A general ordering policy with number-dependent minimal repair and random lead time

In this paper, we consider a general ordering policy with number-dependent minimal repair and random lead time. 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. We show that, under certain conditions, there exists a finite and unique optimum policy. Various special cases are discussed. A numerical example is given to illustrate the method.