Project Management, Easy steps to network construction and critical path determination

1. Easy Steps to Network
Construction and Critical Path
Determination
Project Management
Dr. Mahmoud Abbas Mahmoud
Asst. Prof.
2016

2. Easy Steps to Network
Construction and Critical Path
Determination
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
Example:
For the activities given in the table:
i) Draw the (AOA) network diagram.
ii) Find the critical activities.
iii) Find the critical path (CP).
iv) Find project completion time.
We will illustrate these steps
with the following Example.
Dr. Mahmoud Abbas Mahmoud

3. Dr. Mahmoud Abbas Mahmoud
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG

4. Note:
Practically, nodes numbering
can be start by (0) or (1).
Dr. Mahmoud Abbas Mahmoud
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
1

5. A
1
Dr. Mahmoud Abbas Mahmoud
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG

6. A
1
Dr. Mahmoud Abbas Mahmoud
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
2

7. A
1
Dr. Mahmoud Abbas Mahmoud
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
2
B

8. A
1
Dr. Mahmoud Abbas Mahmoud
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
2
B
3

9. A
1
Dr. Mahmoud Abbas Mahmoud
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
2
B
3
C

10. A
1
Dr. Mahmoud Abbas Mahmoud
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
2
B
3
C
D

11. A
1
Dr. Mahmoud Abbas Mahmoud
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
2
B
3
C
D
4

12. A
1
Dr. Mahmoud Abbas Mahmoud
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
2
B
3
C
D
4
E

13. A
1
Dr. Mahmoud Abbas Mahmoud
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
2
B
3
C
D
4
E
5

14. A
1
Dr. Mahmoud Abbas Mahmoud
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
2
B
3
C
D
4
E
5
F

15. A
1
Dr. Mahmoud Abbas Mahmoud
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
2
B
3
C
D
4
E
5
F
6

16. A
1
Dr. Mahmoud Abbas Mahmoud
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
2
B
3
C
D
4
E
5
F
6
G

17. A
1
Dr. Mahmoud Abbas Mahmoud
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
2
B
3
C
D
4
E
5
F
6
G
???????But
(G) depend on both (D) and (E)

18. A
1
Dr. Mahmoud Abbas Mahmoud
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
2
B
3
C
D
4
E
5
F
6
G
Use Dummy !

19. A
1
Dr. Mahmoud Abbas Mahmoud
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
2
B
3
C
D
4
E
5
F
6
G
Dummy

20. A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
Dr. Mahmoud Abbas Mahmoud
G= 12
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
0

21. A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
Dr. Mahmoud Abbas Mahmoud
G= 12
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
0
(AOA) Network Drawing is Completed

22. A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
Dr. Mahmoud Abbas Mahmoud
G= 12
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
0
Critical Path Calculations

23. A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
Dr. Mahmoud Abbas Mahmoud
G= 12
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
0
Forward Pass:

24. A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
Dr. Mahmoud Abbas Mahmoud
G= 12
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
0
Forward Pass:
Calculating the Earliest Start Time (ES):

25. A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
Dr. Mahmoud Abbas Mahmoud
G= 12
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
0
Forward Pass:
Calculating the Earliest Start Time (ES):
Earliest Start Time (ES)j=Max [ (ES)i + Dij ]

26. A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
Dr. Mahmoud Abbas Mahmoud
G= 12
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
0
0
Earliest Start Time (ES) for Start Event = (0)
NOTE: (ES) for any Start Event = (0)

27. A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
Dr. Mahmoud Abbas Mahmoud
G= 12
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
0
0

28. A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
Dr. Mahmoud Abbas Mahmoud
G= 12
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
0
10[0+10]= 10
0

29. A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
Dr. Mahmoud Abbas Mahmoud
G= 12
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
0
0
10
15 Max [(0+7) , (10+5)] = Max [7,15]= 15

30. A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
Dr. Mahmoud Abbas Mahmoud
G= 12
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
0
0
10
15
16
[10+ 6]= 16

31. A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
Dr. Mahmoud Abbas Mahmoud
G= 12
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
0
0
10
15
16
24
Max [(15+9) , (16+0)] =
Max [24,16]= 24

32. A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
Dr. Mahmoud Abbas Mahmoud
G= 12
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
0
0
10
15
16
24
36
Max [(16+8) , (24+12)]
= Max [24,36]= 36

