Juan R. Trapero, Manuel Cardos and Nikolaos Kourentzes, 2018, International Journal of Forecasting.
The safety stock calculation requires a measure of the forecast error uncertainty. Such errors are usually assumed Gaussian iid (independent, identically distributed). However, deviations from iid deteriorate the supply chain performance. Recent research has shown that, alternatively to theoretical approaches, empirical techniques that do not rely on the aforementioned assumptions, can enhance the safety stock calculation. Particularly, GARCH models cope with time-varying heterocedastic forecast error, and Kernel Density Estimation do not need to rely on a determined distribution. However, if forecast errors are both time-varying heterocedastic and do not follow a determined distribution, the previous approaches are inadequate. To overcome this, we propose an optimal combination of the empirical methods that minimizes the asymmetric piecewise linear loss function, also known as tick loss. The results show that combining quantile forecasts yields safety stocks with a lower cost. The methodology is illustrated with simulations and real data experiments for different lead times.