## Awi Federgruen

*An efficient algorithm for computing an optimal (**r, Q*) policy in continuous review stochastic inventory systems

Coauthor(s): Yu-Sheng Zheng.

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**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 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 (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**).

**Source:** *Operations Research*

**Exact Citation:**

Federgruen, Awi, and Yu-Sheng Zheng. "An efficient algorithm for computing an optimal (*r, Q*) policy in continuous review stochastic inventory systems." *Operations Research* 40, no. 4 (1992): 808-813.

**Volume:** 40

**Number:** 4

**Pages:** 808-813

**Date:**
1992