An electric car manufacturer underestimated the January sales of car by 20 units, while the actual sales was 120 units. If the manufacturer uses exponential smoothing method with a smoothing constant of α = 0.2, then the sales forecast for the month of February of the same year is ___________units (in integer).

The correct answer is 104.

To understand why this is the correct forecast, let us break down the problem step-by-step using the principles of exponential smoothing forecasting.

1. Understand the Given Data:
We are given the following values for the month of January (which serves as the previous period, $t_{-1}$):
- Actual sales in January ($D_{t-1}$) = 120 units
- Smoothing constant ($\alpha$) = 0.2
- Underestimation error ($e$) = 20 units

The error in forecasting ($e$) is defined as the difference between the actual demand and the forecasted demand for that period:
$e=D_{t-1}-F_{t-1}$

Since the manufacturer underestimated the sales by 20 units, it means the actual sales exceeded the forecast by 20 units:
$20=120-F_{t-1}$

Rearranging the equation to find the January forecast ($F_{t-1}$):
$F_{t-1}=120-20=100\text{units}$

2. Calculate the Forecast for February ($F_t$):
The exponential smoothing formula to calculate the forecast for the next period is:
$F_t=\alpha D_{t-1}+(1-\alpha )F_{t-1}$

Substituting the values we have into the formula:
$F_t=0.2\times 120+(1-0.2)\times 100$

Simplify the terms:
$F_t=24+0.8\times 100$
$F_t=24+80=104\text{units}$

Thus, the sales forecast for the month of February is 104 units.