Search theory: A sequential approach
James M. Dobbie · Naval Research Logistics Quarterly · 1963
Abstract Koopman and others have noted that the optimal distribution of effort, to maximize the detection probability with a given effort, has the property that it is the sum of the distributions obtained by optimizing conditionally when the effort is applied sequentially. The approach taken in this present investigation is to reverse the procedure by determining conditions under which the optimal distribution has this property, and then to use this property to find the optimal distribution. This method easily yields essentially all of the known results, both for the discrete and continuous cases, and for the two criteria of maximizing the detection probability with a given effort and minimizing the expected effort to attain a given attainable probability of detection. The method also yields some modest extensions. In the discrete case the method is equivalent to the simplest form of dynamic programming.