Empirical safety stock estimation based on kernel and GARCH models

Abstract

Supply chain risk management has drawn the attention of practitioners and academics alike. One source of risk is demand uncertainty. Demand forecasting and safety stock levels are employed to address this risk. Most previous work has focused on point demand forecasting, given that the forecast errors satisfy the typical normal i.i.d. assumption. However, the real demand for products is difficult to forecast accurately, which means that—at minimum—the i.i.d. assumption should be questioned. This work analyzes the effects of possible deviations from the i.i.d. assumption and proposes empirical methods based on kernel density estimation (non-parametric) and GARCH(1,1) models (parametric), among others, for computing the safety stock levels. The results suggest that for shorter lead times, the normality deviation is more important, and kernel density estimation is most suitable. By contrast, for longer lead times, GARCH models are more appropriate because the autocorrelation of the variance of the forecast errors is the most important deviation. In fact, even when no autocorrelation is present in the original demand, such autocorrelation can be present as a consequence of the overlapping process used to compute the lead time forecasts and the uncertainties arising in the estimation of the parameters of the forecasting model. Improvements are shown in terms of cycle service level, inventory investment and backorder volume. Simulations and real demand data from a manufacturer are used to illustrate our methodology.