MAD (mean absolute deviation) for forecasts shows the deviation of forecasted demand from actual demand. This is the mean deviation per period in absolute terms between a number of period forecasts and the corresponding period demand.

Forecast MAD is used in three contexts.

- As a basis for calculating allowable margin of error for forecasts when checked using forecast alarm 1 and 2.
- To periodically recalculate alpha values when using forecast methods based on adaptive exponential smoothing.
- When calculating the standard deviation for forecast error when setting the dimensions for safety stock.

**Methods for Calculation**

MAD can be calculated in three ways, as follows:

**Exponential Smoothing**

MAD(i + 1) = ((i) * ABS(D(i) - F(i)) + (1 - ((i)) * MAD(i)

**Average Absolute Forecast Errors**

MAD(i + 1) = (ABS(D(i) - F(i)) + ....... + ABS(D(i - (n - 1)) - F(i - (n - 1))) / n

**Average Absolute Error from Mean Demand**

MAD(i + 1) = (ABS(D(i) - A(n)) + ....... + ABS(D(i - (x - 1)) - A(n))) / n

**Key:**

MAD(i) | = | Mean absolute deviation for period (i) |

((i) | = | Smoothing constant for exponential smoothing in period (i) |

ABS( ) | = | The absolute amount of a difference (without minus sign) |

D(i) | = | Base demand during period (i) |

F(i) | = | Base forecast for period (i) |

A(n) | = | Average demand for (n) periods |

i | = | Period number |

n | = | Number of periods included in calculating the mean |

Base demand and base forecast represent demand and forecast, respectively, for a period adjusted for seasonal variations and the effect of a varying number of workdays per period.

The three examples below describe each of the calculation methods.

The following data is entered for the product:

Aug. | Sep. | Oct. | Nov. | |

Base Demand | 120 | 145 | 138 | 129 |

Base Forecast | 136 | 132 | 135 | 133 |

Applicable MAD for Nov. | 10 |

(-factor used | 0.3 |

The following MAD values will be calculated for December using the three methods as listed:

**Exponential Smoothing**

MAD(Dec.) = 0.3 * ABS(D(Nov.) - F(Nov.)) + (1 - 0.3) * MAD(Nov.) = 0.3 * ABS(129 - 133) + 0.7 * 10 = 0.3 * 4 + 0.7 * 10 = 8.2

**Average Absolute Forecast Errors**

MAD(Dec.) = (ABS(D(Nov.) - F(Nov.)) + ABS(D(Oct.) - F(Oct.)) + ABS(D(Sep.) - F(Sep.)) + ABS(D(Aug.) - F(Aug.))) / 4 = (16 + 13 + 3 + 4) / 4 = 9

**Average Absolute Error from Mean Demand**

Mean demand A(4) = (120 + 145 + 138 + 129) / 4 = 133

MAD(Dec.) = (ABS(D(Nov.) - A(4)) + ABS(D(Oct.) - A(4)) + ABS(D(Sep.) - A(4)) + ABS(D(Aug.) - A(4))) / 4 = (13 + 12 + 5 + 4) / 4 = 8.5