In this paper we consider a continuous review inventory system in which the lead time L includes a part of fixed duration, T, and a part whose duration can be either Ta or Te, where Ta > Te. When the net inventory reaches the reorder point r, an order of size Q is released. If the net inventory at time T after the order release is equal to or smaller than re, the order is expedited at a cost comprising a fixed cost and a cost per unit and the lead time is L = T + Te, otherwise the lead time is L = T + Ta. Therefore, the decision variables considered are the order quantity Q, the reorder point r and the order expediting point re. Our aim is to find the inventory policy variables Q, r and re that minimize the average cost rate. We present an algorithm to obtain the policy variables with global minimal costs when the inventory policy decision variables are integers. We also discuss the case in which the decision variables are real valued.
