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


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

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    Bibliographic Info

    Article provided by Elsevier in its journal Omega.

    Volume (Year): 39 (2011)
    Issue (Month): 3 (June)
    Pages: 346-349

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    Handle: RePEc:eee:jomega:v:39:y:2011:i:3:p:346-349

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    Keywords: Inventory control Base stock Fill rate Normal distribution;


    References listed on IDEAS
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    1. de Kok, A. G., 1990. "Hierarchical production planning for consumer goods," European Journal of Operational Research, Elsevier, Elsevier, vol. 45(1), pages 55-69, March.
    2. Matthew J. Sobel, 2004. "Fill Rates of Single-Stage and Multistage Supply Systems," Manufacturing & Service Operations Management, INFORMS, INFORMS, vol. 6(1), pages 41-52, June.
    3. Ward, SC & Chapman, CB & Klein, JH, 1991. "Theoretical versus applied models: The newsboy problem," Omega, Elsevier, Elsevier, vol. 19(4), pages 197-206.
    4. Chen, Fangruo & Zheng, Yu-Sheng, 1993. "Inventory models with general backorder costs," European Journal of Operational Research, Elsevier, Elsevier, vol. 65(2), pages 175-186, March.
    5. Carlson, Marvin L & Miltenburg, G John, 1988. "Using the service point model to control large groups of items," Omega, Elsevier, Elsevier, vol. 16(5), pages 481-489.
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    Cited by:
    1. Fang, Xin & Zhang, Cheng & Robb, David J. & Blackburn, Joseph D., 2013. "Decision support for lead time and demand variability reduction," Omega, Elsevier, Elsevier, vol. 41(2), pages 390-396.
    2. 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, Elsevier, vol. 218(2), pages 442-447.
    3. 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, Elsevier, vol. 40(3), pages 314-327.
    4. Tempelmeier, Horst, 2011. "A column generation heuristic for dynamic capacitated lot sizing with random demand under a fill rate constraint," Omega, Elsevier, Elsevier, vol. 39(6), pages 627-633, December.


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