## Understanding Mean Absolute Deviation (MAD) in Demand Planning

By Intelichain’s Team

Mean Absolute Deviation (MAD) quantifies the average absolute difference between forecasted values and actual sales values over a specific period. Unlike other metrics, MAD focuses solely on the size of the errors, ignoring whether the forecasted values are higher or lower than the actual values. This makes it a useful measure for understanding the typical size of forecast errors.

**Importance of MAD**

**Simplicity and Clarity**: MAD is easy to calculate and interpret, making it accessible to various stakeholders within an organization.**Forecast Performance**: By providing a clear measure of forecast error, MAD helps organizations evaluate the performance of their forecasting models and identify areas for improvement.**Inventory Management**: Accurate MAD values enable better inventory management by highlighting the typical forecast error, allowing companies to adjust safety stock levels appropriately.**Cost Control**: Understanding the magnitude of forecast errors helps in minimizing costs related to overstocking or stockouts.

**Calculating MAD**

MAD is calculated using the following formula:

$$ \text{MAD} = \frac{\sum_{i=1}^n |F_i - A_i|}{n} $$

Tracking Signal (TS) uses MAD to flag if there is a persistent tendency for actuals to be higher or lower systematically. TS should pass a threshold test to be significant. If Tracking Signal > 3.75 then there is persistent under-forecasting. If this is less than -3.75 then, there is persistent over-forecasting. Organizations mostly round the TS range up to (-4) and 4.

**Calculating TS**

TS is calculated using the following formula:

$$ \text{TS} = \frac{\sum_{i=1}^n (F_i - A_i)}{\text{MAD}} $$

where

$$ \sum_{i=1}^n \left( F_i - A_i \right) $$ is the cumulative sum of forecast errors (also known as the Running Sum of Forecast Errors, or RSFE).

**Example**

Consider a company with monthly forecasts and actual sales data for three months. The actual sales were 100, 120, and 80 units, while the forecasted sales were 110, 115, and 90 units. The MAD calculation would be:

$$ \text{MAD} = \frac{|110-100| + |115-120| + |90-80|}{3} = \frac{10 + 5 + 10}{3} = \frac{25}{3} = 8.333 $$

$$ \text{RSFE} = (110-100) + (115-120) + (90-80) = 10 + (-5) + 10 = 15 $$

$$ \text{TS} = \frac{15}{8.333} = 1.8 $$

This MAD value of 8.33 units indicates the average absolute error in the forecasts.

**Strategies to Improve MAD**

**Enhance Data Quality**: Ensure that the data used for forecasting is accurate, complete, and up to date to improve the reliability of the forecasts.**Advanced Forecasting Models**: Use sophisticated forecasting models and techniques, such as machine learning and statistical methods, to capture complex patterns in the data and reduce forecast errors.**Incorporate External Factors**: Consider external factors like market trends, economic indicators, and seasonal variations to refine forecasts.**Regular Monitoring and Adjustment**: Continuously monitor forecast performance and make necessary adjustments based on actual demand data to maintain accuracy.**Cross-Functional Collaboration**: Encourage collaboration between different departments, such as sales, marketing, and supply chain, to gather comprehensive insights and improve forecast accuracy.

Mean Absolute Deviation (MAD) is a crucial metric in demand planning that provides a clear measure of forecast accuracy by focusing on the size of forecast errors. Its simplicity and clarity make it a valuable tool for evaluating forecast performance, managing inventory, and controlling costs.