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Optimum Distribution of Effort: An Extension of the Koopman Basic Theory

Author

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  • Jacques de Guenin

    (Groupe de Recherche Opérationnelle, Esso Standard, Paris, France)

Abstract

The fundamental problem of search theory is to allocate a given amount of search effort in such a way as to maximize the over-all probability of discovering an object located in a given space. The problem has already been solved under the assumption that the probability of detecting the object is a negative exponential function of the search effort density, this assumption seems to be fairly realistic in many military applications, but has definite drawbacks in others. In this paper a method is provided for solving the problem in the general case, where no assumption is made concerning the form of the detection probability function. A theorem is derived that gives a general relation governing the optimal solution.

Suggested Citation

  • Jacques de Guenin, 1961. "Optimum Distribution of Effort: An Extension of the Koopman Basic Theory," Operations Research, INFORMS, vol. 9(1), pages 1-7, February.
    • Handle: RePEc:inm:oropre:v:9:y:1961:i:1:p:1-7
    DOI: 10.1287/opre.9.1.1
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    Cited by:

    1. Stanley J. Benkoski & Michael G. Monticino & James R. Weisinger, 1991. "A survey of the search theory literature," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(4), pages 469-494, August.
    2. Delavernhe, Florian & Jaillet, Patrick & Rossi, André & Sevaux, Marc, 2021. "Planning a multi-sensors search for a moving target considering traveling costs," European Journal of Operational Research, Elsevier, vol. 292(2), pages 469-482.
    3. Frédéric Dambreville & Jean‐Pierre Le Cadre, 2002. "Detection of a Markovian target with optimization of the search efforts under generalized linear constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(2), pages 117-142, March.
    4. Frédéric Dambreville & Jean‐Pierre Le Cadre, 2007. "Constrained minimax optimization of continuous search efforts for the detection of a stationary target," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(6), pages 589-601, September.

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