A General Algorithm for the Optimal Distribution of Effort

William Karush
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William Karush: System Development Corporation, Santa Monica, California

Management Science, 1962, vol. 9, issue 1, 50-72

Abstract: The problem of distribution of effort is that of the optimal allocation of a given resource among various activities, that is, maximize \sum i-1 n f i (x i ) subject to \sum i-1 n x i - w, x i > 0. This paper presents an algorithm for obtaining the optimal allocation as a function of w, when the f i are arbitrary piecewise-linear, continuous functions. The method is recursive and appropriate for hand or machine computation. It is an extension of the well-known technique of ordering the segments of all the f i according to decreasing slope which applies in the special case when each f i has decreasing slopes (that is, is marginally decreasing).

Date: 1962
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:9:y:1962:i:1:p:50-72

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