Question

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	88	88	55	99	1313	99	1313	1212	1010	99	88

Using exponential smoothing with

alphaα

​=

0.400.40

and a forecast for year 1 of

7.07.0​,

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	7.07.0	nothing	nothing	nothing	nothing	nothing	nothing	nothing	nothing	nothing	nothing	nothing

Provide the forecast from periods 2 through 12 using the naive approach ​(enter your responses as whole​ numbers).

Year	2	3	4	5	6	7	8	9	10	11	12
Forecast	nothing	nothing	nothing	nothing	nothing	nothing	nothing	nothing	nothing	nothing	nothing

Answer 1

Using the exponential smoothing method the formula to calculate the forecast is as follows :

Ft = F(t-1) + [A(t-1) - F(t-1)]

Where Ft = forecast for period t

A(t-1)= actual value for period previous to t

F(t - 1)= forecast for period previous to t

= smoothing constant

So using the above formula with =0.40 and year 1 forecast of 7.0 the forecast for year 2 through 12 are

• For year 2 = 7.0 + 0.40(8-7.0) = 7.0+0.40 = 7.4
• For year 3 = 7.4 + 0.40(8-7.4) = 7.4+0.24 = 7.6
• For year 4 = 7.6 + 0.40(5-7.6)= 7.6+(-1.04) = 7.6-1.04 = 6.6
• For year 5 = 6.6 + 0.40(9-6.6) = 6.6+0.96 = 7.6
• For year 6 = 7.6 + 0.40(13-7.6) = 7.6 + 2.16 = 9.8
• For year 7 = 9.8 + 0.40(9-9.8) = 9.8 +(-0.32) = 9.8-0.32 = 9.5
• For year 8 = 9.5+ 0.40(13-9.5) = 9.5 + 1.4 = 10.9
• For year 9 = 10.9 + 0.40(12-10.9) = 10.9+0.44 = 11.3
• For year 10 = 11.3 + 0.40(10-11.3)= 11.3+(-0.52) = 11.3-0.52 = 10.8
• For year 11 = 10.8 + 0.40(9-10.8) = 10.8+(-0.72) = 10.8-0.72 = 10.1
• For year 12 = 10.1 + 0.40(8-10.1) = 10.1+(-0.84) = 10.1-0.84 = 9.3

Using a naive approach the forecast for a period is equal to the actual value of the immediately previous period. So using the naive approach the forecast for year 2 through 12 are

• For year 2 = Actual demand in year 1 = 8
• For year 3 = Actual demand in year 2 = 8
• For year 4 = Actual demand in year 3 = 5
• For year 5 = Actual demand in year 4 = 9
• For year 6 = Actual demand in year 5 = 13
• For year 7 = Actual demand in year 6 = 9
• For year 8 = Actual demand in year 7 = 13
• For year 9 = Actual demand in year 8 = 12
• For year 10 = Actual demand in year 9 = 10
• For year 11 = Actual demand in year 10 = 9
• For year 12 = Actual demand in year 11 = 8