Note: use AOA notation with ascending nodes numbers from beginning to end.
Activity Start End a m b Var E(T) ES EF LF LS Slack
a 1 2 5 6 7 0.11 6.00 0.00 6.00 7.00 1.00 1.00
b 1 4 8 8 11 0.25 8.50 0.00 8.50 10.50 2.00 2.00
c 2 5 6 8 11 0.69 8.17 6.00 14.17 15.17 7.00 1.00
d 1 3 9 12 15 1.00 12.00 0.00 12.00 12.00 0.00 0.00
b. Pert/CPM, Probabilistic Completion Time
Path Expected Times E(t) Variances
spath
Probability
1ace 68.17 6.33 20.5 0.11 0.69 0.44 1.1136 0.9992
2dfg 12 63.5 21.5 10.11 0.69 1.3416 0.9688
3bhi 8.5 4.17 6.83 19.5 0.25 0.03 0.25 0.728 1.0000
Pert/CPM, Probabilistic Completion Time
Path Expected Times E(t) Variances
spath
Probability
1ace 68.17 6.33 20.5 0.11 0.69 0.44 1.1136 0.6733
5
6
7
8
Projected Completion Time: 21 Probability of Completion: 0.2341
c. Pert/CPM, Probabilistic Time Estimates
Note: use AOA notation with ascending nodes numbers from beginning to end.
Activity Start End a m b Var E(T) ES EF LF LS Slack
a 1 2 7 7 7 0.00 7.00 0.00 7.00 8.00 1.00 1.00
b 1 4 7 7 7 0.00 7.00 0.00 7.00 11.50 4.50 4.50
c 2 5 6 8 11 0.69 8.17 7.00 15.17 16.17 8.00 1.00
Pert/CPM, Probabilistic Completion Time
Path Expected Times E(t) Variances
spath
Probability
1ace 78.17 6.33 21.5 00.69 0.44 1.063 0.9907
5
6
7
8
Projected Completion Time: 24 Probability of Completion: 0.9333
Pert/CPM, Probabilistic Completion Time
Path Expected Times E(t) Variances
spath
Probability
1ace 78.17 6.33 21.5 00.69 0.44 1.063 0.3190
d. Assume after part c.
Time-Cost Tradeoffs: Crashing
Project Completion Time: 20.5
Crashing Cost: 23
Normal Crashing
Activity Start End Time Time Cost Time ES EF LF LS Slack
a 1 2 7 7 0 7 7 2E-15 0
b 1 4 7 7 0 7 9.5 2.5 2.5
8. Pert/CPM, Probabilistic Completion Time
Path Expected Times E(t) Variances
spath
Probability
1 A 10 10 1.21 1.1 1.0000
2 B 8 8 2 1.4142 1.0000
Path Expected Times E(t) Variances
spath
Probability
1 A 10 10 1.21 1.1 1.0000
2 B 8 8 2 1.4142 1.0000
3 C 12 12 1 1 0.9987
Path Expected Times E(t) Variances
spath
Probability
1 A 10 10 1.21 1.1 0.9968
2 B 8 8 2 1.4142 0.9998
Chapter 17 – Problems 9-17 Note: This worksheet displays results only, you must copy the shaded area and
<Back
Paste Special/Values into the corresponding template to make additional calculations.
9. Pert/CPM, Probabilistic Completion Time
Path Expected Times E(t) Variances
spath
Probability
1 1-2-3 5 4 9 1.362 11.5369 0.7424
2 1-3 8 8 2.56 1.6 0.8944
3
10a. Pert/CPM, Probabilistic Completion Time
Path Expected Times E(t) Variances
spath
Probability
1 1-2-4 4 6 10 0.49 0.81 1.1402 0.8098
2 1-3-4 3 9 12 0.3844 3.61 1.9986 0.3084
3
Path Expected Times E(t) Variances
spath
Probability
1 1-2-4 4 6 10 0.49 0.81 1.1402 0.9603
2 1-3-4 3 9 12 0.3844 3.61 1.9986 0.5000
11. Pert/CPM, Probabilistic Time Estimates
Note: use AOA notation with ascending nodes numbers from beginning to end.
Activity
Start End a m b Var E(T) ES EF LF LS Slack
1 2 8 8 8 0.00 8.00 0.00 8.00 8.00 0.00 0.00
2 3 11 12 13 0.11 12.00 8.00 20.00 29.50 17.50 9.50
38910 12 0.25 10.17 20.00 30.17 39.67 29.50 9.50
811 5 7 10 0.69 7.17 30.17 37.33 46.83 39.67 9.50
2 4 5 6 7 0.11 6.00 8.00 14.00 17.83 11.83 3.83
Path Expected Times E(t) Variances
spath
Probability
1
1-2-3-8-11
812 10.167 7.1667 37.333 00.1111 0.25 0.6944 1.0274 1.0000
2
1-2-4-6-11
8 6 18.667 10.333 43 00.1111 4 1 2.2608 0.9960
3
1-2-4-7-11
8 6 13 13 40 00.1111 00.6944 0.8975 1.0000
P(more than 49) = 0.0302
Pert/CPM, Probabilistic Completion Time
Path Expected Times E(t) Variances
spath
Probability
1
1-2-3-8-11
812 10.167 7.1667 37.333 00.1111 0.25 0.6944 1.0274 1.0000
2
1-2-4-6-11
1-2-4-7-11
8 6 18.667 10.333 43 00.1111 4 1 2.2608 0.9077
12. Pert/CPM, Probabilistic Time Estimates
Note: use AOA notation with ascending nodes numbers from beginning to end.