33. A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
Dr. Mahmoud Abbas Mahmoud
G= 12
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
0
0
10
15
16
24
36
Therefore, Project
completion time is:
36 weeks

34. A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
Dr. Mahmoud Abbas Mahmoud
G= 12
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
0
0
10
15
16
24
36
Backward Pass:

35. A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
Dr. Mahmoud Abbas Mahmoud
G= 12
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
0
0
10
15
16
24
36

36. A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
Dr. Mahmoud Abbas Mahmoud
G= 12
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
0
0
10
15
16
24
36
36

37. A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
Dr. Mahmoud Abbas Mahmoud
G= 12
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
0
0
10
15
16
24
36
36
Calculating the Latest Completion Time (LC):

38. A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
Dr. Mahmoud Abbas Mahmoud
G= 12
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
0
0
10
15
16
24
36
36
Calculating the Latest Completion Time (LC):
Latest Completion Time (LC)i=Min [ (LC)j - Dij ]

39. A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
Dr. Mahmoud Abbas Mahmoud
G= 12
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
0
0
10
15
16
24
24
36
36
36 – 12 = 24

40. A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
Dr. Mahmoud Abbas Mahmoud
G= 12
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
0
0
10
15
24
16
24
24
36
36
Min [(36-8),(24-0)=
Min[28,24] = 24

41. A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
Dr. Mahmoud Abbas Mahmoud
G= 12
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
0
0
10
15
15
24
16
24
24
36
36
24 – 9 = 15

42. A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
Dr. Mahmoud Abbas Mahmoud
G= 12
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
0
0
10
10
15
15
24
16
24
24
36
36
Min [(24-6),(15-5)=
Min[18,10] = 10

43. A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
Dr. Mahmoud Abbas Mahmoud
G= 12
Duration
(week)
Preceding
Activity
Activity
10-A
7-B
5AC
6AD
9B, CE
8DF
12D, EG
0
0
0
10
10
15
15
24
16
24
24
36
36
Min [(15-7),(10-10)=
Min[8, 0] = 0

44. A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
Dr. Mahmoud Abbas Mahmoud
G= 12
0
0
0
10
10
15
15
24
16
24
24
36
36

45. A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
Dr. Mahmoud Abbas Mahmoud
G= 12
0
0
0
10
10
15
15
24
16
24
24
36
36
How to find the Critical Activities and
the Critical Path ???

46. Dr. Mahmoud Abbas Mahmoud
Remember that only a critical
activity can have a Zero Total
Float (TF)

47. Dr. Mahmoud Abbas Mahmoud
Therefore, we will calculate
the Total Floats for all
activities and each activity
has a ZERO Total Float (TF)
will be a critical activity.

48. Total Float (TF) calculations
Dr. Mahmoud Abbas Mahmoud
TFij = (LC)j – (ES)i – Dij
A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
G= 12
0
0
0
10
10
15
15
24
16
24
24
36
36

49. Dr. Mahmoud Abbas Mahmoud
A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
G= 12
0
0
0
10
10
15
15
24
16
24
24
36
36
CriticalTotal FloatActivity
A
B
C
D
E
F
G
Dummy

50. Dr. Mahmoud Abbas Mahmoud
A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
G= 12
0
0
0
10
10
15
15
24
16
24
24
36
36
CriticalTotal FloatActivity
Yes0A
B
C
D
E
F
G
Dummy
For activity A (1, 2)
TF = 10 – 0 – 10 = 0*

51. Dr. Mahmoud Abbas Mahmoud
A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
G= 12
0
0
0
10
10
15
15
24
16
24
24
36
36
CriticalTotal FloatActivity
Yes0A
B
C
D
E
F
G
Dummy

52. Dr. Mahmoud Abbas Mahmoud
A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
G= 12
0
0
0
10
10
15
15
24
16
24
24
36
36
CriticalTotal FloatActivity
Yes0A
No8B
C
D
E
F
G
Dummy
For activity B (1, 3)
TF = 15 – 0 – 7 = 8

53. Dr. Mahmoud Abbas Mahmoud
A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
G= 12
0
0
0
10
10
15
15
24
16
24
24
36
36
CriticalTotal FloatActivity
Yes0A
No8B
C
D
E
F
G
Dummy

