IDEAS home Printed from
   My bibliography  Save this article

The exact fill rate in a periodic review base stock system under normally distributed demand


  • Silver, Edward A.
  • Bischak, Diane P.


In this paper, we consider a periodic review order-up-to-level (or base stock) inventory control system under normally distributed demand. For such circumstances, an expression for the exact fill rate (fraction of demand satisfied without backordering) has been available in the literature, but has not been widely known, let alone used by practitioners. In this paper, we redevelop the expression and contrast our derivation with the earlier published one. The paper has two purposes. First, we hope that the reappearance of the exact result in this journal will lead to its wider adoption. Second, showing two contrasting approaches to obtaining the same result may be useful for both research and pedagogical purposes.

Suggested Citation

  • Silver, Edward A. & Bischak, Diane P., 2011. "The exact fill rate in a periodic review base stock system under normally distributed demand," Omega, Elsevier, vol. 39(3), pages 346-349, June.
  • Handle: RePEc:eee:jomega:v:39:y:2011:i:3:p:346-349

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. Carlson, Marvin L & Miltenburg, G John, 1988. "Using the service point model to control large groups of items," Omega, Elsevier, vol. 16(5), pages 481-489.
    2. Chen, Fangruo & Zheng, Yu-Sheng, 1993. "Inventory models with general backorder costs," European Journal of Operational Research, Elsevier, vol. 65(2), pages 175-186, March.
    3. Matthew J. Sobel, 2004. "Fill Rates of Single-Stage and Multistage Supply Systems," Manufacturing & Service Operations Management, INFORMS, vol. 6(1), pages 41-52, June.
    4. de Kok, A. G., 1990. "Hierarchical production planning for consumer goods," European Journal of Operational Research, Elsevier, vol. 45(1), pages 55-69, March.
    5. Ward, SC & Chapman, CB & Klein, JH, 1991. "Theoretical versus applied models: The newsboy problem," Omega, Elsevier, vol. 19(4), pages 197-206.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Tempelmeier, Horst, 2011. "A column generation heuristic for dynamic capacitated lot sizing with random demand under a fill rate constraint," Omega, Elsevier, vol. 39(6), pages 627-633, December.
    2. Disney, Stephen M. & Gaalman, Gerard J.C. & Hedenstierna, Carl Philip T. & Hosoda, Takamichi, 2015. "Fill rate in a periodic review order-up-to policy under auto-correlated normally distributed, possibly negative, demand," International Journal of Production Economics, Elsevier, vol. 170(PB), pages 501-512.
    3. Teunter, R.H. & Syntetos, A.A. & Babai, M.Z., 2017. "Stock keeping unit fill rate specification," European Journal of Operational Research, Elsevier, vol. 259(3), pages 917-925.
    4. Lagodimos, A.G. & Christou, I.T. & Skouri, K., 2012. "Computing globally optimal (s,S,T) inventory policies," Omega, Elsevier, vol. 40(5), pages 660-671.
    5. repec:eee:proeco:v:198:y:2018:i:c:p:11-24 is not listed on IDEAS
    6. repec:eee:ejores:v:269:y:2018:i:1:p:244-257 is not listed on IDEAS
    7. Garcia, C.A. & Ibeas, A. & Herrera, J. & Vilanova, R., 2012. "Inventory control for the supply chain: An adaptive control approach based on the identification of the lead-time," Omega, Elsevier, vol. 40(3), pages 314-327.
    8. Guijarro, Ester & Cardós, Manuel & Babiloni, Eugenia, 2012. "On the exact calculation of the fill rate in a periodic review inventory policy under discrete demand patterns," European Journal of Operational Research, Elsevier, vol. 218(2), pages 442-447.
    9. Fang, Xin & Zhang, Cheng & Robb, David J. & Blackburn, Joseph D., 2013. "Decision support for lead time and demand variability reduction," Omega, Elsevier, vol. 41(2), pages 390-396.
    10. Rossi, Roberto & Kilic, Onur A. & Tarim, S. Armagan, 2015. "Piecewise linear approximations for the static–dynamic uncertainty strategy in stochastic lot-sizing," Omega, Elsevier, vol. 50(C), pages 126-140.


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jomega:v:39:y:2011:i:3:p:346-349. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.