Empirical safety stock estimation based on Kernel and GARCH models

Supply chain risk management is drawing the attention of practitioners and academics. A source of risk is demand uncertainty. To deal with it demand forecasting and safety stocks are employed. Most of the work has focused on point demand forecasting, assuming that forecast errors follow the typical normal i.i.d. assumption. The variability of the forecast errors is used to compute the safety stock, in order to reduce the risk of stockouts with a reasonable inventory investment. Nevertheless, real products' demand is very hard to forecast and that means that at minimum the normally i.i.d. assumption should be questioned. This work analyses the effects of possible deviations from these assumptions and it proposes empirical methods based on Kernel density estimators (non-parametric) and GARCH models (parametric) in order to compute the safety stock. The results show that Kernel density estimator is recommended when the forecast errors are fat tailed and GARCH models are well-suited when forecast errors present autocorrelation. Additionally, GARCH models present important improvements for lead time forecast errors, as shown in terms of customer service level, inventory investment and backorders volume. Simulations and real demand data from a manufacturer are used to illustrate our methodology