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

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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.