Empirical Safety Stock Estimation Using GARCH Model, Historical Simulation, and Extreme Value Theory: A Comparative Study

Abstract

Safety stock (SS) is an appropriate tactic to deal with demand and supply uncertainty with the aim of preventing inventory shortages. In the literature, previous work on SS estimation assumes that the forecast error distributions (FED) are independent and identically distributed (i.i.d) following the normal distribution. In order to assess violations of this assumption, there are many solution methods in the recent literature that include the following: (1) Consider the FED as other distribution models, such as gamma distribution or log-normal distribution, etc. (2) Use the Generalized Auto-Regressive Conditional Heteroskedasticity (GARCH) model to consider the Heteroskedasticity phenomena, (3) Use the extreme value theory (EVT) to take into consideration the occurrence of extreme demands, etc. However, the performance of these methods is not guaranteed because there is an absence of comparative studies. Indeed, the estimation of SS is based on the approximation of quantiles of the FED. Such quantiles are related to the cycle service levels (CSL) that are important to achieve company goals. Accordingly, the aim of this research is to propose two combined empirical methods to determine the SS in a more robust fashion and compare them with traditional methods under different supply chain parameters. The first combined method, named Filtered Historical Simulation (FHS), consists of combining the GARCH model with the simulation method. The second combination named Conditional Extreme Value Theory (CEVT) is the GARCH model with EVT. To validate these proposed combined methods, the SS is also estimated using traditional methods, such as simple exponential smoothing (SES), simulation, and kernel density estimation (KDE). The methodology is illustrated with both simulation data and real case study data for different lead times. For the FED, two cases are studied: lognormal distribution and gamma distribution. The results show the superiority of the two proposed combination methods with respect to the tick loss function (TLF) for the different CSL targets and for shorter and longer lead times. Results are confirmed using the ANOVA test.

Keywords

• safety stock estimation
• forecast errors distribution
• heteroscedasticity
• extreme demands
• GARCH model
• simulation