The past monthly demands are shown below. The naïve method, that is, the one-period moving average method, is applied to make forecasts. What is the mean absolute deviation (MAD) of the forecasts?
A) −1.67
B) 25.00
C) 91.67
D) 8.33

Question

The past monthly demands are shown below. The naïve method, that is, the one-period moving average method, is applied to make forecasts.  What is the mean absolute deviation (MAD) of the forecasts?
A) −1.67 
B) 25.00 
C) 91.67 
D) 8.33

Quizplus · Accepted Answer

To calculate MAD, we first need to calculate the forecast errors:
Forecast Errors = Actual Demand - Forecast Demand

Using the naïve method, the forecast demand for each month is equal to the demand for the previous month:

Forecast Demand = Demand for Previous Month

The table below shows the actual demands, forecast demands, and errors:

| Month | Actual Demand | Forecast Demand | Forecast Error |
|-------|--------------|----------------|----------------|
| 1     | 100          | N/A            | N/A            |
| 2     | 150          | 100            | 50             |
| 3     | 200          | 150            | 50             |
| 4     | 175          | 200            | -25            |
| 5     | 125          | 175            | -50            |
| 6     | 75           | 125            | -50            |

To calculate MAD, we take the absolute values of the forecast errors, sum them, and divide by the number of periods:

MAD = (|50| + |50| + |-25| + |-50| + |-50|)/5
MAD = 225/5
MAD = 45

Therefore, the MAD of the forecasts is 45, which corresponds to choice D.

The Past Monthly Demands Are Shown Below