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A comparison between the order and the volume fill rate for a base-stock inventory control system under a compound renewal demand process

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  • C Larsen

    (Aarhus School of Business, University of Aarhus)

  • A Thorstenson

    (Aarhus School of Business, University of Aarhus)

Abstract

The order fill rate (OFR) is sometimes suggested as an alternative to the volume fill rate (VFR) (most often just denoted fill rate) as a performance measure for inventory control systems. We consider a continuous review, base-stock policy, where replenishment orders have a constant lead time and unfilled demands are backordered. For this policy, we develop exact mathematical expressions for the two fill-rate measures when demand follows a compound renewal process. We also elaborate on when the OFR can be interpreted as the (extended) ready rate. For the case when customer orders are generated by a negative binomial distribution, we show that it is the size of the shape parameter of this distribution that determines the relative magnitude of the two fill rates. In particular, we show that when customer orders are generated by a geometric distribution, the OFR and the VFR are equal.

Suggested Citation

  • C Larsen & A Thorstenson, 2008. "A comparison between the order and the volume fill rate for a base-stock inventory control system under a compound renewal demand process," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(6), pages 798-804, June.
    • Handle: RePEc:pal:jorsoc:v:59:y:2008:i:6:d:10.1057_palgrave.jors.2602407
    DOI: 10.1057/palgrave.jors.2602407
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    References listed on IDEAS

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    Cited by:

    1. Babai, M.Z. & Jemai, Z. & Dallery, Y., 2011. "Analysis of order-up-to-level inventory systems with compound Poisson demand," European Journal of Operational Research, Elsevier, vol. 210(3), pages 552-558, May.
    2. Anh Ninh, 2021. "Robust newsvendor problems with compound Poisson demands," Annals of Operations Research, Springer, vol. 302(1), pages 327-338, July.
    3. Kouki, Chaaben & Babai, M. Zied & Jemai, Zied & Minner, Stefan, 2019. "Solution procedures for lost sales base-stock inventory systems with compound Poisson demand," International Journal of Production Economics, Elsevier, vol. 209(C), pages 172-182.
    4. Sofia Estelles-Miguel & Manuel Cardos & Jose Miguel Albarracin Guillem & Marta Palmer Gato, 2014. "Calculation of the Approaches to Cycle Service Level in Continuous Review Policy: A Tool for Corporate Entrepreneur," Business and Management Research, Business and Management Research, Sciedu Press, vol. 3(1), pages 54-60, March.
    5. Du, Bisheng & Larsen, Christian, 2011. "Base stock policies with degraded service to larger orders," International Journal of Production Economics, Elsevier, vol. 133(1), pages 326-333, September.
    6. 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.
    7. Prak, Dennis & Rogetzer, Patricia, 2022. "Timing intermittent demand with time-varying order-up-to levels," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1126-1136.
    8. Rossetti, Manuel D. & Yasin Ünlü, 2011. "Evaluating the robustness of lead time demand models," International Journal of Production Economics, Elsevier, vol. 134(1), pages 159-176, November.
    9. Teunter, R.H. & Syntetos, A.A. & Babai, M.Z., 2010. "Determining order-up-to levels under periodic review for compound binomial (intermittent) demand," European Journal of Operational Research, Elsevier, vol. 203(3), pages 619-624, June.
    10. Christian Larsen, 2017. "Inventory control with and without deliveries in several pieces," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(2), pages 607-622, March.
    11. Larsen, C. & Thorstenson, A., 2014. "The order and volume fill rates in inventory control systems," International Journal of Production Economics, Elsevier, vol. 147(PA), pages 13-19.

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