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Determining Reorder Points When Demand is Lumpy

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  • J. B. Ward

    (Pacific Power & Light Company, Portland, Oregon)

Abstract

Lumpy or sporadic demand patterns with highly skewed distributions are common in parts and supplies types of stockholdings, and much of available inventory control methodology is not appropriate for such items. This paper presents a simple, easily used regression model to calculate order points for lumpy items from knowledge of demand parameters and the desired service level. It is derived from the particular compound Poisson distribution commonly called "stuttering Poisson." Results are derived and presented in the following framework, though application is not limited to these conditions. The control discipline is the order quantity, order point (Q, R) approach with continuous review. Lead time is assumed to be known and constant. An assigned service level is assumed based on fraction of demand supplied without backorder. Joint optimization of Q and R is not addressed, but rather order point is based on an independently calculated order quantity. Forecasting methods are not addressed, but the mean and variance of lead time demand forecasts are assumed available.

Suggested Citation

  • J. B. Ward, 1978. "Determining Reorder Points When Demand is Lumpy," Management Science, INFORMS, vol. 24(6), pages 623-632, February.
    • Handle: RePEc:inm:ormnsc:v:24:y:1978:i:6:p:623-632
    DOI: 10.1287/mnsc.24.6.623
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    Cited by:

    1. Uttarayan Bagchi, 1987. "Modeling lead‐time demand for lumpy demand and variable lead time," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(5), pages 687-704, October.
    2. Larsen, Christian, 2008. "Derivation of confidence intervals of service measures in a base-stock inventory control system with low-frequent demand," CORAL Working Papers L-2008-03, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    3. Hahn, G.J. & Leucht, A., 2015. "Managing inventory systems of slow-moving items," International Journal of Production Economics, Elsevier, vol. 170(PB), pages 543-550.
    4. Prak, Derk & Teunter, Rudolf & Babai, M. Z. & Syntetos, A. A. & Boylan, D, 2018. "Forecasting and Inventory Control with Compound Poisson Demand Using Periodic Demand Data," Research Report 2018010, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    5. Willemain, Thomas R. & Smart, Charles N. & Schwarz, Henry F., 2004. "A new approach to forecasting intermittent demand for service parts inventories," International Journal of Forecasting, Elsevier, vol. 20(3), pages 375-387.
    6. Bartezzaghi, Emilio & Verganti, Roberto & Zotteri, Giulio, 1999. "Measuring the impact of asymmetric demand distributions on inventories," International Journal of Production Economics, Elsevier, vol. 60(1), pages 395-404, April.
    7. Ali Caner Türkmen & Tim Januschowski & Yuyang Wang & Ali Taylan Cemgil, 2021. "Forecasting intermittent and sparse time series: A unified probabilistic framework via deep renewal processes," PLOS ONE, Public Library of Science, vol. 16(11), pages 1-26, November.
    8. Lengu, D. & Syntetos, A.A. & Babai, M.Z., 2014. "Spare parts management: Linking distributional assumptions to demand classification," European Journal of Operational Research, Elsevier, vol. 235(3), pages 624-635.
    9. Mahdavi, Mojtaba & Olsen, Tava Lennon, 2021. "The dual-serving problem: What is the right choice of inventory strategy?," Omega, Elsevier, vol. 103(C).
    10. Minner, Stefan & Silver, Edward A. & Robb, David J., 2003. "An improved heuristic for deciding on emergency transshipments," European Journal of Operational Research, Elsevier, vol. 148(2), pages 384-400, July.
    11. Turrini, Laura & Meissner, Joern, 2019. "Spare parts inventory management: New evidence from distribution fitting," European Journal of Operational Research, Elsevier, vol. 273(1), pages 118-130.
    12. Z S Hua & B Zhang & J Yang & D S Tan, 2007. "A new approach of forecasting intermittent demand for spare parts inventories in the process industries," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(1), pages 52-61, January.
    13. Syntetos, Aris A. & Boylan, John E., 2006. "On the stock control performance of intermittent demand estimators," International Journal of Production Economics, Elsevier, vol. 103(1), pages 36-47, September.
    14. Mak, K. L. & Lai, K. K. & Ng, W. C. & Yiu, K. F. C., 2005. "Analysis of optimal opportunistic replenishment policies for inventory systems by using a (s,S) model with a maximum issue quantity restriction," European Journal of Operational Research, Elsevier, vol. 166(2), pages 385-405, October.
    15. Banerjee, Snehamay & Banerjee, Avijit & Burton, Jonathan & Bistline, William, 2001. "Controlled partial shipments in two-echelon supply chain networks: a simulation study," International Journal of Production Economics, Elsevier, vol. 71(1-3), pages 91-100, May.
    16. Lau, Amy Hing Ling & Lau, Hon-Shiang, 2008. "An improved (Q, R) formulation when the stockout cost is incurred on a per-stockout basis," International Journal of Production Economics, Elsevier, vol. 111(2), pages 421-434, February.
    17. R H Teunter & L Duncan, 2009. "Forecasting intermittent demand: a comparative study," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(3), pages 321-329, March.
    18. Banerjee, Avijit & Burton, Jonathan & Banerjee, Snehamay, 1996. "Heuristic production triggering mechanisms under discrete unequal inventory withdrawals," International Journal of Production Economics, Elsevier, vol. 45(1-3), pages 83-90, August.
    19. Larsen, Christian, 2011. "Derivation of confidence intervals of service measures in a base-stock inventory control system with low-frequent demand," International Journal of Production Economics, Elsevier, vol. 131(1), pages 69-75, May.
    20. Bacchetti, Andrea & Saccani, Nicola, 2012. "Spare parts classification and demand forecasting for stock control: Investigating the gap between research and practice," Omega, Elsevier, vol. 40(6), pages 722-737.
    21. A A Syntetos & M Z Babai & Y Dallery & R Teunter, 2009. "Periodic control of intermittent demand items: theory and empirical analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(5), pages 611-618, May.
    22. Prak, Dennis & Teunter, Ruud & Babai, Mohamed Zied & Boylan, John E. & Syntetos, Aris, 2021. "Robust compound Poisson parameter estimation for inventory control," Omega, Elsevier, vol. 104(C).
    23. E A Shale & J E Boylan & F R Johnston, 2006. "Forecasting for intermittent demand: the estimation of an unbiased average," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(5), pages 588-592, May.
    24. John W. Bradford & Paul K. Sugrue, 1991. "Inventory rotation policies for slow moving items," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(1), pages 87-105, February.
    25. 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.

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