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Optimal discrete search with technological choice

Author

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  • Joseph B. Kadane

    (Carnegie Mellon University)

Abstract

Consider a search problem in which a stationary object is in one of $$L \epsilon \mathcal {N}$$ L ϵ N locations. Each location can be searched using one of $$T \epsilon \mathcal {N}$$ T ϵ N technologies, and each location-technology pair has a known associated cost and overlook probability. These quantities may depend on the number of times that the technology is applied to the location. This paper finds a search policy that maximizes the probability of finding the object given a constraint on the available budget. It also finds the policy that maximizes the probability of correctly stating at the end of a search where the object is. Additionally it exhibits another policy that minimizes the expected cost required to find the object and the optimal policy for stopping.

Suggested Citation

  • Joseph B. Kadane, 2015. "Optimal discrete search with technological choice," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(3), pages 317-336, June.
    • Handle: RePEc:spr:mathme:v:81:y:2015:i:3:d:10.1007_s00186-015-0499-8
    DOI: 10.1007/s00186-015-0499-8
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    References listed on IDEAS

    as
    1. Joseph B. Kadane, 1971. "Optimal Whereabouts Search," Operations Research, INFORMS, vol. 19(4), pages 894-904, August.
    2. Keith P. Tognetti, 1968. "Letter to the Editor—An Optimal Strategy for a Whereabouts Search," Operations Research, INFORMS, vol. 16(1), pages 209-211, February.
    3. Moshe Kress & Kyle Lin & Roberto Szechtman, 2008. "Optimal discrete search with imperfect specificity," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(3), pages 539-549, December.
    4. Nah-Oak Song & Demosthenis Teneketzis, 2004. "Discrete search with multiple sensors," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(1), pages 1-13, September.
    5. 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.
    6. Scott Shorey Brown, 1980. "Optimal Search for a Moving Target in Discrete Time and Space," Operations Research, INFORMS, vol. 28(6), pages 1275-1289, December.
    7. Donald F. Mela, 1961. "Letter to the Editor---Information Theory and Search Theory as Special Cases of Decision Theory," Operations Research, INFORMS, vol. 9(6), pages 907-909, December.
    8. Bernard O. Koopman, 1957. "The Theory of Search," Operations Research, INFORMS, vol. 5(5), pages 613-626, October.
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