Optimum Search for Objects Having Unknown Arrival Times
Nelson M. Blachman, Frank Proschan · Operations Research · 1959
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.