A Problem in Optimal Search and Stop

Sheldon M. Ross
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Sheldon M. Ross: University of California, Berkeley, California

Operations Research, 1969, vol. 17, issue 6, 984-992

Abstract: We are told that an object is hidden in one of m ( m p i 0 that the object is in the i th box. A search of box i costs c i and finds the object with probability α, if the object is in the box. Also, we suppose that a reward R i is earned if the object is found in the i th 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 α i p i / c i or else it never searches such boxes. Also, if rewards are equal, then an optimal strategy either searches a box with maximal α i p i / c i or else it stops.

Date: 1969
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