This article studies (nQ,r) inventory policies, under which the order quantity is restricted to be an integer multiple of a base lot size Q. Both Q and r are decision variables. Assuming the one-period expected holding and backorder cost function is unimodal, the authors develop an efficient algorithm to compute the optimal Q and r. The algorithm is facilitated by simple observations about the cost function and by tight upper bounds on the optimal Q. The total number of elementary operations required by the algorithm is linear in these upper bounds. By using the algorithm, the authors compare the performance of the optimal (nQ,r) policy with that of the optimal (s,S) policy through a numerical study, and the present results show that the difference between them is small. Further analysis of the model shows that the cost performance of an (nQ,r) policy is insensitive to the choice of Q. These results establish that (nQ,r) models are potentially useful in many settings where quantized ordering is beneficial.
