1. Critical Path Method (CPM)
David S.W. Lai
Sept 9, 2013

2. Immediate Predecessors
Example
Activity
Immediate Predecessors
Time estimate
(days) A - 30 B 15 C 25 D 3 E 7 F 1 G
D, F 5 H 2 I
E, F 4 J
H, I 10 K
G, J 8
from Shtub, Bard, Globerson, Project Management, 2nd Edition, Pearson, 2005.

3. Activity-on-Node Network30 3 5 A D G 8 K
END 15 7 2 B E H
Start 10 J 25 1 4 C F I
Notations ES EF LS LF
ES: Earliest Start LS: Latest Start TS: Total Slack
EF: Earliest Finish LF: Latest Finish FS: Free Slack

4. Earliest Start and Earliest Finish30 - 30 33 - 33 38 - 46 54 - 54 - 30 3 5 A D G 8 K
END 15 - 25 32 - 33 35 - - 15 7 2 B E H
Start 10 J 25 1 4 36 46 - C F I 25 - 15 16 - 32 36 -
Notations ES EF LS LF
ES: Earliest Start LS: Latest Start TS: Total Slack
EF: Earliest Finish LF: Latest Finish FS: Free Slack

5. Latest Start and Latest Finish30 1 31 30 - 30 33 - 30 33 31 34 33 38 - 33 38 41 46 46 54 54 46 54 - 54 - 30 3 5 A D G 8 K
END 15 - 15 16 31 25 32 25 32 - 33 35 34 36 33 35 - - 15 7 2 B E H
Start 10 J 25 1 4 36 46 36 46 - C F I 25 25 - 15 16 31 32 15 16 - 32 36 - 32 36
Notations ES EF LS LF
ES: Earliest Start LS: Latest Start TS: Total Slack
EF: Earliest Finish LF: Latest Finish FS: Free Slack

6. TS = 8 FS = 8 TS = 1 FS = 0 TS = 1 FS = 0 TS = 0 FS = 0 TS = 0 FS = 030 1 31 30 33 31 34 33 38 41 46 46 54 54 30 3 5 A D G 8
TS = 0
FS = 0 K
END 15 16 31 25 32 33 35 34 36 15
TS = 16
FS = 0 7
TS = 0
FS = 0 2
TS = 1
FS = 1 B E H
Start 10 J 25 1 4 36 46 C F I
TS = 0
FS = 0 25 15 16 31 32 32 36
TS = 0
FS = 0
TS = 16
FS = 16
TS = 0
FS = 0
Notations ES EF LS LF
ES: Earliest Start LS: Latest Start TS: Total Slack
EF: Earliest Finish LF: Latest Finish FS: Free Slack

7. TS = 8 FS = 8 TS = 1 FS = 0 TS = 1 FS = 0 TS = 0 FS = 0 TS = 0 FS = 030 1 31 30 33 31 34 33 38 41 46 46 54 54 30 3 5 A D G 8
TS = 0
FS = 0 K
END 15 16 31 25 32 33 35 34 36 15
TS = 16
FS = 0 7
TS = 0
FS = 0 2
TS = 1
FS = 1 B E H
Critical Path
Start 10 J 25 1 4 36 46 C F I
TS = 0
FS = 0 25 15 16 31 32 32 36
TS = 0
FS = 0
TS = 16
FS = 16
TS = 0
FS = 0
Notations ES EF LS LF
ES: Earliest Start LS: Latest Start TS: Total Slack
EF: Earliest Finish LF: Latest Finish FS: Free Slack

8. Immediate Predecessors
Exercise
Activity
Immediate Predecessors
Time estimate
(days) A - 3 B 4 C D 2 E 1 F 5 G H I 11 J
D, E K
F, G L M
J, H
Question:
Determine the critical path and the slacks.
Interpret their meanings.
To check your solution:
The project duration is 14 days.
The critical path is (C, I).
from Shtub, Bard, Globerson, Project Management, 1st Edition, Prentice-Hall, 1994.