A Non-Parametric Approach for Setting Safety Stock Levels

Abstract

In practice, lead time demand (LTD) can be non-standard: skewed, multi-modal or highly variable; factors that compromise the validity of the classic approaches for setting safety stock levels. Motivated by encountering this problem at our industry partner, we develop an approach for setting safety stock levels using the bootstrap, a widely-used statistical procedure. We extend prior research that has used the bootstrap for quantile estimation to address the multi-parameter estimation of safety stocks. We develop a multivariate central limit theorem for the bootstrap mean and bootstrap quantile -- components of the safety stock calculation -- highlighting why the generalization of these bootstrap methods is critical for inventory management. These results provide a theoretical underpinning for the bootstrap estimator of safety stock and permit the construction of confidence intervals for safety stock estimates, allowing decision makers to understand the reliability with which the desired service level will be achieved. Building on our theoretical results, and supported by numerical experiments, we provide insights on the behavior of the bootstrap for various LTD distributions, which our results demonstrate are critical when employing the bootstrap method. Implementation results with our industry partner indicate our approach is quite effective in setting safety stock levels.