Sales of tablet computers at Ted Glickman\'s electronics store in Washington, D.
ID: 469644 • Letter: S
Question
Sales of tablet computers at Ted Glickman's electronics store in Washington, D.C., over the past 10 weeks are shown in the table below:
Week
1
2
3
4
5
6
7
8
9
10
Demand
21
21
29
38
26
29
35
22
26
30
a) The forecast for weeks 2 through 10 using exponential smoothing with
alpha
=
0.55
and a week 1 initial forecast of
21.0
are (round your responses to two decimalplaces):
Week
1
2
3
4
5
6
7
8
9
10
Demand
21
21
29
38
26
29
35
22
26
30
Forecast
21.0
__
__
__
__
__
__
__
__
__
Week
1
2
3
4
5
6
7
8
9
10
Demand
21
21
29
38
26
29
35
22
26
30
Explanation / Answer
Exponential smoothing method
In exponential smoothing method, the new forecast is based on the previous forecast, plus a percentage of the difference between that forecast and the actual forecast of the series at that point.
Next forecast = Previous forecast + (Actual Previous forecast)
The equation is:
Ft = Ft-1 + (At-1 Ft-1)
Ft = Ft-1 + At-1 Ft-1
Ft = At-1 + (1 – )Ft-1
Where,
Ft = Forecast for time period t
Ft1 = Forecast for time period t1
At1 = Actual value in period (t1)
= Smoothing constant (percentage)
Let the forecast of first period be equal to actual service calls of same week 1.
Forecast for the period t by exponential smoothing method ( = 0.55)
Ft = 0.55At-1 + (1 – 0.55)Ft-1 = 0.55At-1 + 0.45Ft-1
Week
1
2
3
4
5
6
7
8
9
10
At
Demand
21
21
29
38
26
29
35
22
26
30
Ft
Forecast
21
21
21
25.4
32.33
28.85
28.93
32.27
26.62
26.28
Note:
F2 = 0.55A1 + 0.45F1 = 0.55 x 21 + 0.45 x 21 = 21
F4 = 0.55A3 + 0.45F3 = 0.55 x 29 + 0.45 x 21 = 25.4
Week
1
2
3
4
5
6
7
8
9
10
At
Demand
21
21
29
38
26
29
35
22
26
30
Ft
Forecast
21
21
21
25.4
32.33
28.85
28.93
32.27
26.62
26.28