Period 1 2 3 4 5 6 7 8 9 10 Actual demand 425 415 420 430 427 418 422 416 426 421 Forecast 427 422 416 422 423 420 419 418 430 415
Demand Forecast Analysis: MFE and MAD Calculation
This solution explains how to calculate two important metrics for evaluating demand forecasts: the Mean Forecast Error (MFE) and the Mean Absolute Deviation (MAD). We will use the provided data for a product's actual demand and its forecast over 10 periods.
Forecast Error Metrics Explained
Forecast Error is the difference between the actual demand ($A_t$) and the forecasted demand ($F_t$) for a specific period ($t$). It can be positive (forecast was too low) or negative (forecast was too high).
Formula: $ \text{Error}_t = A_t - F_t $
Mean Forecast Error (MFE) measures the average bias of the forecast. A positive MFE indicates the forecast tends to be too low, while a negative MFE indicates it tends to be too high.
Formula: $ \text{MFE} = \frac{\sum_{t=1}^{n} (A_t - F_t)}{n} $
Mean Absolute Deviation (MAD) measures the average magnitude of the forecast errors, ignoring their direction. It provides a better understanding of the overall accuracy of the forecast.
Formula: $ \text{MAD} = \frac{\sum_{t=1}^{n} |A_t - F_t|}{n} $
Where '$n$' is the total number of periods.
Demand and Forecast Data Table
First, let's list the actual demand and forecast values and calculate the error and absolute error for each period.
| Period | Actual Demand ($A_t$) | Forecast ($F_t$) | Error ($E_t = A_t - F_t$) | Absolute Error ($|E_t|$) |
|---|---|---|---|---|
| 1 | 425 | 427 | -2 | 2 |
| 2 | 415 | 422 | -7 | 7 |
| 3 | 420 | 416 | 4 | 4 |
| 4 | 430 | 422 | 8 | 8 |
| 5 | 427 | 423 | 4 | 4 |
| 6 | 418 | 420 | -2 | 2 |
| 7 | 422 | 419 | 3 | 3 |
| 8 | 416 | 418 | -2 | 2 |
| 9 | 426 | 430 | -4 | 4 |
| 10 | 421 | 415 | 6 | 6 |
| Sum | 8 | 42 |
Calculating Mean Forecast Error (MFE)
Using the sum of errors calculated in the table:
Total number of periods, $ n = 10 $.
Sum of Errors = $ 8 $.
MFE = $ \frac{\text{Sum of Errors}}{n} $
MFE = $ \frac{8}{10} $
MFE = $ 0.8 $
Calculating Mean Absolute Deviation (MAD)
Using the sum of absolute errors calculated in the table:
Total number of periods, $ n = 10 $.
Sum of Absolute Errors = $ 42 $.
MAD = $ \frac{\text{Sum of Absolute Errors}}{n} $
MAD = $ \frac{42}{10} $
MAD = $ 4.2 $
Final MFE and MAD Values
Based on the step-by-step calculations, the Mean Forecast Error is $ 0.8 $ and the Mean Absolute Deviation is $ 4.2 $.
Important Questions from Forecasting
Name the human resource demand (need) forecasting technique, which solicits estimates of personnel needs from a group of experts, usually managers. The HRP experts act as intermediaries, summarise the various responses and report the findings back to the experts. The experts are surveyed again after they receive this feedback. Summaries and surveys are repeated until the experts' opinions begin to agree. The agreement reached is the forecast of the personnel needs.
Select the correct option :
The sensitivity of forecast in simple moving average forecasting method, for the increase of the length of average period,
For a product, the forecast and the actual sales for December 2008 were 25 and 20 respectively. If the exponential smoothing constant (α) is taken as 0.2, the forecast sales for January 2009 would be.
For a product the forecast and actual sales for December 2002 were 25 and 20 respectively. If the exponential smoothing constant is taken as 0.2, then forecast sale for January 2003 would be
- The difference between the actual demand for any time period and the forecast for the same period is termed as _______.
