Mean Absolute Percentage Error (MAPE)

MAPE expresses error as a percentage, making it inherently scale-independent. This allows for direct accuracy comparisons between forecasts for items with vastly different lead times—for example, comparing a 2-day domestic transit forecast against a 45-day ocean freight forecast. Unlike scale-dependent metrics such as Mean Absolute Error (MAE) or Root Mean Squared Error (RMSE), MAPE normalizes the error by the actual value, enabling cross-SKU and cross-supplier benchmarking without requiring data standardization.

A MAPE of 15% communicates immediately to supply chain stakeholders that the average forecast deviates from the actual lead time by 15%. This percentage-based interpretation bridges the gap between data science teams and business planners. When a procurement director sees that a supplier's lead time forecast has a MAPE of 8%, they can intuitively grasp the model's precision without needing to understand the underlying statistical mechanics. This interpretability makes MAPE the default metric in many executive dashboards and Supplier Reliability Scorecards.

A critical limitation of MAPE is that it becomes undefined when the actual value is zero. The formula divides by the actual value, so any period with zero actual lead time causes a division-by-zero error. In supply chain contexts, this occurs when a shipment is recorded with a lead time of 0 days due to data entry errors or same-day deliveries. To handle this, practitioners often:

• Exclude zero-actual observations from the calculation
• Apply a small epsilon value to avoid division by zero
• Use symmetric MAPE (sMAPE) as an alternative bounded metric

MAPE imposes an asymmetric penalty on over-forecasts versus under-forecasts. When the forecast exceeds the actual value (over-forecast), the error is capped at 100% if the forecast is double the actual. However, when the forecast is lower than the actual (under-forecast), there is no upper bound—the percentage error can exceed 100% arbitrarily. This asymmetry means MAPE inherently penalizes under-forecasting more severely. In lead time prediction, this property can be advantageous when late deliveries carry higher business costs than early arrivals.

MAPE uses the absolute value of percentage errors, which provides some robustness against outliers compared to squared-error metrics like RMSE. However, individual observations with very small actual values can produce disproportionately large percentage errors that skew the aggregate metric. For example, if an actual lead time is 1 day and the forecast is 3 days, that single observation contributes a 200% error. Techniques to mitigate this include:

• Winsorizing extreme percentage errors at a threshold (e.g., 100%)
• Using weighted MAPE (WMAPE) to prioritize high-volume items
• Complementing MAPE with Prediction Intervals for uncertainty quantification

Standard MAPE treats all observations equally, which can be problematic when forecasting lead times for items with vastly different business importance. Weighted MAPE (WMAPE) addresses this by weighting each percentage error by the actual value or another relevance metric such as revenue impact or order volume. The formula becomes: Σ(weight × |Actual - Forecast|) / Σ(weight × Actual). In supply chain applications, WMAPE ensures that a 10% error on a high-volume critical component is prioritized over a 10% error on a low-volume consumable, aligning model evaluation with business impact.