Activity
Start End a m b Var E(T) ES EF LF LS Slack
a 1 2 2 4 6 0.44 4.00 0.00 4.00 5.83 1.83 1.83
d 2 5 6 8 10 0.44 8.00 4.00 12.00 13.83 5.83 1.83
e 5 9 7 9 12 0.69 9.17 12.00 21.17 23.00 13.83 1.83
h 9 12 2 3 5 0.25 3.17 21.17 24.33 26.17 23.00 1.83
f 2 6 3 4 8 0.69 4.50 4.00 8.50 19.17 14.67 10.67
g 6 12 5 7 9 0.44 7.00 8.50 15.50 26.17 19.17 10.67
Pert/CPM, Probabilistic Completion Time
Path Expected Times E(t) Variances
spath
Probability
1 adeh 4 8 9.1667 3.1667 24.333 0.4444 0.4444 0.6944 0.25 1.354 0.8908
2 afg 4 4.5 715.5 0.4444 0.6944 0.4444 1.2583 1.0000
Path Expected Times E(t) Variances
spath
Probability
1 adeh 4 8 9.1667 3.1667 24.333 0.4444 0.4444 0.6944 0.25 1.354 0.9756
5
6
13.
Initial solution:
Time-Cost Tradeoffs: Crashing
Project Completion Time: 15
Crashing Cost: 0
Normal Crashing
Activity
Start End Time Time Cost Time ES EF LF LS Slack
125 505611
246 6511 12 6 1
4 7 3 3 11 14 15 12 1
After crashing 3 weeks:
Time-Cost Tradeoffs: Crashing
Project Completion Time: 12
Crashing Cost: 56
Normal Crashing
Activity
Start End Time Time Cost Time ES EF LF LS Slack
12518404400
24617549940
473 3912 12 9 0
14. Time-Cost Tradeoffs: Crashing
Project Completion Time: 49
Initial Solution: Crashing Cost: 0
Normal Crashing
Activity
Start End Time Time Cost Time ES EF LF LS Slack
a 1 2 12 12 012 26 14 14
b 2 3 14 14 12 26 40 26 14
c 1 4 10 10 010 10 0 0
d 4 5 17 17 10 27 31 14 4
e 4 6 18 18 10 28 30 12 2
f 4 7 12 12 10 22 22 10 0
g 5 8 15 15 27 42 46 31 4
Project Completion Time: 44
Final solution after crashing 5 times. Crashing Cost: 73000
Normal Crashing
Activity
Start End Time Time Cost Time ES EF LF LS Slack
a 1 2 12 12 012 21 9 9
b 2 3 14 14 12 26 35 21 9
c 1 4 10 210000 8 0 8 8 0 0
d 4 5 17 17 825 26 9 1
e 4 6 18 116000 17 825 25 8 0
f 4 7 12 227000 10 818 18 8 0
g 5 8 15 15 25 40 41 26 1
15. Time-Cost Tradeoffs: Crashing
Project Completion Time: 35
Initial Solution: Crashing Cost: 0
Normal Crashing
Activity
Start End Time Time Cost Time ES EF LF LS Slack
125 505500
258 8513 13 5 0
5 7 7 7 13 20 20 13 0
711 4 4 20 24 24 20 0
11 13 11 11 24 35 35 24 0
10 12 8 8 24 32 34 26 2
Project Completion Time: 29
Final solution after crashing 6 times. Crashing Cost: 185
Normal Crashing
Activity
Start End Time Time Cost Time ES EF LF LS Slack
1 2 5 2 40 3 0 3 3 0 0
258 8311 11 3 0
5 7 7 7 11 18 18 11 0
711 4 2 35 218 20 20 18 0
11 13 11 263 920 29 29 20 0
1 3 4 1 12 3 0 3 3 0 0
3 8 12 12 315 15 3 0
16. Time-Cost Tradeoffs: Crashing
Project Completion Time: 39
Initial Solution: Crashing Cost: 0
Normal Crashing
Activity
Start End Time Time Cost Time ES EF LF LS Slack
K 1 2 9 9 0 9 9 0 0
L 2 3 7 7 9 16 16 9 0
N 2 4 5 5 9 14 14 9 0
Project Completion Time: 34
Final solution after crashing 5 times. Crashing Cost: 1030
Normal Crashing
Activity
Start End Time Time Cost Time ES EF LF LS Slack
K 1 2 9 9 0 9 9 0 0
L 2 3 7 1 125 6 9 15 15 9 0
N 2 4 5 2 90 3 9 12 12 9 0
M 3 5 4 1 300 315 18 18 15 0
17a. Pert/CPM, Probabilistic Time Estimates
Note: use AOA notation with ascending nodes numbers from beginning to end.
Activity
Start End a m b Var E(T) ES EF LF LS Slack
1 2 4 5 6 0.11 5.00 0.00 5.00 5.00 0.00 0.00
2 4 7 8 10 0.25 8.17 5.00 13.17 13.17 5.00 0.00
4 6 3 5 9 1.00 5.33 13.17 18.50 18.50 13.17 0.00
b. Pert/CPM, Probabilistic Completion Time
Path Expected Times E(t) Variances
spath
Probability
1 1-2-4-6 5 8.1667 5.3333 18.5 0.1111 0.25 11.1667 0.3341