GATE 2022 ME (ME2) – Question 32
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 $\alpha=0.2$, then the sales forecast for the month of February of the same year is ______ units (in integer).
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Correct answer: 104
Explanation
**Step 1: the January forecast.** The manufacturer underestimated by 20 units and the actual sales were 120, so the forecast was
$$F_{Jan}=120-20=100 .$$
**Step 2: exponential smoothing.** The next forecast is
$$F_{Feb}=F_{Jan}+\alpha\,(A_{Jan}-F_{Jan}).$$
**Step 3: numbers.**
$$F_{Feb}=100+0.2\,(120-100)=100+4=\mathbf{104}\text{ units}.$$