A Problem in Optimal Search and Stop

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Abstract
We are told that an object is hidden in one of m(m < ∞) boxes and we are given prior probabilities pi0 that the object is in the ith box. A search of box i costs ci and finds the object with probability α, if the object is in the box. Also, we suppose that a reward Ri is earned if the object is found in the ith box. A strategy is any rule for determining when to search, and, if so, which box. The major result is that an optimal strategy either searches a box with maximal value of αipi/ci or else it never searches such boxes. Also, if rewards are equal, then an optimal strategy either searches a box with maximal αipi/ci or else it stops.

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