54. Dr. Mahmoud Abbas Mahmoud
A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
G= 12
0
0
0
10
10
15
15
24
16
24
24
36
36
CriticalTotal FloatActivity
Yes0A
No8B
Yes0C
D
E
F
G
Dummy
For activity C (2, 3)
TF = 15 – 10 – 5 = 0*

55. Dr. Mahmoud Abbas Mahmoud
A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
G= 12
0
0
0
10
10
15
15
24
16
24
24
36
36
CriticalTotal FloatActivity
Yes0A
No8B
Yes0C
D
E
F
G
Dummy

56. Dr. Mahmoud Abbas Mahmoud
A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
G= 12
0
0
0
10
10
15
15
24
16
24
24
36
36
CriticalTotal FloatActivity
Yes0A
No8B
Yes0C
No8D
E
F
G
Dummy
For activity D (3, 4)
TF = 24 – 10 – 6 = 8

57. Dr. Mahmoud Abbas Mahmoud
A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
G= 12
0
0
0
10
10
15
15
24
16
24
24
36
36
CriticalTotal FloatActivity
Yes0A
No8B
Yes0C
No8D
E
F
G
Dummy

58. Dr. Mahmoud Abbas Mahmoud
A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
G= 12
0
0
0
10
10
15
15
24
16
24
24
36
36
CriticalTotal FloatActivity
Yes0A
No8B
Yes0C
No8D
Yes0E
F
G
Dummy
For activity E (3, 5)
TF = 24 – 15 – 9 = 0*

59. Dr. Mahmoud Abbas Mahmoud
A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
G= 12
0
0
0
10
10
15
15
24
16
24
24
36
36
CriticalTotal FloatActivity
Yes0A
No8B
Yes0C
No8D
Yes0E
F
G
Dummy

60. Dr. Mahmoud Abbas Mahmoud
A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
G= 12
0
0
0
10
10
15
15
24
16
24
24
36
36
CriticalTotal FloatActivity
Yes0A
No8B
Yes0C
No8D
Yes0E
No12F
G
Dummy
For activity F (4, 6)
TF = 36 – 16 – 8 = 12

61. Dr. Mahmoud Abbas Mahmoud
A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
G= 12
0
0
0
10
10
15
15
24
16
24
24
36
36
CriticalTotal FloatActivity
Yes0A
No8B
Yes0C
No8D
Yes0E
No12F
G
Dummy

62. Dr. Mahmoud Abbas Mahmoud
A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
G= 12
0
0
0
10
10
15
15
24
16
24
24
36
36
CriticalTotal FloatActivity
Yes0A
No8B
Yes0C
No8D
Yes0E
No12F
Yes0G
Dummy
For activity G (5, 6)
TF = 36 – 24 – 12 = 0*

63. Dr. Mahmoud Abbas Mahmoud
A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
G= 12
0
0
0
10
10
15
15
24
16
24
24
36
36
CriticalTotal FloatActivity
Yes0A
No8B
Yes0C
No8D
Yes0E
No12F
Yes0G
Dummy

64. Dr. Mahmoud Abbas Mahmoud
A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
G= 12
0
0
0
10
10
15
15
24
16
24
24
36
36
CriticalTotal FloatActivity
Yes0A
No8B
Yes0C
No8D
Yes0E
No12F
Yes0G
No8Dummy
For Dummy activity (4, 5)
TF = 24 – 16 – 0 = 8

65. Dr. Mahmoud Abbas Mahmoud
A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
G= 12
0
0
0
10
10
15
15
24
16
24
24
36
36
CriticalTotal FloatActivity
Yes0A
No8B
Yes0C
No8D
Yes0E
No12F
Yes0G
No8Dummy

66. Dr. Mahmoud Abbas Mahmoud
A= 10
B= 7
1
2
3
C= 5
D= 6
E= 9
4
5
6Dummy
F= 8
G= 12
0
0
0
10
10
15
15
24
16
24
24
36
36
CriticalTotal FloatActivity
Yes0A
No8B
Yes0C
No8D
Yes0E
No12F
Yes0G
No8Dummy
The Critical Activities are: (A, C, E, G)
Critical Path is: (A C E G)
Project completion time is: 36 weeks

67. Dr. Mahmoud Al-Naimi