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# (AOA) and (AON) Network construction and critical path calculations (using four methods)

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Project Management: Network construction and critical path calculations (using four methods)

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### (AOA) and (AON) Network construction and critical path calculations (using four methods)

1. 1. Project Management (AOA) and (AON) Network Construction and Critical Path Calculations (Using Four Methods) Dr. Mahmoud Abbas Mahmoud Assistant Professor
2. 2. (AOA) and (AON) Network Construction and Critical Path Calculations (Using Four Methods) EXAMPLE: Construct the (AOA) and (AON) networks for the project whose activities, their durations and their precedence relationships are as given in the table, also find: i) [ES, EF, LS, LF, Slack] for all activities. ii) Critical path(s). iii) Project completion time. Activity Predecessor Activity Duration (days) A - 2 B A 8 C A 10 D B 6 E B 3 F C 3 G C 7 H D, F 5 I E 2 J G 8
3. 3. Solution (1): (AOA) network Activity Path (i - j) Duration (days) ES EF LS LF TF (Slack) Critical A (1 – 2) 2 0 2 0 2 0* Yes B (2 – 3) 8 2 10 8 16 6 No C (2 – 4) 10 2 12 2 12 0* Yes D (3 – 5) 6 10 16 16 22 6 No E (3 – 6) 3 10 13 22 25 12 No F (4 – 5) 3 12 15 19 22 7 No G (4 – 7) 7 12 19 12 19 0* Yes H (5 – 8) 5 16 21 22 27 6 No I (6 – 8) 2 13 15 25 27 12 No J (7 – 8) 8 19 27 19 27 0* Yes Therefore: Critical path: A --- C --- G --- J Project completion time = 27 days
4. 4. Solution (2): (AOA) network (calculations in node) Activity Path (i - j) Duration (days) ES EF LS LF TF (Slack) Critical A (1 – 2) 2 0 2 0 2 0* Yes B (2 – 3) 8 2 10 8 16 6 No C (2 – 4) 10 2 12 2 12 0* Yes D (3 – 5) 6 10 16 16 22 6 No E (3 – 6) 3 10 13 22 25 12 No F (4 – 5) 3 12 15 19 22 7 No G (4 – 7) 7 12 19 12 19 0* Yes H (5 – 8) 5 16 21 22 27 6 No I (6 – 8) 2 13 15 25 27 12 No J (7 – 8) 8 19 27 19 27 0* Yes Note: (LC = LF) & (EC = EF) Therefore: Critical path: A --- C --- G --- J Project completion time = 27 days
5. 5. Solution (3): (AOA) network (calculations on arrow) Activity Path (i - j) Duration (days) ES EF LS LF TF (Slack) Critical A (1 – 2) 2 0 2 0 2 0* Yes B (2 – 3) 8 2 10 8 16 6 No C (2 – 4) 10 2 12 2 12 0* Yes D (3 – 5) 6 10 16 16 22 6 No E (3 – 6) 3 10 13 22 25 12 No F (4 – 5) 3 12 15 19 22 7 No G (4 – 7) 7 12 19 12 19 0* Yes H (5 – 8) 5 16 21 22 27 6 No I (6 – 8) 2 13 15 25 27 12 No J (7 – 8) 8 19 27 19 27 0* Yes Therefore: Critical path: A --- C --- G --- J Project completion time = 27 days
6. 6. Solution (4): (AON) network Activity Path (i - j) Duration (days) ES EF LS LF TF (Slack) Critical A (1 – 2) 2 0 2 0 2 0* Yes B (2 – 3) 8 2 10 8 16 6 No C (2 – 4) 10 2 12 2 12 0* Yes D (3 – 5) 6 10 16 16 22 6 No E (3 – 6) 3 10 13 22 25 12 No F (4 – 5) 3 12 15 19 22 7 No G (4 – 7) 7 12 19 12 19 0* Yes H (5 – 8) 5 16 21 22 27 6 No I (6 – 8) 2 13 15 25 27 12 No J (7 – 8) 8 19 27 19 27 0* Yes Therefore: Critical path: A --- C --- G --- J Project completion time = 27 days