Quantile forecast optimal combination to enhance safety stock estimation

Abstract

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.

Operations research models and methods for safety stock determination: A review

“…Table 4 provides an overall characterization of the papers included in this subsection. Here, we found that only 6 of the 17 studies included in this category reported real-world case studies [see, [21] , [63] , [66] , [67] , [73] , [74] ], suggesting that further research with empirical validations is warranted.…”

“…When demand distributions do not follow the common normality assumption, one can adopt a non-parametric forecasting approach to estimate safety stocks: where Q L ( α ) is the lead time forecast error quantile at the target service level α . This quantile can be obtained, in a non-parametrical fashion, from the empirical distribution of the lead time forecast errors [21] .…”

“…Here, the use of non-parametric kernel density approaches seem to be promising to avoid the so common assumption of normal and i.i.d. forecasting errors [see [21] , [63] ]. We additionally found that many authors have assumed normally distributed lead times which, in certain cases, also bears no relation to reality.…”

“…Inventory, production and backordered costs Trapero et al. [21] , [63] Analytic/GARCH models; Kernel density estimation 1. Inventory costs (understocking and overstocking); 2.…”

“… [63] Fast-moving consumer goods manufacturer, UK VFE A/O – – – Parametric and non-parametric approaches for safety stock determination Trapero et al. [21] Fast-moving consumer goods manufacturer, UK VFE A/O – – – Quantile combination of empirical approaches for safety stock determination Tsou [44] , [45] Pharmaceutical industry VD A/O – – – Flexible multi-objective optimization methods providing suitable lot sizes and safety stocks according to decision-makers’ preferences Tsou and Kao [43] Pharmaceutical industry VD A/O – – – Safety stock determination without using any surrogate measure (e.g., service level or shortage cost) and prior preference information from decision-makers Zhang et al. [120] International logistics group, China O A/O – – …”