A Study on Generalized Ordering Policy

We discuss the generalized ordering policy: When an ordered spare is delivered after a randomized lead time, the spare is put into the inventory if an original unit is still operating, and it is replaced/exchanged by the spare in stock when it fails/passes a prespecified time. We derive the expected cost per unit time in the steady state as a criterion of optimality and obtain the optimal ordering policies to minimize the expected cost. We take up either the extreme policy in which the delivered spare is put into the inventory until the original unit fails, or the spare takes over the operation as soon as it is delivered.