13 – 21
Chapter 13
Project Scheduling: PERT/CPM
Case Problem: R.C. Coleman
1. R.C. Coleman’s Project Network
Activity
Expected Time
Variance
A
6
0.44
B
9
2.78
C
4
0.44
D
12
7.11
E
10
1.00
F
6
0.44
G
8
7.11
H
6
0.44
7
2.78
4
0.11
K
4
0.44
Activity
Earliest
Start
Latest
Start
Earliest
Finish
Latest
Finish
Slack
Critical
Activity
A
0
3
6
9
3
B
0
0
9
9
0
Yes
C
9
9
13
13
0
Yes
D
13
17
25
29
4
13
13
23
23
0
Yes
23
23
29
29
0
Yes
G
13
21
21
29
8
H
29
29
35
35
0
Yes
29
32
36
39
3
35
35
39
39
0
Yes
K
39
39
43
43
0
Yes
Chapter 13
The expected project completion time is 43 weeks. The critical path activities are B-C-E-F-H-J-K.
The variance of the critical path is 5.67.
2.
For 80% chance,
z = +0.84
Thus
Solve for E(T) = 38 weeks.
20%
80%
13 – 23
3. In this section, we will use expected activity times as normal times and use a linear programming
model based on expected times to make the crashing decisions.
Let xi = the completion time for activity i
yi = the amount of crash time for activity i
xA + yA 6
xB + yB 9
xC + yC – xA 4
xC + yC – xB 4
xD + yD – xC 12
xH + yH – xF 6
xH + yH – xG 6
xI + yI – xD 7
xI + yI – xF 7
xK 38
yA 2
yB 2
yC 2
yD 4
yH 2
yI 3
yJ 1
yK 1
The optimal crashing decisions are as follows:
Crash Activity
Weeks
Cost
B
2
800
F
1
550
1
400
K
1
500
Chapter 13
13 – 24
A revised activity schedule based on these crashing decisions is as follows:
Activity
Earliest
Start
Latest
Start
Earliest
Finish
Latest
Finish
Slack
Critical
Activity
A
0
1
6
7
1
B
0
0
7
7
0
Yes
C
7
7
11
11
0
Yes
D
11
14
23
26
3
11
11
21
21
0
Yes
21
21
26
26
0
Yes
H
26
26
32
32
0
Yes
26
28
33
35
2
32
32
35
35
0
Yes
K
35
35
38
38
0
Yes
The student should comment on the fact that the crashing decisions may alter the variance in the
project completion time. By defining revised optimistic, most probable, and pessimistic times for