimax Approach," Operations Research, INFORMS, vol. 47(3), pages 361-378, June.

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