Homework Answers
Since the activities are probabilistic in nature, apply Project Evaluation and Review Technique (PERT). The PERT considers that the activity duration follows beta-distribution, for which the expected time and variance of the activities is determined as follows:
|
Activity |
Precedence |
Optimistic time |
Most Likely time |
Pessimistic time |
Activity time |
Variance |
|
o |
m |
p |
te =(o+4m+p)/6 |
=σ2 = [(p-o)/6]2 |
||
|
a |
- |
18 |
25 |
31 |
24.83 |
4.69 |
|
b |
- |
15 |
23 |
30 |
22.83 |
6.25 |
|
c |
- |
25 |
40 |
56 |
40.17 |
26.69 |
|
d |
c |
20 |
30 |
45 |
30.83 |
17.36 |
|
e |
a, b |
12 |
21 |
30 |
21 |
9 |
|
f |
d |
10 |
17 |
25 |
17.17 |
6.25 |
|
g |
f |
5 |
12 |
18 |
11.83 |
4.69 |
|
h |
e |
10 |
20 |
25 |
19.17 |
6.25 |
|
i |
e |
9 |
15 |
22 |
15.17 |
4.69 |
|
j |
g |
8 |
10 |
15 |
10.5 |
1.36 |
|
k |
h, i, j |
20 |
27 |
40 |
28 |
11.11 |
|
l |
h, i, j |
6 |
10 |
15 |
10.17 |
2.25 |
|
m |
k, l |
4 |
7 |
10 |
7 |
1 |
|
n |
k, l |
10 |
14 |
20 |
14.33 |
2.78 |
|
o |
k, l |
7 |
15 |
20 |
14.5 |
4.69 |
|
p |
k, l |
3 |
4 |
6 |
4.17 |
0.25 |
|
q |
m |
4 |
6 |
7 |
5.83 |
0.25 |
|
r |
o |
5 |
8 |
10 |
7.83 |
0.69 |
The network Diagram:
The activity schedules are as follows:
|
Forward Pass Schedule to determine Earliest times of activity |
Backward Pass Schedule to determine latest times of activity |
||||||
|
Activity |
Activity time |
Precedence |
Early Start |
Early Finish |
Late Start |
Late Finish |
Slack |
|
Ti |
ES = max(EF of preceding activities) |
EF = ES + ti |
LS = LF – ti |
LF = min(LS of succeeding activities) |
(LF-EF) |
||
|
a |
24.83 |
- |
0.00 |
24.83 |
45.50 |
70.33 |
45.50 |
|
b |
22.83 |
- |
0.00 |
22.83 |
47.50 |
70.33 |
47.50 |
|
c |
40.17 |
- |
0.00 |
40.17 |
0.00 |
40.17 |
0.00 |
|
d |
30.83 |
c |
40.17 |
71.00 |
40.17 |
71.00 |
0.00 |
|
e |
21 |
a, b |
24.83 |
45.83 |
70.33 |
91.33 |
45.50 |
|
f |
17.17 |
d |
71.00 |
88.17 |
71.00 |
88.17 |
0.00 |
|
g |
11.83 |
f |
88.17 |
100.00 |
88.17 |
100.00 |
0.00 |
|
h |
19.17 |
e |
45.83 |
65.00 |
91.33 |
110.50 |
45.50 |
|
i |
15.17 |
e |
45.83 |
61.00 |
95.33 |
110.50 |
49.50 |
|
j |
10.5 |
g |
100.00 |
110.50 |
100.00 |
110.50 |
0.00 |
|
k |
28 |
h, i, j |
110.50 |
138.50 |
110.50 |
138.50 |
0.00 |
|
l |
10.17 |
h, i, j |
110.50 |
120.67 |
128.33 |
138.50 |
17.83 |
|
m |
7 |
k, l |
138.50 |
145.50 |
148.00 |
155.00 |
9.50 |
|
n |
14.33 |
k, l |
138.50 |
152.83 |
146.50 |
160.83 |
8.00 |
|
o |
14.5 |
k, l |
138.50 |
153.00 |
138.50 |
153.00 |
0.00 |
|
p |
4.17 |
k, l |
138.50 |
142.67 |
156.67 |
160.83 |
18.17 |
|
q |
5.83 |
m |
145.50 |
151.33 |
155.00 |
160.83 |
9.50 |
|
r |
7.83 |
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