On the calculation of safety stocks
In forecasting and inventory control textbooks and software applications, the variance of the cumulative lead-time forecast error is, almost invariably, taken as the sum of the error variances of the individual forecast intervals. For stationary demand and a constant lead time, this implies multiplying the single period variance (or Mean Squared Error) by the lead-time. This standard approach is shown in this paper to always underestimate the true lead-time demand variability, resulting in too low safety stocks and poor service. For two of the most widely applied forecasting techniques (Single Exponential Smoothing and Simple Moving Average) we present corrected expressions and show that the error in the standard approach is often considerable. The same fundamental problem exists for all forecasting techniques and all demand processes, and so this issue deserves wider recognition and offers ample opportunities for further research.
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- Heuts, R.M.J. & Strijbosch, L.W.G. & van der Schoot, E.H.M., 1999. "A Combined Forecast-Inventory Control Procedure for Spare Parts," Research Memorandum 772, Tilburg University, School of Economics and Management.
- Harvey, Andrew & Snyder, Ralph D., 1990. "Structural time series models in inventory control," International Journal of Forecasting, Elsevier, vol. 6(2), pages 187-198, July.
- Snyder, Ralph D. & Koehler, Anne B. & Hyndman, Rob J. & Ord, J. Keith, 2004. "Exponential smoothing models: Means and variances for lead-time demand," European Journal of Operational Research, Elsevier, vol. 158(2), pages 444-455, October.
- Stephen C. Graves, 1999. "A Single-Item Inventory Model for a Nonstationary Demand Process," Manufacturing & Service Operations Management, INFORMS, vol. 1(1), pages 50-61.
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