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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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    4. 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.
    5. 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.
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    7. Rostami-Tabar, Bahman & Disney, Stephen M., 2023. "On the order-up-to policy with intermittent integer demand and logically consistent forecasts," International Journal of Production Economics, Elsevier, vol. 257(C).
    8. Lolli, Francesco & Coruzzolo, Antonio Maria & Peron, Mirco & Sgarbossa, Fabio, 2022. "Age-based preventive maintenance with multiple printing options," International Journal of Production Economics, Elsevier, vol. 243(C).
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    10. Mohammed Hichame Benbitour & Evren Sahin & Yves Dallery, 2019. "The use of rush deliveries in periodic review assemble-to-order systems," Post-Print hal-01997380, HAL.
    11. Briskorn, Dirk & Zeise, Philipp & Packowski, Josef, 2016. "Quasi-fixed cyclic production schemes for multiple products with stochastic demand," European Journal of Operational Research, Elsevier, vol. 252(1), pages 156-169.
    12. Sasanuma, Katsunobu & Hibiki, Akira & Sexton, Thomas, 2022. "An opaque selling scheme to reduce shortage and wastage in perishable inventory systems," Operations Research Perspectives, Elsevier, vol. 9(C).

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