Here are the actual tabulated demands for an item for a nine-month period (January through September). Your supervisor wants to test two forecasting methods to see which method was better over this period.

MONTHACTUALJanuary

114

February

134

March

152

April

170

May

154

June

180

July

135

August

135

September

136

**b.** Use simple exponential smoothing with an alpha of 0.10 to estimate April through September, using the average of January through March as the initial forecast for April.

**Note: Round your answers to 2 decimal places.**

To apply **simple exponential smoothing** (SES) with an alpha of 0.10, we need to follow the formula:

\[
F_{t+1} = \alpha A_t + (1 - \alpha) F_t
\]

Where:
- \( F_{t+1} \) is the forecast for the next period.
- \( A_t \) is the actual demand for the current period.
- \( F_t \) is the forecast for the current period.
- \( \alpha \) is the smoothing constant (in this case, 0.10).

### Step 1: Calculate the initial forecast for April (using the average of January to March)

To calculate the initial forecast for April, we take the average of actual demands from January to March:

\[
\text{Average of January to March} = \frac{114 + 134 + 152}{3} = \frac{400}{3} = 133.33
\]

So, the forecast for April is \( F_{\text{April}} = 133.33 \).

### Step 2: Calculate the forecasts for April through September

Now, we will apply the SES formula to forecast for each month from April to September.

#### April Forecast:
\[
F_{\text{April}} = 0.10 \times 170 + (1 - 0.10) \times 133.33 = 17 + 120.00 = 137.00
\]

#### May Forecast:
\[
F_{\text{May}} = 0.10 \times 154 + (1 - 0.10) \times 137.00 = 15.40 + 123.30 = 138.70
\]

#### June Forecast:
\[
F_{\text{June}} = 0.10 \times 180 + (1 - 0.10) \times 138.70 = 18 + 124.83 = 142.83
\]

#### July Forecast:
\[
F_{\text{July}} = 0.10 \times 135 + (1 - 0.10) \times 142.83 = 13.50 + 128.55 = 142.05
\]

#### August Forecast:
\[
F_{\text{August}} = 0.10 \times 135 + (1 - 0.10) \times 142.05 = 13.50 + 127.85 = 141.35
\]

#### September Forecast:
\[
F_{\text{September}} = 0.10 \times 136 + (1 - 0.10) \times 141.35 = 13.60 + 127.22 = 140.82
\]

### Final Forecasts for April through September:

- **April:** 137.00
- **May:** 138.70
- **June:** 142.83
- **July:** 142.05
- **August:** 141.35
- **September:** 140.82

---

Would you like more details or explanations about any of the steps?

Here are 5 related questions to explore:
1. How does the choice of alpha affect the forecast in exponential smoothing?
2. What are the advantages and disadvantages of using simple exponential smoothing compared to other forecasting methods?
3. How would you apply exponential smoothing if you had more historical data (e.g., a full year)?
4. What is the interpretation of the forecast errors in exponential smoothing?
5. How can you calculate the Mean Absolute Error (MAE) for these forecasts?

Tip: **Experiment with different values of alpha** (e.g., 0.05, 0.20) to see how it influences the forecast and smoothing behavior.

Here are the actual tabulated demands for an item for a nine-month period (January through September). Your supervisor wants to test two forecasting methods to see which method was better over this period. Use simple exponential smoothing with an alpha of 0.10 to estimate April through September, using the average of January through March as the initial forecast for April.

Learn how to use simple exponential smoothing with an alpha of 0.10 to forecast demand for April through September. This example uses actual demands from January to March and calculates step-by-step forecasts, including the initial forecast and updates for each subsequent month. Suitable for advanced high school or college-level statistics students.

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