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**Critical Path Method (CPM)**

David S.W. Lai Sept 9, 2013

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**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.

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**Activity-on-Node Network**

30 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

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**Earliest Start and Earliest Finish**

30 - 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

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**Latest Start and Latest Finish**

30 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

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**TS = 8 FS = 8 TS = 1 FS = 0 TS = 1 FS = 0 TS = 0 FS = 0 TS = 0 FS = 0**

30 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

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**TS = 8 FS = 8 TS = 1 FS = 0 TS = 1 FS = 0 TS = 0 FS = 0 TS = 0 FS = 0**

30 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

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**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.

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