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MONOTONE OPTIMAL CONTROL OF ARRIVALS DISTINGUISHED BY REWARD AND SERVICE TIME Sh6ichi Nishimura University of Tsukuba (Received September 6,1980; Final April 15, 1982) We consider a monotone optimal policy for a discrete time problem of controlling the arriving customers. At each period one customer arrives at a manufacturing factory to order a job distinguished by the reward and the service time with a constant delivery interval_ The basic properties of optimal policies are obtained. It is shown that, contrary to intuition, from counterexamples an optimal policy cannot generally be monotone in such cases as finite-horizon problems with and without discounting and an infinite-horizon problem with discounting, while there exists a monotone optimal policy for infinite-horizon problems without discounting.