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Analysis of order-up-to-level inventory systems with compound Poisson demand

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  • Babai, M.Z.
  • Jemai, Z.
  • Dallery, Y.

Abstract

We analyse a single echelon single item inventory system where the demand and the lead time are stochastic. Demand is modelled as a compound Poisson process and the stock is controlled according to a continuous time order-up-to (OUT) level policy. We propose a method for determining the optimal OUT level for cost oriented inventory systems where unfilled demands are backordered. We first establish an analytical characterization of the optimal OUT level. The actual calculation is based on a numerical procedure the accuracy of which can be set as highly as desired. By means of a numerical investigation, we show that the method is very efficient in calculating the optimal OUT level. We compare our results with those obtained using an approximation proposed in the literature and we show that there is a significant difference in accuracy for slow moving items. Our work allows insights to be gained on stock control related issues for both fast and slow moving Stock Keeping Units (SKUs).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:210:y:2011:i:3:p:552-558
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    References listed on IDEAS

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    1. Kamran Moinzadeh, 1989. "Operating Characteristics of the (S - 1, S) Inventory System with Partial Backorders and Constant Resupply Times," Management Science, INFORMS, vol. 35(4), pages 472-477, April.
    2. Zied Babai, M. & Syntetos, Aris A. & Teunter, Ruud, 2010. "On the empirical performance of (T, s, S) heuristics," European Journal of Operational Research, Elsevier, vol. 202(2), pages 466-472, April.
    3. 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.
    4. Evan L. Porteus, 1985. "Numerical Comparisons of Inventory Policies for Periodic Review Systems," Operations Research, INFORMS, vol. 33(1), pages 134-152, February.
    5. Janssen, F.B.S.L.P., 1998. "Inventory management systems : Control and information issues," Other publications TiSEM 710d54d2-5447-4e2f-bb60-0, Tilburg University, School of Economics and Management.
    6. Porras, Eric & Dekker, Rommert, 2008. "An inventory control system for spare parts at a refinery: An empirical comparison of different re-order point methods," European Journal of Operational Research, Elsevier, vol. 184(1), pages 101-132, January.
    7. 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.
    8. 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.
    9. Blyth C. Archibald & Edward A. Silver, 1978. "(s, S) Policies Under Continuous Review and Discrete Compound Poisson Demand," Management Science, INFORMS, vol. 24(9), pages 899-909, May.
    10. G. J. Feeney & C. C. Sherbrooke, 1966. "The (S - 1, S) Inventory Policy Under Compound Poisson Demand," Management Science, INFORMS, vol. 12(5), pages 391-411, January.
    11. 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.
    12. Willemain, Thomas R. & Smart, Charles N. & Shockor, Joseph H. & DeSautels, Philip A., 1994. "Forecasting intermittent demand in manufacturing: a comparative evaluation of Croston's method," International Journal of Forecasting, Elsevier, vol. 10(4), pages 529-538, December.
    13. Eric Smeitink, 1990. "A Note on "Operating Characteristics of the (S-1, S) Inventory System with Partial Backorders and Constant Resupply Times"," Management Science, INFORMS, vol. 36(11), pages 1413-1414, November.
    14. 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.
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