A generalized model for jointly determining the optimal ordering point and the optimal number of minimal repairs before replacement

Many maintenance policies have assumed that whenever a unit is to he replaced, a new unit is immediately available. However, if the procurement lead time is not negligible, an ordering policy should be considered that determines when to order a spare and when to replace the operating unit after it has begun operating. A generalized model is presented to jointly determine the optimal ordering point and the optimal number of minimal repairs before replacement. By introducing costs due to ordering, repairs, shortage and holding, the expected cost per unit time in the long run is derived as a criterion of optimality, and the optimal ordering point and the optimal number of minimal repairs before replacement are sought by minimizing that cost. Various special cases are discussed. Finally, a numerical example is given.