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Robustness of the normal approximation of lead‐time demand in a distribution setting

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  • John E. Tyworth
  • Liam O'Neill

Abstract

Previous studies criticize the general use of the normal approximation of lead‐time demand on the grounds that it can lead to serious errors in safety stock. We reexamine this issue for the distribution of fast‐moving finished goods. We first determine the optimal reorder points and quantities by using the classical normal‐approximation method and a theoretically correct procedure. We then evaluate the misspecification error of the normal approximation solution with respect to safety stock, logistics‐system costs, total costs (logistics costs, including acquisition costs), and fill rates. The results provide evidence that the normal approximation is robust with respect to both cost and service for seven major industry groups. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 165–186, 1997

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  • John E. Tyworth & Liam O'Neill, 1997. "Robustness of the normal approximation of lead‐time demand in a distribution setting," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(2), pages 165-186, March.
    • Handle: RePEc:wly:navres:v:44:y:1997:i:2:p:165-186
    DOI: 10.1002/(SICI)1520-6750(199703)44:23.0.CO;2-7
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    References listed on IDEAS

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    1. Tadikamalla, Pandu R, 1984. "A comparison of several approximations to the lead time demand distribution," Omega, Elsevier, vol. 12(6), pages 575-581.
    2. M. Eric Johnson & Hau L. Lee & Tom Davis & Robert Hall, 1995. "Expressions for item fill rates in periodic inventory systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(1), pages 57-80, February.
    3. Eliezer Naddor, 1978. "Note--Sensitivity to Distributions in Inventory Systems," Management Science, INFORMS, vol. 24(16), pages 1769-1772, December.
    4. Gary D. Eppen & R. Kipp Martin, 1988. "Determining Safety Stock in the Presence of Stochastic Lead Time and Demand," Management Science, INFORMS, vol. 34(11), pages 1380-1390, November.
    5. Tyworth, John E. & Rao, Kent & Stenger, Alan J., 1991. "A Logistics Cost Model for Purchasing Transportation to Replenish High Demand Items," Journal of the Transportation Research Forum, Transportation Research Forum, vol. 32(1).
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    Cited by:

    1. Janssen, E. & Strijbosch, L.W.G. & Brekelmans, R.C.M., 2006. "Assessing the Effects of using Demand Parameters Estimates in Inventory Control," Discussion Paper 2006-90, Tilburg University, Center for Economic Research.
    2. Barros, Júlio & Cortez, Paulo & Carvalho, M. Sameiro, 2021. "A systematic literature review about dimensioning safety stock under uncertainties and risks in the procurement process," Operations Research Perspectives, Elsevier, vol. 8(C).
    3. Chatfield, Dean C. & Pritchard, Alan M., 2018. "Crossover aware base stock decisions for service-driven systems," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 114(C), pages 312-330.
    4. Li, Xiaoming, 2020. "Valuing lead-time and its variance in batch-ordering inventory policies," International Journal of Production Economics, Elsevier, vol. 228(C).
    5. Dominguez, Roberto & Cannella, Salvatore & Ponte, Borja & Framinan, Jose M., 2020. "On the dynamics of closed-loop supply chains under remanufacturing lead time variability," Omega, Elsevier, vol. 97(C).
    6. Birisci, Esma & McGarvey, Ronald G., 2022. "Cost-versus environmentally-optimal production in institutional food service operations," Socio-Economic Planning Sciences, Elsevier, vol. 82(PA).
    7. Saldanha, John P., 2022. "Estimating the reorder point for a fill-rate target under a continuous review policy in the presence of non-standard lead-time demand distributions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 164(C).
    8. Minken, Harald & Johansen, Bjørn Gjerde, 2019. "A logistics cost function with explicit transport costs," Economics of Transportation, Elsevier, vol. 19(C), pages 1-1.
    9. Mamonov, Nikolay & Golubyatnikov, Evgeny & Kanevskiy, Daniel & Gusakov, Igor, 2022. "GoodsForecast second-place solution in M5 Uncertainty track: Combining heterogeneous models for a quantile estimation task," International Journal of Forecasting, Elsevier, vol. 38(4), pages 1434-1441.
    10. Ting-Chen Hu & Kuo-Chen Hung & Kuo-Lung Yang, 2019. "The Convergence of Gallego’s Iterative Method for Distribution-Free Inventory Models," Mathematics, MDPI, vol. 7(5), pages 1-10, May.

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