Yolanda Muñoz-Ocaña

arXiv2026

Safety stock calculation with heteroscedastic, autocorrelated and heavy-tailed forecast errors, an adaptive parametric method.e

This study develops and validates an adaptive parametric method for sizing safety stock when forecast errors are autocorrelated, heteroscedastic, asymmetric, and heavy-tailed. Using four years of weekly forecasts from a fast-moving consumer goods company, the analysis identifies substantial positive autocorrelation, departures from normality, systematic forecast optimism, and heterogeneous relationships between forecast volume and error variance. The proposed method integrates several corrections into a modular, sequential safety-stock architecture. It constructs cumulative forecast errors over the operational action period, selects an SKU-specific parametric distribution, and determines a baseline protection point using an expected-shortage condition consistent with the target beta fill rate. A forecast-scaled module adjusts dispersion when error variance depends on forecast volume, while a Cycle-End Exposure safeguard limits within-cycle shortage risk when large replenishment lots increase exposure. Performance is evaluated through discrete-event simulation against the company's current method. The proposed method reduces average inventory by 9.9% and maximum inventory by 19.5%, with no statistically significant deterioration in beta fill rate or average stockout duration. The proportion of weeks without stockouts declines slightly, without evidence of more persistent or operationally severe shortages. The heteroscedasticity module provides selective benefits, with greater service improvements as variance dependence intensifies. The resulting framework is interpretable, adapts to SKU-specific statistical profiles, links distributional features to safety-stock outcomes, and can be integrated into existing ERP environments.

math.OC↗

arXiv2026

Beyond recency and magnitude: Learning-aware uncertainty estimation for safety stock under evolving forecast-error distributions

We develop a non-parametric approach to refine forecast-error histories for safety stock estimation without relying on error magnitude or recency alone. Using forecast-error data from a fast-moving consumer goods environment, we show that one year of errors is insufficient to characterize service-level risk, while pooling several years is problematic because error distributions change over time. Non-parametric annual comparisons indicate a progressive reduction in bias and dispersion, consistent with learning in the forecasting process. We propose LOWDII (Leave-One-Out Wasserstein Distributional Influence Index), a diagnostic that evaluates the distributional influence of each historical forecast error on the empirical uncertainty distribution used for safety stock calibration. LOWDII identifies observations whose influence is disproportionate to their representativeness, separating transient distortions from persistent tail behaviour without imposing parametric assumptions. We evaluate the method in a discrete-event simulation using subsequent-year demand realizations as validation. The results show that LOWDII achieves the target service level while reducing average stock by 5.1% to 22.6% relative to benchmark methods. From a managerial perspective, LOWDII helps firms translate improvements in the forecasting process into safety stock decisions, avoiding the projection of obsolete historical errors into the future and capturing the economic benefit of lower uncertainty requirements earlier.

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