Prediction Intervals

A model-agnostic framework that generates statistically valid prediction intervals with guaranteed coverage probabilities. Unlike traditional methods that assume a specific error distribution, conformal prediction wraps around any black-box model and provides rigorous, distribution-free uncertainty quantification. It works by using a held-out calibration dataset to determine the threshold needed to achieve a desired confidence level (e.g., 90%). This is critical for supply chain applications where the underlying forecasting model may be a complex neural network, and planners require legally defensible guarantees on interval reliability.

A statistical technique that estimates the conditional median or other quantiles of a response variable, directly modeling the boundaries of a prediction interval. Instead of predicting a single mean value, quantile regression fits separate models for the 5th and 95th percentiles, for example, to construct a 90% prediction interval. This naturally handles asymmetric uncertainty, which is common in lead times where delays are unbounded but early deliveries have a physical floor. It is a fundamental building block for gradient boosting machines and deep learning models that output probabilistic forecasts.

A forecasting methodology that outputs a full probability distribution of possible future outcomes rather than a single deterministic point estimate. This approach explicitly quantifies the uncertainty inherent in any prediction, enabling downstream decision systems to optimize for risk-adjusted outcomes. Key outputs include:

• Prediction intervals at multiple confidence levels (50%, 80%, 95%)
• Probability density functions for expected delivery dates
• Quantile estimates for worst-case and best-case scenarios This is essential for dynamic safety stock calculation and order promising logic.

A scale-independent accuracy metric that measures the average absolute percentage difference between forecasted and actual lead times. While widely used to benchmark point forecasts, MAPE has significant limitations when evaluating prediction intervals. It penalizes over-forecasting and under-forecasting asymmetrically and cannot assess whether an interval's stated confidence level matches its empirical coverage. For interval evaluation, metrics like Prediction Interval Coverage Probability (PICP) and Mean Prediction Interval Width (MPIW) are preferred, as they jointly assess reliability and sharpness.

A state-of-the-art attention-based deep learning model designed for interpretable multi-horizon time-series forecasting. The TFT explicitly handles static covariates (e.g., supplier category, lane origin), known future inputs (e.g., planned holidays, carrier schedules), and observed historical data. Critically, it natively outputs quantile forecasts across multiple horizons, enabling the direct construction of prediction intervals at any desired confidence level. Its variable selection networks and attention mechanisms provide explainability, revealing which features drive interval width at each timestep.

The phenomenon where the statistical properties of the target variable change over time in unforeseen ways, degrading the predictive accuracy and interval validity of a deployed model. In lead time forecasting, concept drift can be triggered by:

• A supplier moving to a new manufacturing facility
• A carrier altering its hub-and-spoke routing logic
• Macroeconomic shifts changing port labor availability When concept drift occurs, a model's prediction intervals may become overconfident (too narrow) or miscalibrated, requiring continuous monitoring and automated retraining pipelines to restore valid coverage.