Optimal Selection of the T Best of a Sequence with Sampling Cost

TSis paper deals with the problem of select ing the t best of n independent and i den t i ca l l y d ist r ibu ted random variables which are observed sequen t ia l l y with sampling cost c per un i t . Assume that a decision for acceptance or re jec t ion must be made a f ter each sampling and that the reward for each observation with value x is given by px c where p is 1 i f the observation is accepted or 0 otherwise. The optimal decision procedure (st rategy) for maximizing the to ta l expected reward is obtained. The c r i t i c a l numbers which are necessary to carry out the optimal decision procedure is presented by two recursive equations. The l i m i t values of the c r i t i c a l numbers and the expected sample size are also studied. KEY WORDSSequential decision problem, to ta l expected reward, dynamic programming, sampling cost.