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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. 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.
    2. 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.

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