![(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](https://image.slidesharecdn.com/aoaandaonnetworkconstructionandcriticalpathcalculationsusingfourmethods-161219151039/85/AOA-and-AON-Network-construction-and-critical-path-calculations-using-four-methods-2-320.jpg)
(AOA) and (AON) Network construction and critical path calculations (using four methods)
- 1. Project Management (AOA) and (AON) Network Construction and Critical Path Calculations (Using Four Methods) Dr. Mahmoud Abbas Mahmoud Assistant Professor
- 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. 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. 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. 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. 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