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

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Example ActivityImmediate Predecessors Time estimate (days) A-30 B-15 C-25 DA3 EC7 FB1 GD, F5 H 2 IE, F4 JH, I10 KG, J8 from Shtub, Bard, Globerson, Project Management, 2 nd Edition, Pearson, 2005.

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Activity-on-Node Network A B C D E F G H I J K END Start ESEF LSLF Notations ES: Earliest Start LS: Latest Start TS: Total Slack EF: Earliest Finish LF: Latest Finish FS: Free Slack 0 30 15 25 3 7 1 5 2 4 8 10 0

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A B C D E F G H I J K END Start 00 -- 030 -- 015 -- 025 -- 1516 -- 3033 -- 38 -- 4654 -- 2532 -- 3335 -- 3236 -- 46 -- 54 -- 0 30 15 25 3 7 1 5 2 4 8 10 0 Earliest Start and Earliest Finish ESEF LSLF Notations ES: Earliest Start LS: Latest Start TS: Total Slack EF: Earliest Finish LF: Latest Finish FS: Free Slack

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A B C D E F G H I J K END Start 00 -- 030 -- 015 -- 025 -- 1516 -- 3033 -- 38 -- 4654 -- 2532 -- 3335 -- 3236 -- 46 -- 54 -- 0 30 15 25 3 7 1 5 2 4 8 10 0 Latest Start and Latest Finish 00 00 030 131 015 1631 025 0 1516 3132 3033 3134 3338 4146 54 4654 2532 2532 3335 3436 3236 3236 46 3646 54 ESEF LSLF Notations ES: Earliest Start LS: Latest Start TS: Total Slack EF: Earliest Finish LF: Latest Finish FS: Free Slack

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A B C D E F G H I J K END Start 00 00 030 131 015 1631 025 0 1516 3132 3033 3134 3338 4146 54 4654 2532 2532 3335 3436 3236 3236 46 3646 54 0 30 15 25 3 7 1 5 2 4 8 10 0 TS = 0 FS = 0 TS = 0 FS = 0 TS = 0 FS = 0 TS = 0 FS = 0 TS = 16 FS = 16 TS = 0 FS = 0 TS = 1 FS = 0 TS = 1 FS = 0 TS = 8 FS = 8 TS = 16 FS = 0 TS = 0 FS = 0 TS = 0 FS = 0 TS = 1 FS = 1 ESEF LSLF Notations ES: Earliest Start LS: Latest Start TS: Total Slack EF: Earliest Finish LF: Latest Finish FS: Free Slack

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A B C D E F G H I J K END Start 00 00 030 131 015 1631 025 0 1516 3132 3033 3134 3338 4146 54 4654 2532 2532 3335 3436 3236 3236 46 3646 54 0 30 15 25 3 7 1 5 2 4 8 10 0 TS = 0 FS = 0 TS = 0 FS = 0 TS = 0 FS = 0 TS = 0 FS = 0 TS = 16 FS = 16 TS = 0 FS = 0 TS = 1 FS = 0 TS = 1 FS = 0 TS = 8 FS = 8 TS = 16 FS = 0 TS = 0 FS = 0 TS = 0 FS = 0 TS = 1 FS = 1 Critical Path ESEF LSLF Notations ES: Earliest Start LS: Latest Start TS: Total Slack EF: Earliest Finish LF: Latest Finish FS: Free Slack

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Exercise ActivityImmediate Predecessors Time estimate (days) A-3 B-4 C-3 DC2 EB1 FA5 GB2 HB3 IC11 JD, E3 KF, G1 LK4 MJ, H4 from Shtub, Bard, Globerson, Project Management, 1st Edition, Prentice-Hall, 1994. 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.

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