An Efficient Algorithm for Computing an Optimal (r, Q) Policy in Continuous Review Stochastic Inventory Systems

Operations Research · 1992 · Volume 40 · Issue 4

Abstract

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 parameters 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 (6 r * + 13 Q *) 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 *).

Keywords

inventory/production: stochastic policies

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