The reorder point/reorder quantity policies, also referred to as (r, Q) policies, are widely used in industry and extensively studied in the literature. However, for a period of almost 30 years there has been no efficient algorithm for computing optimal control parameteres for such policies. In this paper, we present a surprisingly simple and efficient algorithm for the determination of an optimal (r*, Q*) policy. The computational complexity of the algorithm is linear in Q*. For the most prevalent case of linear holding, backlogging and stockout penalty costs (in addition to fixed order costs), the algorithm requires at most (6r* + 13Q*) elementary operations (additions, comparisons and multiplications), and hence, no more than 13 times the amount of work required to do a single evaluation of the long-run average cost function in the point (r*, Q*).