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The Linear Sharing Problem

Author

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  • J. Randall Brown

    (Kent State University, Kent, Ohio)

Abstract

The linear sharing problem is defined as a linear programming problem with a maximin objective function comprised of nondecreasing, continuous tradeoff functions. This paper develops some properties, including optimality conditions, for this problem. It also develops an efficient algorithm that alternately calculates a new global upper bound on the objective function and then determines if a feasible solution exists that meets the new objective function global upper bound. The process continues until the algorithm finds a feasible and, thus, an optimal solution. The algorithm also determines if the problem contains no feasible solution or if the objective function is unbounded. A technique to handle problems with unbounded tradeoff variables is developed and computational experience is given.

Suggested Citation

  • J. Randall Brown, 1984. "The Linear Sharing Problem," Operations Research, INFORMS, vol. 32(5), pages 1087-1106, October.
    • Handle: RePEc:inm:oropre:v:32:y:1984:i:5:p:1087-1106
    DOI: 10.1287/opre.32.5.1087
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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.
    2. Ahuja, Ravindra K., 1997. "The balanced linear programming problem," European Journal of Operational Research, Elsevier, vol. 101(1), pages 29-38, August.
    3. Klein, Rachelle S. & Luss, Hanan & Rothblum, Uriel G., 1995. "Multiperiod allocation of substitutable resources," European Journal of Operational Research, Elsevier, vol. 85(3), pages 488-503, September.

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