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

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.