Optimum planned maintenance with discounting

In this paper we treat the optimum ordering policy, in which when an ordered spare is delivered, it can be put into inventory until a prespecified time if the original unit is still operating. We apply the expected total discounted cost as a criterion of optimality, introducing, with an exponential discount rate, two types of lead times and several costs. It is shown that under certain conditions there exist optimum ordering policies minimizing that expected cost. Finally, the results in this paper include those in an earlier paper by Kaio and Osaki (1978) as special cases.