Abstract
A decision maker will allocate his resources to appearing targets during a random number fo periods. There are finite types of targets. Each type of them appears with some fixed probability at the beginning of each period. When the target appears, he expends some of his resources to obtain the reward which depends on the number of resources expended and the type of appearing target. The objective is to find a sequence of number of resources to be expended which maximizes the total expected reward. The case of a given horizon was discussed in the previous paper [9] . It will be shown that the similar structure of an optimal policy also holds for the case of random horizon if a reasonable assumption is satisfied.
