Generalized spare ordering policies with allowable inventory time

In this paper, a generalized ordering policy of a one-unit system with age-dependent minimal repair and random lead time is considered. We treat the general order-replacement model with two decision variables: ordering time and allowable inventory time. The allowable inventory period is measured from the time instant that the ordered spare is delivered. By introducing costs due to ordering, repairs, shortage, and holding, we derive the expected cost per unit time in the long run as a criterion of optimality, and seek the optimum policy by minimizing that cost. And we can prove under some mild conditions that there exists a finite and unique optimum policy. Various special cases are discussed.