A nonparametric approach for setting safety stock levels

In practice, lead time demand (LTD) can be skewed, multi-modal or highly variable, and these factors compromise the validity of typical approaches used 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. Existing bootstrap approaches for inventory management either operate directly on observed LTD or assume deterministic lead times, permitting direct application of the bootstrap approach for univariate quantile estimation. As LTD is a convolution of multiple random demands over a random lead time, a multivariate bootstrap approach is required. As we demonstrate, when lead times are stochastic, our multivariate approach provides improved safety stock estimates. 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 of our approach with our industry partner resulted in an inventory investment reduction of $1.17 million combined with an overall increase in service level. Our approach is general and can be implemented without modification in other settings.