Solution: 1.
a) Weighted Moving Average:
Month
Demand
Forecast
Error
Error
1
60
2
55
3
43
4
65
50.0
15.0
15.0
5
52
56.4
-4.4
4.4
6
42
54.1
-12.1
12.1
7
47
49.6
-2.6
2.6
8
59
46.5
12.5
12.5
9
63
52.0
11.0
11.0
10
44
58.6
-14.6
-14.6
11
55
52.7
2.3
2.3
12
49
53.3
-4.3
4.3
13
?
49.8
Total
78.8
Forecast for Period 4 = 430.5 + 550.3 + 60*0.2
Forecast for Period 5 = 650.5 + 430.3 + 55*0.2
Forecast for Period 13 = 490.5 + 550.3 + 44*0.2 = 49.8
b) Exponential Smoothing:
𝛼=0.2
Month Demand Forecast Error
Error
Month
Demand
Forecast
Error
Error
1
60
60.00
2
55
60.00
-5.00
5.00
3
43
59.00
-16.00
16.00
4
65
55.0
9.20
9.20
5
52
55.8
-5.64
5.64
6
42
57.64
-14.51
14.51
7
47
56.51
-6.61
6.61
8
59
53.61
6.71
6.71
9
63
53.63
9.37
9.37
10
44
55.50
-11.50
11.50
11
55
53.2
1.80
1.80
12
49
53.56
-4.56
4.56
13
?
52.65
Total
90.90
Ft+1 =Ft +α(At –Ft) or Ft+1 =αAt +(1–α)Ft
F1 = A1 (Supposed) = 60
F2 =F1 +α(A1 –F1)=60+0.2(60–60)=60
F3 =F2 +α(A2 –F2)=60+0.2(55–60)=59
F13 =F12 +α(A12 –F12)=53.56+0.2(49–53.56)=52.65
MAD
MAD = ∑ |Actual Demand – Forecast| / n
a) Weighted Moving Average:
MAD=78.8/9=8.76
b) Exponential Smoothing:
MAD=90.90/11=8.26
As MAD of Exponential Smoothing is less than that of Weighted Moving Average, it is concluded that Exponential Smoothing is more appropriate.
. Evaluate by green’s theorem. 
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