Application of Programs with Maximin Objective Functions to Problems of Optimal Resource Allocation

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Abstract
A mathematical program with a maximin objective function is defined as an optimization problem of the following type: Maxz = minicixi, subject to AX = b, X ≠ﾧ 0. Although the ci can be in the interval ('—' ∞, ∞), the paper discusses the more common practical case where all ci ≠ﾧ 0. It shows that problems of this type arise in a variety of applications where it is required to maximize a production function of the \"fixed proportion\" type subject to a set of linear constraints. Although it is well known that the solution to this type of problem can be found by linear programming, this paper shows that, if the existence of a certain condition can be demonstrated, then a simplified method can be used to determine the optimum solution. Many problems of practical interest can be solved by this simplified method; an example involving the readiness of a ship is presented.

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