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Optimal Stopping in a Discrete Search Problem

In a search among m locations for an object possibly hidden in one, we are given prior probabilities of location pi, searching costs ci, and overlook probabilities αi. It is known also that an "unsearchable" location contains the object with prior probability p0, and, in addition, a penalty cost C is charged if the search is terminated unsuccessfully. Although an optimal search strategy for the problem is known, the best stopping rule is not. Under a certain constraint on C, independent of the prior probabilities pi, the optimal stopping rule is shown to be determined by the optimal m-stage look-ahead strategy.