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Technical Note—Comments on the Distribution of Inventory Position in a Continuous-Review ( s , S ) Inventory System

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  • F. R. Richards

    (Naval Postgraduate School, Monterey, California)

Abstract

This paper comments on the limiting distribution of the inventory position in a continuous-review ( s , S ) inventory system with arbitrary customer interarrival-time distribution. The limiting distribution is derived for the general case in which the demand quantity is random. We show that the limiting distribution is uniform on ( s + 1, …, S ) if and only if units are demanded one at a time. However, with a slight modification of the procurement policy, the uniform distribution is recaptured even with random demand quantities.

Suggested Citation

  • F. R. Richards, 1975. "Technical Note—Comments on the Distribution of Inventory Position in a Continuous-Review ( s , S ) Inventory System," Operations Research, INFORMS, vol. 23(2), pages 366-371, April.
    • Handle: RePEc:inm:oropre:v:23:y:1975:i:2:p:366-371
    DOI: 10.1287/opre.23.2.366
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    Cited by:

    1. Y. Barron, 2019. "A state-dependent perishability (s, S) inventory model with random batch demands," Annals of Operations Research, Springer, vol. 280(1), pages 65-98, September.
    2. Kochel, P., 2007. "Order optimisation in multi-location models with hub-and-spoke structure," International Journal of Production Economics, Elsevier, vol. 108(1-2), pages 368-387, July.
    3. Li Chen & Hau L. Lee, 2012. "Bullwhip Effect Measurement and Its Implications," Operations Research, INFORMS, vol. 60(4), pages 771-784, August.
    4. Frenk, J.B.G. & Kleijn, M.J., 1997. "On regenerative processes and inventory control," Econometric Institute Research Papers EI 9741/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    5. Jing-Sheng Song, 2000. "A Note on Assemble-to-Order Systems with Batch Ordering," Management Science, INFORMS, vol. 46(5), pages 739-743, May.
    6. Noblesse, Ann M. & Boute, Robert N. & Lambrecht, Marc R. & Van Houdt, Benny, 2014. "Characterizing order processes of continuous review (s,S) and (r,nQ) policies," European Journal of Operational Research, Elsevier, vol. 236(2), pages 534-547.

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