TY - JOUR

T1 - Approximations for the Lead Time Variance

T2 - a Forecasting and Inventory Evaluation

AU - Saoud, Patrick

AU - Kourentzes, Nikolaos

AU - Boylan, John E.

N1 - This is the author’s version of a work that was accepted for publication in Omega. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Omega, 110, 2022 DOI: 10.1016/j.omega.2022.102614

PY - 2022/7/31

Y1 - 2022/7/31

N2 - 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.

AB - 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.

KW - Forecasting

KW - Lead time demand variance

KW - Demand uncertainty

KW - Safety stock

KW - Forecast errors correlations

U2 - 10.1016/j.omega.2022.102614

DO - 10.1016/j.omega.2022.102614

M3 - Journal article

VL - 110

JO - Omega

JF - Omega

SN - 0305-0483

M1 - 102614

ER -