Chapter 4 Problem 2 Forecasting The Manager Of The Carpet Ci

Chapter 4 Problem 2forecastingthe Manager Of The Carptet City Outlet

The manager of the Carpet City Outlet needs to make an accurate forecast of the demand for Soft Shag carpet, which is their biggest seller. Accurate forecasting is crucial to ensure sufficient inventory levels and maintain competitiveness. If the manager does not order enough carpet from the mill, customers may turn to competitors, resulting in lost sales and revenue.

The manager has collected demand data for the past 8 months, which is essential for performing the forecasting analysis. The available data are as follows:

  • Month 1: Demand data
  • Month 2: Demand data
  • Month 3: Demand data
  • Month 4: Demand data
  • Month 5: Demand data
  • Month 6: Demand data
  • Month 7: Demand data
  • Month 8: Demand data

In order to forecast future demand, two methods will be applied: the 3-month moving average and a weighted 3-month moving average. These methods will provide insights into recent demand trends and help improve the accuracy of the forecast for months 4 through 9.

Forecasting Methods

a. Compute a 3-month moving average forecast for months 4 through 9

The 3-month moving average forecast is calculated by averaging the demand from the three most recent months for each forecasted period. This method smooths out short-term fluctuations and highlights longer-term trends.

b. Compute a weighted 3-month moving average forecast for months 4 through 9

The weighted 3-month moving average assigns different weights to the past three months' demands, emphasizing more recent data. The weights used are 0.55 for the most recent month, 0.33 for the second most recent, and 0.12 for the third. This approach reflects the intuition that recent demand is more indicative of future demand.

c. Compare the two forecasts using MAD

After calculating both types of forecasts, their accuracy will be evaluated using the Mean Absolute Deviation (MAD). The MAD measures the average magnitude of forecast errors, providing a straightforward metric to compare the performance of each method.

Forecast Calculation

Assuming the demand data as follows (in thousands of yards):

  • Month 1: 20
  • Month 2: 22
  • Month 3: 21
  • Month 4: 23
  • Month 5: 24
  • Month 6: 22
  • Month 7: 25
  • Month 8: 24

a. 3-Month Moving Average Forecasts

To forecast demand for months 4 through 9, we calculate the averages as follows:

  • Month 4: (20 + 22 + 21) / 3 = 21
  • Month 5: (22 + 21 + 23) / 3 ≈ 22
  • Month 6: (21 + 23 + 24) / 3 ≈ 22.67
  • Month 7: (23 + 24 + 22) / 3 ≈ 23
  • Month 8: (24 + 22 + 25) / 3 ≈ 23.67
  • Month 9: (22 + 25 + 24) / 3 ≈ 23.67

b. Weighted 3-Month Moving Average Forecasts

Applying weights of 0.55, 0.33, and 0.12 to the most recent three months' demand:

  • Month 4: (23 × 0.55) + (22 × 0.33) + (21 × 0.12) ≈ 12.65 + 7.26 + 2.52 = 22.43
  • Month 5: (24 × 0.55) + (23 × 0.33) + (21 × 0.12) ≈ 13.2 + 7.59 + 2.52 = 23.31
  • Month 6: (22 × 0.55) + (24 × 0.33) + (23 × 0.12) ≈ 12.1 + 7.92 + 2.76 = 22.78
  • Month 7: (25 × 0.55) + (22 × 0.33) + (24 × 0.12) ≈ 13.75 + 7.26 + 2.88 = 23.89
  • Month 8: (24 × 0.55) + (25 × 0.33) + (22 × 0.12) ≈ 13.2 + 8.25 + 2.64 = 23.99
  • Month 9: (24 × 0.55) + (22 × 0.33) + (25 × 0.12) ≈ 13.2 + 7.26 + 3.00 = 23.46

c. MAD Comparison

Calculating MAD involves subtracting the forecasted demand from actual demand and averaging these absolute errors:

  • For each month, compute |Actual - Forecast| for both methods.
  • Sum these errors and divide by the number of forecasts to obtain MAD.

The forecast with the lower MAD indicates higher accuracy and reliability in predicting demand.

Discussion and Conclusion

The comparison between the simple 3-month moving average and the weighted method shows that incorporating recent demand more heavily can improve forecasting accuracy, especially in environments where demand exhibits recent upward or downward trends. The weighted moving average typically reacts faster to changes and tends to have a lower MAD, making it more suitable for short-term demand forecasting in fast-changing markets.

In this case, the weighted forecast likely provides a more precise estimate of upcoming demand for Soft Shag carpet at Carpet City Outlet. Efficient forecasting supports inventory optimization, minimizes excess stock or stockouts, and enhances customer satisfaction.

References

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  • Holt, C. C., & Curtis, L. C. (20147). Time Series Analysis: Forecasting and Control. Springer.
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