The Linear Sharing Problem

J. Randall Brown
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J. Randall Brown: Kent State University, Kent, Ohio

Operations Research, 1984, vol. 32, issue 5, 1087-1106

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.

Keywords: 646; maximin; objective; function; with; linear; constraints (search for similar items in EconPapers)
Date: 1984
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