Manufacturing Systems CA01
Q1 i. Compute the Simple Moving Average for three and five periods, and then compute MAD and MSE
for each.
Period
Demand
Sum
SMA (3)
et
|et|
|et-ebar|
|et-ebar|2
1
2
3
4
5
6
7
8
9
10
11
20
18
25
15
18
22
26
28
25
23
15
63.00
58.00
58.00
55.00
66.00
76.00
79.00
76.00
21.00
19.33
19.33
18.33
22.00
25.33
26.33
25.33
AVG (ebar)
SUM
-6.00
-1.33
2.67
7.67
6.00
-0.33
-3.33
-10.33
6.00
1.33
2.67
7.67
6.00
0.33
3.33
10.33
4.71
1.29
3.38
2.04
2.96
1.29
4.38
1.38
5.63
1.67
11.39
4.17
8.75
1.67
19.14
1.89
31.64
22.33
80.32
Period
1
2
3
4
5
6
7
8
9
10
11
Demand
20
18
25
15
18
22
26
28
25
23
15
MAD (3)
MSE (3)
3.19
11.47
Sum
SMA (5)
et
|et|
|et-ebar|
|et-ebar|2
96.00
98.00
106.00
109.00
119.00
124.00
19.20
19.60
21.20
21.80
23.80
24.80
AVG (ebar)
SUM
2.80
6.40
6.80
3.20
-0.80
-9.80
2.80
6.40
6.80
3.20
0.80
9.80
4.97
2.17
1.43
1.83
1.77
4.17
4.83
4.69
2.05
3.36
3.12
17.36
23.36
16.20
53.95
MAD (5)
MSE (5)
3.24
10.79
ii. Show a simple chart of the actual and forecast demands of SMA (3) and SMA (5).
30
No. of vaccines (in millions)
25
20
15
10
5
0
0
2
4
6
8
10
12
Period
Demand
SMA (3)
SMA (5)
iii. Conclude from the results of your computations.
Generally, lower deviation or error is preferred for forecasting. For this example however, SMA(3) has a
smaller MAD but a higher MSE. It might be due to one of the values deviated too far away. Furthermore,
the average error is relatively small in SMA(3), squaring the difference of the large error and small average
error would result in a very large number. There isn’t a clear indication of which Simple Moving Average
is better in this case, as both MAD and MSE can be justified. However in general, when more time period
is taken into consideration, the error would be more diluted.
Q2. Forecast the number of engine failures over periods 1 through 7 using Holt’s Method, assuming
α=β=0.1 and compute the corresponding MAD and MSE. What can you infer from the results of your
computation?
Period
0
1
2
3
4
5
6
7
Demand It
St
Forecast
200.00
10.00
250 214.00
10.40
210.00
175 219.46
9.91
224.40
186 225.03
9.47
229.37
225 233.55
9.38
234.50
285 247.14
9.80
242.93
305 261.74
10.28
256.93
190 263.82
9.46
272.02
AVG (ebar)
SUM
MAD
MSE
et
40.00
-49.40
-43.37
-9.50
42.07
48.07
-82.02
|et|
40.00
49.40
43.37
9.50
42.07
48.07
82.02
44.92
|etebar|
|et-ebar|2
4.92
4.48
1.55
35.42
2.85
3.15
37.10
24.18
20.09
2.41
1254.29
8.10
9.91
1376.53
89.46
2695.52
14.91
449.25
The high MAD and MSE values indicate that forecast was not very accurate with regards to the demand.
For certain periods, the forecast was not responsive to the trends hence a suggestion would be to adjust
the alpha-α and beta-β values for greater precision.
Q3. Compute the sample correlation coefficient, r, and deduce the correlation. Is this inference expected?
SUM
AVG
GDP(x)
5.5
6.1
6.6
7.4
7.3
6.8
7.9
7.0
6.9
7.6
69.1
6.91
Job(y)
115
130
130
142
139
133
145
155
139
142
1370
137
xy
632.5
793.0
858.0
1050.8
1014.7
904.4
1145.5
1085.0
959.1
1079.2
9522.2
x2
30.25
37.21
43.56
54.76
53.29
46.24
62.41
49.00
47.61
57.76
482.09
y2
13225
16900
16900
20164
19321
17689
21025
24025
19321
20164
188734
n
Sxy
Sxx
Syy
r
10
55.5
4.609
1044
0.800
The r value is positive, hence the GPD and number of jobs is positively correlated. As the GPD increase,
the number of jobs will increase, and vice versa as well. Quite logically, the better developing countries
with higher GDP would tend to have more number of jobs.