A company uses exponential smoothing with trend to forecast

A company uses exponential smoothing with trend to forecast monthly sales of its product, which show a trend pattern.
At the end of week 5, the company wants to forecast sales for week 6. The trend through week 4 has been twenty additional cases sold per week.
Average sales have been eighty-five cases per week. The demand for week 5 was ninety cases. The company uses ? = 0.20 and ? = 0.10. Make a forecast including trend for week 6.

(Round your answers to 1 decimal place, the tolerance is +/- 0.3)

Solution

Given: T4 = 20, A5 = 90, S4 = 85

Step 1: we need to calculate smoothing the level of the series

Smoothing the level of the series: S5 = A5 + (1 - )(S4 + T4) = 0.20(90) + 0.80(85 + 20) = 102

Step 2: finding smoothing the trend

Smoothing the trend: T5 = (S5-S4) + (1 - )T4 = 0.10(102 – 85) + 0.90(20) = 19.7

Step 3: finally the forecast including trend

Forecast Including Trend FIT6 = S5 + T5 = 102 + 19.7 = 121.7