Exponential Smoothing Calculation

The forecast for the next period ($F_{t+1}$) using exponential smoothing is calculated based on the previous forecast ($F_t$) and the actual demand of the current period ($A_t$). The formula is:

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

Where $A_t$ is the actual demand for period $t$, $F_t$ is the forecast for period $t$, and $\alpha$ is the smoothing constant.

Forecast for February 2026

We are given:

• Actual demand for January ($A_1$): 500 units
• Forecast for January ($F_1$): 250 units
• Smoothing constant ($\alpha$): 0.7

First, calculate the forecast for February ($F_2$) using the January data:

$ F_2 = \alpha A_1 + (1-\alpha) F_1 $ $ F_2 = (0.7 \times 500) + (1 - 0.7) \times 250 $ $ F_2 = (350) + (0.3 \times 250) $ $ F_2 = 350 + 75 $ $ F_2 = 425 \text{ units} $

Forecast for March 2026

Now, calculate the forecast for March ($F_3$) using the February data:

• Actual demand for February ($A_2$): 635 units
• Forecast for February ($F_2$): 425 units (calculated above)
• Smoothing constant ($\alpha$): 0.7

Using the exponential smoothing formula:

$ F_3 = \alpha A_2 + (1-\alpha) F_2 $ $ F_3 = (0.7 \times 635) + (1 - 0.7) \times 425 $ $ F_3 = (444.5) + (0.3 \times 425) $ $ F_3 = 444.5 + 127.5 $ $ F_3 = 572 \text{ units} $

The forecast demand for March 2026 is 572 units.