Optimal Search and Stop in Continuous Search Process

This paper investigates an optimal search policy with stopping for a stationary target being in one of n boxes. It is assumed that the search is conducted continuously with a total search cost C per unit time and the search in box i costs ci per unit search effort. The conditional probability of detecting the target with unit search effort is Oli and a reward Ri is given to the searcher when he successfully detects the target in box i. We derive conditions for the optimal search and stop policy which minimizes the expected risk of the search (the expected search cost minus the expected reward). The physical meaning of the conditions and several properties of the optimal policy are elucidated. The optimal policy for two-box case is examined in detail, and necessary and sufficient conditions for the optimal policy and the closed form risk function are obtained.