A dry cleaner uses exponential smoothing to forecast equipment usage at its main plant. August usage was forecasted to be 54 percent of capacity; actual usage was 52 percent of capacity. A smoothing constant of .10 is used.




To compute the forecast for September using exponential smoothing, we'll apply the formula for exponential smoothing:

\[
\text{New Forecast} = \alpha \times (\text{Actual Demand}) + (1 - \alpha) \times (\text{Previous Forecast})
\]

where:
- \(\alpha\) is the smoothing constant (in this case, 0.10),
- Actual Demand is the actual usage (52 percent of capacity for August),
- Previous Forecast is the forecasted usage (54 percent of capacity for August).

### Step-by-Step Calculation

1. **Given values**:
   - Smoothing constant, \(\alpha = 0.10\)
   - Actual usage for August = **52%** of capacity
   - Forecasted usage for August = **54%** of capacity

2. **Plug these values into the exponential smoothing formula**:
   \[
   \text{New Forecast} = 0.10 \times 52 + (1 - 0.10) \times 54
   \]

3. **Calculate each component**:
   \[
   0.10 \times 52 = 5.2
   \]
   \[
   (1 - 0.10) = 0.90
   \]
   \[
   0.90 \times 54 = 48.6
   \]

4. **Compute the New Forecast**:
   \[
   \text{New Forecast} = 5.2 + 48.6 = 53.8
   \]

### Result
The forecasted usage for September is **53.8%** of capacity.

This value represents the updated forecast incorporating the actual usage from August with the exponential smoothing method.

Would you like more details on how exponential smoothing works, or do you have any other questions?

Here are 5 related questions you might consider next:

1. How does the choice of smoothing constant (\(\alpha\)) affect the forecast?
2. What would be the forecast for October if the actual usage for September is available?
3. How does exponential smoothing compare to other forecasting methods like moving averages?
4. What are the advantages and disadvantages of using exponential smoothing in forecasting?
5. How would you adjust the smoothing constant for more volatile data?

**Tip:** A lower smoothing constant (\(\alpha\)) gives more weight to past forecasts, resulting in a smoother, less responsive forecast. Conversely, a higher \(\alpha\) makes the forecast more responsive to recent changes in the actual data.

Learn how to calculate a forecast using exponential smoothing with a specific example. This problem involves forecasting equipment usage at a dry cleaner's main plant using a smoothing constant of 0.10. Includes step-by-step calculations and interpretation of results.

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