MAPE and Bias - Introduction

MAPE stands for Mean Absolute Percent Error - Bias refers to persistent forecast error - Bias is a component of total calculated forecast error - Bias refers to consistent under-forecasting or over-forecasting - MAPE can be misinterpreted and miscalculated, so use caution in the interpretation.

Accurate and timely demand plans are a vital component of a manufacturing supply chain. Inaccurate demand forecasts typically would result in supply imbalances when it comes to meeting customer demand.  Forecast accuracy at the SKU level is critical for proper allocation of resources.

When we talk about forecast accuracy in the supply chain, we typically have one measure in mind namely, the Mean Absolute Percent Error or MAPE. However, there is a lot of confusion between Academic Statisticians and corporate Supply Chain Planners in interpreting this metric. Most academics define MAPE as an average of percentage errors over a number of products. Whether it is erroneous is subject to debate. However, this interpretation of MAPE is useless from a manufacturing supply chain perspective.   The following is a discussion of forecast error and an elegant method to calculate meaningful MAPE.

Definition of Forecast Error

Forecast Error is the deviation of the Actual from the forecasted quantity.

	Error = absolute value of {(Actual – Forecast) = |(A - F)|
	Error (%) = |(A – F)|/A

We take absolute values because the magnitude of the error is more important than the direction of the error.

The Forecast Error can be bigger than Actual or Forecast but NOT both. Error above 100% implies a zero forecast accuracy or a very inaccurate forecast.

	Error close to 0% => Increasing forecast accuracy
	Forecast Accuracy is the converse of Error
	Accuracy (%) = 1 – Error (%)

How do you define Forecast Accuracy?

What is the impact of Large Forecast Errors? Is Negative accuracy meaningful?
Regardless of huge errors, and errors much higher than 100% of the Actuals or Forecast, we interpret accuracy a number between 0% and 100%. Either a forecast is perfect or relative accurate or inaccurate or just plain incorrect. So we constrain Accuracy to be between 0 and 100%.

More formally, Forecast Accuracy is a measure of how close the actuals are to the forecasted quantity.

	If actual quantity is identical to Forecast => 100% Accuracy
	Error > 100% => 0% Accuracy
	More Rigorously, Accuracy = maximum of (1 – Error, 0)

	Sku A	Sku B	Sku X	Sku Y
Forecast	75	0	25	75
Actual	25	50	75	74
Error	50	50	50	1
Error (%)	200%	100%	67%	1%
Accuracy (%)	0%	0%	33%	99%

Simple Methodology for MAPE

This is a simple but Intuitive Method to calculate MAPE.

	Add all the absolute errors across all items, call this A
	Add all the actual (or forecast) quantities across all items, call this B
	Divide A by B
	MAPE is the Sum of all Errors divided by the sum of Actual (or forecast)