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Exact fill rates for (R, s, S) inventory control with gamma distributed demand

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  • J J A Moors

    (Center for Economic Research, Tilburg University)

  • L W G Strijbosch

    (Center for Economic Research, Tilburg University)

Abstract

For the familiar (R, s, S) inventory control system only approximate expressions exist for the fill rate, ie the fraction of demand that can be satisfied from stock. Best-known are the approximations derived from renewal theory, holding under specific conditions; in particular, S–s should be reasonably large. Here, an exact expression for the fill rate is derived, holding generally in the situation that demand has a gamma distribution with known integer-valued shape parameter, while lead time is constant. These exact results allow a check of the renewal theory based approximations. In addition, an extremely fast simulation program was written, obviously holding for general shape parameter values.

Suggested Citation

  • J J A Moors & L W G Strijbosch, 2002. "Exact fill rates for (R, s, S) inventory control with gamma distributed demand," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(11), pages 1268-1274, November.
    • Handle: RePEc:pal:jorsoc:v:53:y:2002:i:11:d:10.1057_palgrave.jors.2601441
    DOI: 10.1057/palgrave.jors.2601441
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    1. Strijbosch, L.W.G. & Moors, J.J.A., 1999. "Simple Expressions for Safety Factors in Inventory Control," Discussion Paper 1999-112, Tilburg University, Center for Economic Research.
    2. Strijbosch, L.W.G. & Moors, J.J.A., 1999. "Simple Expressions for Safety Factors in Inventory Control," Other publications TiSEM 2f1bb350-ce71-4adf-beca-b, Tilburg University, School of Economics and Management.
    3. Sridhar Bashyam & Michael C. Fu, 1998. "Optimization of (s, S) Inventory Systems with Random Lead Times and a Service Level Constraint," Management Science, INFORMS, vol. 44(12-Part-2), pages 243-256, December.
    4. Helmut Schneider & Jeffrey L. Ringuest, 1990. "Power Approximation for Computing (s, S) Policies Using Service Level," Management Science, INFORMS, vol. 36(7), pages 822-834, July.
    5. Tijms, H. C. & Groenevelt, H., 1984. "Simple approximations for the reorder point in periodic and continuous review (s, S) inventory systems with service level constraints," European Journal of Operational Research, Elsevier, vol. 17(2), pages 175-190, August.
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    Cited by:

    1. Noordhoek, Marije & Dullaert, Wout & Lai, David S.W. & de Leeuw, Sander, 2018. "A simulation–optimization approach for a service-constrained multi-echelon distribution network," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 114(C), pages 292-311.
    2. Strijbosch, L. W. G. & Moors, J. J. A., 2005. "The impact of unknown demand parameters on (R,S)-inventory control performance," European Journal of Operational Research, Elsevier, vol. 162(3), pages 805-815, May.
    3. E A Silver & H Naseraldin & D P Bischak, 2009. "Determining the reorder point and order-up-to-level in a periodic review system so as to achieve a desired fill rate and a desired average time between replenishments," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(9), pages 1244-1253, September.
    4. Strijbosch, L.W.G. & Moors, J.J.A., 2003. "Modified Normal Demand Distributions in (R,S)-Inventory Models," Discussion Paper 2003-76, Tilburg University, Center for Economic Research.
    5. Strijbosch, L.W.G. & Moors, J.J.A., 2003. "Modified Normal Demand Distributions in (R,S)-Inventory Models," Other publications TiSEM 8cb6e884-a1d3-4619-b506-9, Tilburg University, School of Economics and Management.
    6. Strijbosch, L.W.G. & Moors, J.J.A., 2006. "Modified normal demand distributions in (R, S)-inventory control," European Journal of Operational Research, Elsevier, vol. 172(1), pages 201-212, July.
    7. Jiang, R., 2008. "A Gamma–normal series truncation approximation for computing the Weibull renewal function," Reliability Engineering and System Safety, Elsevier, vol. 93(4), pages 616-626.
    8. Eugenia Babiloni & Ester Guijarro & Juan R. Trapero, 2023. "Stock control analytics: a data-driven approach to compute the fill rate considering undershoots," Operational Research, Springer, vol. 23(1), pages 1-25, March.
    9. Tal Avinadav, 2015. "Continuous accounting of inventory costs with Brownian-motion and Poisson demand processes," Annals of Operations Research, Springer, vol. 229(1), pages 85-102, June.

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    More about this item

    Keywords

    fill rate; gamma demand; inventory control; (R; s; S)-policy; simulation;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

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