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A General Algorithm for the Optimal Distribution of Effort

Author

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  • William Karush

    (System Development Corporation, Santa Monica, California)

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).

Suggested Citation

  • William Karush, 1962. "A General Algorithm for the Optimal Distribution of Effort," Management Science, INFORMS, vol. 9(1), pages 50-72, October.
    • Handle: RePEc:inm:ormnsc:v:9:y:1962:i:1:p:50-72
    DOI: 10.1287/mnsc.9.1.50
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    Cited by:

    1. Patriksson, Michael, 2008. "A survey on the continuous nonlinear resource allocation problem," European Journal of Operational Research, Elsevier, vol. 185(1), pages 1-46, February.
    2. Thomas L. Morin & Roy E. Marsten, 1974. "Brand-and-Bound Strategies for Dynamic Programming," Discussion Papers 106, Northwestern University, Center for Mathematical Studies in Economics and Management Science.

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