A Problem in Optimal Search and Stop

We are told that an object is hidden in one of m(m < ») boxes and we are given prior probabilities p. that the object is In the i box. A search of box i costs c. and finds the object with probability a. if the object is in the box. Also, we suppose that a reward R. is earned if the object Is found in the i 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 teith maximal value of o.p./c. or else it never searches those boxes. Also, if rewards are equal, then an optimal strategy either searches a box with maximal a.p./c. or else It stops. A PROBLEM IN OPTIMAL SEARCH AND STOP Sheldon M. Ross University of California, Berkeley