PERT Networks

1
PERT Networks

• In PERT the duration of any activity is
  indeterministic. It bases the duration of an
  activity on three estimates
• Optimistic Time, a
• Most Likely Time, m
• Pessimistic Time, b

2
The range a, b is assumed to enclose all
possible estimates of the duration of an
activity. Based on these estimates, the average
time,?D, and variance , ?, are computed as
follows
CPM calculations given earlier will be applied
directly, with ?D replacing the single estimate D.
3
Consider the network with the estimates of the
activities given below
4
Activity a m b
?D ?
(1,2) 2 5 8
5 1
(1,3) 1 4 7
4 1
(2,3) 0 0 0
0 0
4 0.44
(2,4) 2 4 6
(2,6) 5 7 12
7.5 1.36
(3,4) 3 5 10
5.5 1.36
(3,5) 3 6 9
6 1
(4,5) 4 10 6
6.33 1
(4,6) 2 5 8
5 1
(5,6) 2 4 6
4 0.44
5
16.83
5
5
16.83
6
3
5
20.83
10.5
0
20.83
6.33
4
5.5
10.5
4
0
0
6
4
Dummy
1
5
4
7.5
5
2
5
5
6
Thus the mean duration of the project 20.83
days The variance of the duration of the project
sum of the variances of the activities on the
critical path 101.3610.44 3.80 Thus P(
project will be completed within 23 days)
7
Problem 1(a) Set 6.6E Page 285
Consider the network with the estimates of the
activities given below
8
Activity a m b
?D ?
(1,2) 5 6 8
6.17 0.25
(1,4) 1 3 4
2.83 0.25
(1,5) 2 4 5
3.83 0.25
5 0.11
(2,3) 4 5 6
(2,5) 7 8 10
8.15 0.25
(2,6) 8 9 13
9.5 0.69
(3,4) 5 9 19
10 5.44
(3,6) 3 4 5
4 0.11
(4,6) 4 8 10
7.67 1
10.67 1
(5,6) 9 10 15
9
Activity a m b
?D ?
(5,7) 4 6 8
6 0.44
(6,7) 3 4 5
4 0.11
10
21.17
21.17
4
11.17
0
2.83
6.17
10
11.17
0
6.17
3
5
7.67
6.17
6.17
2
4
32.84
1
28.84
28.84
32.84
9.57
4
8.17
6
3.83
7
10.67
18.17
5
6
14.34