Model Answer
0 min readIntroduction
Exponential smoothing is a time series forecasting method that assigns exponentially decreasing weights to past observations. It’s a widely used technique in inventory management, demand planning, and other areas where predicting future values based on historical data is crucial. The smoothing constant (alpha) determines the rate at which past observations are discounted. A higher alpha gives more weight to recent observations, while a lower alpha gives more weight to past observations. This question requires us to apply this method given a specific alpha value and actual demand.
Understanding Exponential Smoothing
The formula for exponential smoothing is:
Ft+1 = α * At + (1 - α) * Ft
Where:
- Ft+1 = Forecast for the next period (next week in this case)
- α = Smoothing constant (given as 0.10)
- At = Actual demand in the current period (current week, given as 21500)
- Ft = Forecast for the current period (current week)
Determining the Current Period Forecast (Ft)
The question implicitly requires us to know the forecast for the current week (Ft). Since part (ii) is referenced, we assume part (i) provided this information. Let's assume, for the sake of completing the calculation, that the forecast for the current week (Ft) was 21000. (This is a crucial assumption; in a real exam, this value would be provided).
Calculating the Forecast for the Next Week (Ft+1)
Now, we can plug the values into the exponential smoothing formula:
Ft+1 = 0.10 * 21500 + (1 - 0.10) * 21000
Ft+1 = 0.10 * 21500 + 0.90 * 21000
Ft+1 = 2150 + 18900
Ft+1 = 21050
Therefore, the forecast for the next week is 21050.
It's important to note that the accuracy of this forecast depends heavily on the value of alpha and the stability of the demand pattern. A higher alpha would result in a forecast closer to the actual demand of 21500, while a lower alpha would result in a forecast closer to the previous forecast of 21000.
Conclusion
In conclusion, using the exponential smoothing method with an alpha of 0.10 and assuming a current week forecast of 21000, the forecast for the next week is calculated to be 21050. This method provides a simple yet effective way to incorporate recent demand data into future predictions. The choice of alpha is critical and should be based on the characteristics of the time series data being analyzed.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.