Question

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 with a smoothing constant of $\alpha = 0.2$, then the sales forecast for the month of February of the same year is ________________ units (in integer).

Hint:

Exponential smoothing corrects forecast errors slowly when $\alpha$ is small and quickly when $\alpha$ is large.

Answer 1

Correct Answer: 104

Exponential smoothing uses the formula:
\[ F_{t+1} = F_t + \alpha (A_t - F_t) \] The manufacturer underestimated sales by 20 units. Therefore, forecast for January was:
\[ F_{Jan} = 120 - 20 = 100 \] Actual January sales:
\[ A_{Jan} = 120 \] Now compute forecast for February:
\[ F_{Feb} = 100 + 0.2(120 - 100) \] \[ F_{Feb} = 100 + 4 = 104 \] Thus, the forecasted sales for February is:
\[ \boxed{104} \]