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
The correlation coefficient between two variables X and Y is found to be 0.6. All the observations on X and Y are transformed using the transformations U = 2 – 3X and V = 4Y + 1. The correlation coefficient between the transformed variables U and V will be
Which of the following lines is known as the trend line?
An XYZ television supplier found a demand of 200 sets in July, 225 sets in August and 245 sets in September. Find the demand forecast for the month for the month of October using simple average method.
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 :
Which of the following is a technique used for forecasting?
