Critical Path Method CPM David S W Lai
- Slides: 8
Critical Path Method (CPM) David S. W. Lai Sept 9, 2013
Example Activity Immediate Predecessors Time estimate (days) A - 30 B - 15 C - 25 D A 3 E C 7 F B 1 G D, F 5 H D, F 2 I E, F 4 J H, I 10 K G, J 8 from Shtub, Bard, Globerson, Project Management, 2 nd Edition, Pearson, 2005.
Activity-on-Node Network 30 A 15 B 0 Start 25 C 3 D 7 E 1 F Notations ES EF LS LF ES: Earliest Start LS: Latest Start EF: Earliest Finish LF: Latest Finish TS: Total Slack FS: Free Slack 5 G 2 H 4 I 8 K 10 J 0 END
Earliest Start and Earliest Finish 0 30 30 33 33 38 - - - 30 A 0 0 - - 3 D 5 G 15 25 32 33 35 - - - 0 Start 7 E 25 2 H 1 F C ES EF LS LF 25 15 16 32 36 - - - TS: Total Slack FS: Free Slack 54 - - J 0 ES: Earliest Start LS: Latest Start EF: Earliest Finish LF: Latest Finish 54 10 4 I Notations 54 8 K 0 15 B 46 36 46 - - 0 END
Latest Start and Latest Finish 0 30 30 33 33 38 1 - 31 - 34 - 41 - 46 - 30 A 0 0 0 - 3 D 5 G 15 25 32 33 35 16 - 31 - 25 - 32 - 34 - 36 - 0 Start 7 E 25 2 H 1 F C ES EF LS LF 25 15 16 32 36 0 - 25 - 31 - 32 - 36 - TS: Total Slack FS: Free Slack 54 46 - 54 - J 0 ES: Earliest Start LS: Latest Start EF: Earliest Finish LF: Latest Finish 54 10 4 I Notations 54 8 K 0 15 B 46 36 - 46 - 0 END
0 0 TS = 1 FS = 0 0 30 30 33 33 38 TS = 0 FS = 0 1 31 31 34 41 46 46 54 54 54 30 A TS = 0 FS = 0 3 D 25 32 33 35 16 31 25 32 34 36 Start 25 LS LF 7 E TS = 0 FS = 0 1 F C EF 8 K 15 0 ES 5 G 0 15 TS = 16 B FS = 0 Notations TS = 8 FS = 8 TS = 1 FS = 0 2 TS = 1 H FS = 1 J 4 I 0 25 15 16 32 36 0 25 31 32 32 36 TS = 0 FS = 0 ES: Earliest Start LS: Latest Start EF: Earliest Finish LF: Latest Finish TS = 16 FS = 16 TS: Total Slack FS: Free Slack 10 TS = 0 FS = 0 36 46 TS = 0 FS = 0 0 END
0 0 TS = 1 FS = 0 0 30 30 33 33 38 TS = 0 FS = 0 1 31 31 34 41 46 46 54 54 54 30 A TS = 0 FS = 0 3 D 25 32 33 35 16 31 25 32 34 36 Start 25 LS LF 7 E TS = 0 FS = 0 1 F C EF 8 K 15 0 ES 5 G 0 15 TS = 16 B FS = 0 Notations TS = 8 FS = 8 TS = 1 FS = 0 2 TS = 1 H FS = 1 0 25 15 16 32 36 0 25 31 32 32 36 TS = 0 FS = 0 ES: Earliest Start LS: Latest Start EF: Earliest Finish LF: Latest Finish TS = 16 FS = 16 TS: Total Slack FS: Free Slack TS = 0 FS = 0 0 END Critical Path 10 J 4 I TS = 0 FS = 0 36 46 TS = 0 FS = 0
Exercise Immediate Predecessors Time estimate (days) A - 3 B - 4 C - 3 D C 2 E B 1 F A 5 G B 2 H B 3 I C 11 J D, E 3 K F, G 1 L K 4 M J, H 4 Question: Determine the critical path and the slacks. Interpret their meanings. To check your solution: The critical path is (C, I). The project duration is 14 days. Activity from Shtub, Bard, Globerson, Project Management, 1 st Edition, Prentice-Hall, 1994.
