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

Author

Listed:
  • Awi Federgruen

    (Columbia University, New York, New York)

  • Yu-Sheng Zheng

    (University of Pennsylvania, Philadelphia, Pennsylvania)

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 *).

Suggested Citation

  • Awi Federgruen & Yu-Sheng Zheng, 1992. "An Efficient Algorithm for Computing an Optimal (r, Q) Policy in Continuous Review Stochastic Inventory Systems," Operations Research, INFORMS, vol. 40(4), pages 808-813, August.
    • Handle: RePEc:inm:oropre:v:40:y:1992:i:4:p:808-813
    DOI: 10.1287/opre.40.4.808
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