In this paper, we have studied analytically the implication of a controllable lead-time and a random supplier capacity on the continuous review inventory policy, in which the order quantity, reorder point and lead-time are decision variables. Two models are considered: the normal lead-time demand and lead-time demand is distributed free. For both cases, after formulating the general model, some properties of the optimal ordering policy have been developed. Particularly, we have shown that the expected annual total cost is a unimodal function and quasi-convex in the order quantity. When the variable capacity distribution is exponential, we develop effective procedures for finding the optimal solutions. Furthermore, the effects of parameters are also performed.
