Optimal Search of a Moving Target
Y. C. Kan · Operations Research · 1977
There are n boxes. A target is initially in box i with a given probability pı, where pı ≧ 0, ∑pı = 1. Then at discrete time t = 1, 2, …, it moves from box to box. If at time t the target is in box i, then it will be in box i with probability pij at time t + 1, where pij ≧ 0, ∑j pij = 1. A search of box i costs Cı(cı > 0) and finds the target with probability αı if the target is in that box. A sequential search is made. The objective is either to maximize the probability of finding the target in a given number of searches or to minimize the expected searching cost before finding the target. Optimal strategies are characterized for special types of probability matrices [pij] for the n-box model.