Problem 3-21 (Algo)
Two different forecasting techniques (F1 and F2) were used to forecast demand for cases of bottled water. Actual demand and the two sets of forecasts are as follows:

Period	Demand	PREDICTED DEMAND
F1	F2
1	68	67	64
2	75	70	60
3	70	75	70
4	74	71	72
5	69	71	73
6	72	65	76
7	80	71	75
8	78	77	85
Click here for the Excel Data File

Compute MAD for each set of forecasts. Given your results, which forecast appears to be more accurate?

Note: Round your answers to 2 decimal places.

Compute the MSE for each set of forecasts. Given your results, which forecast appears to be more accurate?

Note: Round your answers to 2 decimal places.

In practice, either MAD or MSE would be employed to compute forecast errors. What factors might lead a manager to choose one rather than the other?

Compute MAPE for each data set. Which forecast appears to be more accurate?

Note: Round your intermediate calculations to 2 decimal places and and final answers to 2 decimal places.

Let's walk through the steps to calculate the following error measures for both F1 and F2 forecasting techniques:

1. **MAD (Mean Absolute Deviation)**: 
   \[
   \text{MAD} = \frac{\sum | \text{Actual Demand} - \text{Forecast Demand} |}{n}
   \]
   where \(n\) is the number of periods.

2. **MSE (Mean Squared Error)**:
   \[
   \text{MSE} = \frac{\sum (\text{Actual Demand} - \text{Forecast Demand})^2}{n}
   \]

3. **MAPE (Mean Absolute Percentage Error)**:
   \[
   \text{MAPE} = \frac{100}{n} \sum \left| \frac{\text{Actual Demand} - \text{Forecast Demand}}{\text{Actual Demand}} \right|
   \]

### Step 1: Organize the data

| Period | Demand | F1 | F2 |
|--------|--------|----|----|
| 1      | 68     | 67 | 64 |
| 2      | 75     | 70 | 60 |
| 3      | 70     | 75 | 70 |
| 4      | 74     | 71 | 72 |
| 5      | 69     | 71 | 73 |
| 6      | 72     | 65 | 76 |
| 7      | 80     | 71 | 75 |
| 8      | 78     | 77 | 85 |

### Step 2: Compute the MAD for F1 and F2
MAD is the average of the absolute differences between the actual demand and forecasted demand.

I'll now calculate the MAD for each forecast set (F1 and F2).The **MAD (Mean Absolute Deviation)** for each forecasting method is:

- MAD for F1: 4.13
- MAD for F2: 5.13

Based on MAD, **F1** appears to be more accurate as it has a lower deviation from actual demand.

### Step 3: Compute the MSE for F1 and F2
MSE is the average of the squared differences between the actual demand and forecasted demand. I'll calculate that next.The **MSE (Mean Squared Error)** for each forecasting method is:

- MSE for F1: 24.38
- MSE for F2: 43.88

Again, **F1** appears more accurate based on the lower MSE value.

### Step 4: Compute the MAPE for F1 and F2
MAPE represents the average percentage error relative to actual demand. Let's calculate that next.The **MAPE (Mean Absolute Percentage Error)** for each forecasting method is:

- MAPE for F1: 5.56%
- MAPE for F2: 6.90%

Once again, **F1** is more accurate, as it has a lower MAPE value.

### Summary of Results:
- **MAD**: F1 (4.13) is better than F2 (5.13).
- **MSE**: F1 (24.38) is better than F2 (43.88).
- **MAPE**: F1 (5.56%) is better than F2 (6.90%).

### In practice, why choose MAD over MSE or vice versa?
- **MAD** is easier to interpret because it measures the average magnitude of errors in the same units as the data.
- **MSE** penalizes larger errors more heavily due to squaring, making it more sensitive to outliers, which could be important if avoiding large errors is critical.
- **MAPE** provides a relative error measure, which is useful when comparing errors across different scales.

---

Would you like more details on any of the calculations, or help with a specific question? Here are 5 related questions:

1. How does MSE sensitivity to outliers affect forecast accuracy decisions?
2. Why might a manager prefer MAPE when analyzing forecasting techniques?
3. Can MAD or MSE give misleading results under certain conditions?
4. What are other common error metrics used in forecasting accuracy?
5. How can outliers be identified and managed in forecast evaluations?

**Tip**: Always check the distribution of errors before choosing between MAD, MSE, and MAPE to ensure the right method aligns with your goals.

Two different forecasting techniques (F1 and F2) were used to forecast demand for cases of bottled water. Actual demand and the two sets of forecasts are as follows: Period: 1 to 8, Demand, F1, F2. Compute MAD, MSE, and MAPE for each set of forecasts. Given your results, which forecast appears to be more accurate? Additionally, what factors might lead a manager to choose one error measure over another?

Analyze forecast accuracy using MAD, MSE, and MAPE for bottled water demand. This example compares two forecasting techniques (F1 and F2) across 8 periods. Learn how to calculate and interpret MAD (4.13 vs. 5.13), MSE (24.38 vs. 43.88), and MAPE (5.56% vs. 6.90%) to determine which forecast is more accurate. Suitable for university-level statistics or operations research students.

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