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A Note on the Optimality of (S, s) Policies in Inventory Theory

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  • Edward Zabel

    (The University of Rochester)

Abstract

In this paper a proof of Herbert Scarf's on the optimality of (S, s) policies in inventory theory is extended to cases where differentiability of cost functions may not be available. In addition to an ordering cost composed of a unit cost plus a reorder cost all that is needed in the proof is that the expected holding and shortage cost function be convex.

Suggested Citation

  • Edward Zabel, 1962. "A Note on the Optimality of (S, s) Policies in Inventory Theory," Management Science, INFORMS, vol. 9(1), pages 123-125, October.
    • Handle: RePEc:inm:ormnsc:v:9:y:1962:i:1:p:123-125
    DOI: 10.1287/mnsc.9.1.123
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    Cited by:

    1. Bijvank, Marco & Vis, Iris F.A., 2011. "Lost-sales inventory theory: A review," European Journal of Operational Research, Elsevier, vol. 215(1), pages 1-13, November.
    2. Jian Yang & Jim (Junmin) Shi, 2023. "Discrete‐item inventory control involving unknown censored demand and convex inventory costs," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 45-64, January.
    3. Eugene A. Feinberg & Mark E. Lewis, 2018. "On the convergence of optimal actions for Markov decision processes and the optimality of (s, S) inventory policies," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(8), pages 619-637, December.
    4. Sandun C. Perera & Suresh P. Sethi, 2023. "A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Discrete‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 131-153, January.
    5. Eugene A. Feinberg & Yan Liang, 2022. "Structure of optimal policies to periodic-review inventory models with convex costs and backorders for all values of discount factors," Annals of Operations Research, Springer, vol. 317(1), pages 29-45, October.

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