4. Quarterly demand for smartphones at a retailer is as shown. After obtaining initial estimates for level, trend, and seasonal factors, forecast quarterly demand for year 5 using Winter's model with alpha=0.05, beta = 0.10, and gamma = 0.15. Evaluate the MAD, MAPE, and MSE for the forecast. Can you find values of a, ß, and, y that result in a lower MAD or MSE? Year 1 2 3 st 4 Quarter I || ||| IV 1 || ||| IV 1 || ||| IV I || IV Demand 513 932 1,509 1,902 693 1,163 1,857 2,469 846 1,439 2,271 3,079 1,070 1,751 2,785 3,613

Practical Management Science
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Chapter2: Introduction To Spreadsheet Modeling
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**Quarterly Demand Forecasting for Smartphones**

**Objective:**
Analyze the quarterly smartphone demand data at a retailer and forecast the demand for year 5 using Winter's model. The model involves smoothing parameters, alpha (α) = 0.05, beta (β) = 0.10, and gamma (γ) = 0.15. Evaluate the accuracy of the forecast by calculating the Mean Absolute Deviation (MAD), Mean Absolute Percentage Error (MAPE), and Mean Squared Error (MSE). Explore alternative values for α, β, and γ to achieve a lower MAD or MSE.

**Data Table:**

| **Year** | **Quarter** | **Demand** |
|----------|-------------|------------|
| 1        | I           | 513        |
|          | II          | 932        |
|          | III         | 1,509      |
|          | IV          | 1,902      |
| 2        | I           | 693        |
|          | II          | 1,163      |
|          | III         | 1,857      |
|          | IV          | 2,469      |
| 3        | I           | 846        |
|          | II          | 1,439      |
|          | III         | 2,271      |
|          | IV          | 3,079      |
| 4        | I           | 1,070      |
|          | II          | 1,751      |
|          | III         | 2,785      |
|          | IV          | 3,613      |

**Instructions:**

1. **Evaluate the Model:**
   - Use the given initial values for α, β, and γ to implement Winter’s model.
   - Calculate the MAD, MAPE, and MSE to assess forecast accuracy.

2. **Optimize Parameters:**
   - Experiment with different values of α, β, and γ.
   - Identify combinations that result in lower MAD or MSE for improved forecast accuracy.

**Diagrams:**
- The table provides raw demand data that should be visualized using time series plots to better understand seasonal variations and trends.
- Compare forecasted demand against actual demand visually to identify discrepancies.

**Conclusion:**
This analysis provides insights into both historical demand patterns and forecasts, which are crucial for inventory management and strategic planning in the retail sector.
Transcribed Image Text:**Quarterly Demand Forecasting for Smartphones** **Objective:** Analyze the quarterly smartphone demand data at a retailer and forecast the demand for year 5 using Winter's model. The model involves smoothing parameters, alpha (α) = 0.05, beta (β) = 0.10, and gamma (γ) = 0.15. Evaluate the accuracy of the forecast by calculating the Mean Absolute Deviation (MAD), Mean Absolute Percentage Error (MAPE), and Mean Squared Error (MSE). Explore alternative values for α, β, and γ to achieve a lower MAD or MSE. **Data Table:** | **Year** | **Quarter** | **Demand** | |----------|-------------|------------| | 1 | I | 513 | | | II | 932 | | | III | 1,509 | | | IV | 1,902 | | 2 | I | 693 | | | II | 1,163 | | | III | 1,857 | | | IV | 2,469 | | 3 | I | 846 | | | II | 1,439 | | | III | 2,271 | | | IV | 3,079 | | 4 | I | 1,070 | | | II | 1,751 | | | III | 2,785 | | | IV | 3,613 | **Instructions:** 1. **Evaluate the Model:** - Use the given initial values for α, β, and γ to implement Winter’s model. - Calculate the MAD, MAPE, and MSE to assess forecast accuracy. 2. **Optimize Parameters:** - Experiment with different values of α, β, and γ. - Identify combinations that result in lower MAD or MSE for improved forecast accuracy. **Diagrams:** - The table provides raw demand data that should be visualized using time series plots to better understand seasonal variations and trends. - Compare forecasted demand against actual demand visually to identify discrepancies. **Conclusion:** This analysis provides insights into both historical demand patterns and forecasts, which are crucial for inventory management and strategic planning in the retail sector.
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