Approximations for the Lead Time Variance: a Forecasting and Inventory Evaluation

Abstract

Safety stock is necessary for firms in order to manage the uncertainty of demand. A key component in its determination is the estimation of the variance of the forecast error over lead time. Given the multitude of demand processes that lack analytical expressions of the variance of forecast error, an approximation is needed. It is common to resort to finding the one-step ahead forecast errors variance and scaling it by the lead time. However, this approximation is flawed for many processes as it overlooks the autocorrelations that arise between forecasts made at different lead times. This research addresses the issue of these correlations first by demonstrating their existence for some fundamental demand processes, and second by showing through an inventory simulation the inadequacy of the approximation. We propose to monitor the empirical variance of the lead time errors, instead of estimating the point forecast error variance and extending it over the lead time interval. The simulation findings indicate that this approach provides superior results to other approximations in terms of cycle-service level. Given its lack of assumptions and computational simplicity, it can be easily implemented in any software, making it appealing to both practitioners and academics.