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Optimum Search for Objects Having Unknown Arrival Times

Author

Listed:
  • Nelson Blachman

    (Electronic Defense Laboratory, Sylvania Electric Products, Inc., Mountain View, California)

  • Frank Proschan

    (Electronic Defense Laboratory, Sylvania Electric Products, Inc., Mountain View, California)

Abstract

In defense against missiles, early detection is crucial. This is the motivation for the mathematical solution of the following general search problem. Objects arrive in accordance with a Poisson process. Having arrived, the object appears (and remains until detected) in box i with probability p i . A single scan of box i costs Ci (possibly including the cost of false alarms), takes time t i , and, if the object is present in box i at the beginning of the scan, will detect it with probability Pi . The resultant gain g i ( t ) is a nonincreasing function of t , the delay between arrival and the beginning of the detecting look, i = 1, 2, ..., n . An asymptotically optimum search procedure is obtained. A number of particular cases of interest are solved.

Suggested Citation

  • Nelson Blachman & Frank Proschan, 1959. "Optimum Search for Objects Having Unknown Arrival Times," Operations Research, INFORMS, vol. 7(5), pages 625-638, October.
    • Handle: RePEc:inm:oropre:v:7:y:1959:i:5:p:625-638
    DOI: 10.1287/opre.7.5.625
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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.

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