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The following table shows the actual demand observed over the last 11 years:
| Year | 1 2 3 4 5 6 7 8 9 10 11 |
| Demand | 8 8 6 10 11 7 12 13 10 9 8 |
Using exponential smoothing with α = 0.50 and a forecast for year 1 of 7.0, provide the forecast from periods 2 through 12 (round your responses to one decimal place).
| Year | 1 2 3 4 5 6 7 8 9 10 11 12 |
| Forecast | 7.0 |
Revelant knowledge
Exponential smoothing is an method of thumb method for smoothing data from time series data by using an exponential window function. While in an ordinary moving average, straightforward move average the previous observations are equally weighted exponential functions are employed to assign decreasing weights over time. It is a simple and quickly applied method of making a decision that is based on assumptions previously made that are made by users, for example, seasonality. Exponential smoothing is commonly employed to analyze time-series data.
Use the exponential smoothing technique:
F(2) = 0.5 x Actual demand (1) + (1-0.5) x F(1)
= 0.5 x 8 + 0.5 x 7
= 7.5
F(3) = 0.5 x Actual demand (2) + (1-0.5) x F(2)
= 0.5 x 8 + 0.5 x 7.5
= 7.8
F(4) = 0.5 x Actual demand (3) + (1-0.5) x F(3)
= 0.5 x 6 + 0.5 x 7.8
= 6.9
F(5) = 0.5 x Actual demand (4) + (1-0.5) x F(4)
= 0.5 x 10 + 0.5 x 6.9
= 8.5
F(6) = 0.5 x Actual demand (5) + (1-0.5) x F(5)
= 0.5 x 11 + 0.5 x 8.5
= 9.8
F(7) = 0.5 x Actual demand (6) + (1-0.5) x F(6)
= 0.5 x 7 + 0.5 x 9.8
= 8.4
F(8) = 0.5 x Actual demand (7) + (1-0.5) x F(7)
= 0.5 x 12 + 0.5 x 8.4
= 10.2
F(9) = 0.5 x Actual demand (8) + (1-0.5) x F(8)
= 0.5 x 13 + 0.5 x 10.2
= 11.6
F(10) = 0.5 x Actual demand (9) + (1-0.5) x F(9)
= 0.5 x 10 + 0.5 x 11.6
= 10.8
F(11) = 0.5 x Actual demand (10) + (1-0.5) x F(10)
= 0.5*9 + 0.5*10.8
= 9.9
F(12) = 0.5 x Actual demand (11) + (1-0.5) x F(11)
= 0.5 x 8 + 0.5 x 9.9
= 9