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An Allocation Problem with Applications to Operations Research and Statistics

Author

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  • Samuel Zahl

    (Cambridge Air Force Research Laboratories, Bedford, Mass)

Abstract

A considerable number of problems in operations research and statistics have the following form maximize (integral) f [ x , y ( x )] dx subject to (integral) g [ x , y ( x )] dx = constant with respect to bounded y ( x ). We give a necessary and sufficient condition for a maximizing function under fairly weak restrictions and prove its existence. The solution is applied to a general version of B. O. Koopman's search problem, and to the Neyman, Pearson lemma of statistics. We also show that in the discrete version of this problem, where x is replaced by an index and sums replace integrals, our condition is sufficient but not necessary and give, as illustration of the sufficiency, a solution to an assignment problem.

Suggested Citation

  • Samuel Zahl, 1963. "An Allocation Problem with Applications to Operations Research and Statistics," Operations Research, INFORMS, vol. 11(3), pages 426-441, June.
    • Handle: RePEc:inm:oropre:v:11:y:1963:i:3:p:426-441
    DOI: 10.1287/opre.11.3.426
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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. Knut K. Aase, 2022. "Optimal Risk Sharing in Society," Mathematics, MDPI, vol. 10(1), pages 1-31, January.

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