1. CPM Network Computation
Activity
Depends on t
AOA AON
1-2 A ─ 3
2-3 B A 4
Spring 2008, Activity on Node 1
King Saud University Dr. Khalid Al-Gahtani

2. AOA A ct ivit y N a m e
1 3
A
B
3
4
2 A ct ivit y D urat io n
AON
3 4
A B
Spring 2008, Activity on Node 2
King Saud University Dr. Khalid Al-Gahtani

3. Drawing CPM Networks
• Prerequisites: Before drawing a CPM
network, we must have:
– List of all activities comprising the project
– Order of precedence of each activity
– Duration estimate of each activity
Spring 2008, Activity on Node 3
King Saud University Dr. Khalid Al-Gahtani

4. Example:
Depends on Duration (Day)
Activity
(Immediate Predecessor(s)) (Time to perform)
a ─ 14
b ─ 3
c ─ 7
d a, b 4
e b, c 10
Spring 2008, Activity on Node 4
King Saud University Dr. Khalid Al-Gahtani

5. Activity on arrow Solution
a
d
b D um m y
c
e
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King Saud University Dr. Khalid Al-Gahtani

6. Activity-on-node Solution
a
d
ST A RT b F IN IS H
e
c
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King Saud University Dr. Khalid Al-Gahtani

7. Class work#1:
Draw AON Network for the fowling project:
Activity Depends upon Activity Depends upon
A G F
B A I F
F A J H
H A K I, J, F
C B, A L G, D, E
D B M K
E C N L, M
Spring 2008, Activity on Node 7
King Saud University Dr. Khalid Al-Gahtani

8. “Activity on Node”
• Nodes = Activities
• Links = Precedence Relationships
• Dummy activities are not required
ES t ES
Activity Name
LS TF LF
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King Saud University Dr. Khalid Al-Gahtani

9. Example
Activity Depends on Duration (Days)
A 5
B A 15
C A 10
D B 15
E B, C 10
F D, E 5
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King Saud University Dr. Khalid Al-Gahtani

10. AON
ES t EF
N am e
B D LS TF LF
F FIN ISH
ST A R T A
C E
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King Saud University Dr. Khalid Al-Gahtani

11. AON
ES t EF
N am e
5 15 20 20 15 35
B D LS TF LF
5 20 20 35
35 5 40 40 0 40
0 0 0 0 5 5
F FIN ISH
ST A R T A
35 40 40 40
0 0 0 5
5 10 15 20 10 30
C E
15 25 25 35
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King Saud University Dr. Khalid Al-Gahtani

12. Constraints with Lead/lag time
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King Saud University Dr. Khalid Al-Gahtani

13. Finish-to-Start (FSij):
• FSij is equal to the minimum number of
time units that must transpire from the
completion of the predecessor (i) prior to
the start of the successor (j).
• The time between the finish of one activity
and the start of its successor is called
“Lag”.
Spring 2008, Activity on Node 13
King Saud University Dr. Khalid Al-Gahtani

14. Finish-to-Start (FSij):
• If the relationship is not listed on the
dependency arrow, FS is assumed with
Lag= 0.
• Example: a planner may wish to have an
activity of removing formwork from a new
building component follow the concrete
pour by some pre-defined lag period to
allow setting.
Spring 2008, Activity on Node 14
King Saud University Dr. Khalid Al-Gahtani

15. Start-to-Start (SSij):
• SSij is equal to the minimum number of
time units that must be complete on the
preceding activity (i) prior to the start of the
successor (j).
Spring 2008, Activity on Node 15
King Saud University Dr. Khalid Al-Gahtani

16. Start-to-Start (SSij):
• “Lag” is always applied to SS relation.
• Example: parallel in starting of Installing
and Finishing the walls activity of 100
rooms on a project must be 10 days
difference (SS=10 days).
– You don’t have to wait installing 100 wall’s
room to start doing the finishing work.
Spring 2008, Activity on Node 16
King Saud University Dr. Khalid Al-Gahtani

17. Finish-to-Finish (FFij):
• FFij is equal to the minimum number of
time units that must remain to be
completed on the successor (j) after the
completion of the predecessor (i).
• It is applied as productivity control.
Spring 2008, Activity on Node 17
King Saud University Dr. Khalid Al-Gahtani

18. Finish-to-Finish (FFij):
• The finish date of Installing and Finishing
walls’ activity of 100 rooms on a project
must have 10 days difference in order to
control productivity (FF=10 days).
– In this example, the productivity of installing
the walls’ activity might be less than finishing
the rooms’ activity.
• “Lag” is always applied to FF relation as
buffer between the two activities.
Spring 2008, Activity on Node 18
King Saud University Dr. Khalid Al-Gahtani

19. Start-to-Finish (SFij):
• SFij is equal to the minimum number of
time units that must transpire from the
start of the predecessor (i) to the
completion of the successor (j).
• It is applied also for controlling productivity
Spring 2008, Activity on Node 19
King Saud University Dr. Khalid Al-Gahtani

20. Start-to-Finish (SFij):
Example: The start date of Installing 100
rooms’ wall’s activity and the finish date of
Finishing same walls’ activity of a project
must maintain 30 days difference to
control productivity (SF=30 days).
“Lag” is always applied to SF relation as
buffer between the two activities.
• It is not recommended to use by planner.
Spring 2008, Activity on Node 20
King Saud University Dr. Khalid Al-Gahtani

21. Start-to-Start and Finish-to-Finish
(ZZij):
• ZZij is a combination of two constraints.
i.e., a start-to-start and finish-to-finish
relationship. It is written with the SSij time
units first, followed by the FFij time units.
• These two relations are used combined to
maintain buffer between the start and
finish of two activities.
Spring 2008, Activity on Node 21
King Saud University Dr. Khalid Al-Gahtani

22. Forward Pass Computations
Initial T im e
E Fi F S ij
E S j = M ax all i ESi SS ij
E Fi F F ij Dj
ESi SF ij Dj
EFj = ESj + Dj
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King Saud University Dr. Khalid Al-Gahtani

23. Backward Pass Computation
T erm inal T im e
LS j F S ij
L F i = M in all j LF j F Fij
LSi SS ij Di
LF j SFij Di
LSi = LFi Dj
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King Saud University Dr. Khalid Al-Gahtani

24. Example
2 2 6
B FS 4 C SF 5 D
SS 3
FF 1
SF 5
4 1 3 6
A F SF 4 L E
5 1 2 ES D EF
K G FS 4 H A ctivity
LS F LF
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King Saud University Dr. Khalid Al-Gahtani

25. Example Solution
4 2 6 10 2 12 9 6 15
B FS 4 C SF 5 D
5 1 7 SS 3 11 1 13 10 1 16
FF 1
SF 5
0 4 4 4 1 5 9 3 12 16 6 22
A F SF 4 L E
0 0 4 10 6 11 11 2 14 16 0 22
ES D EF
4 5 9 9 1 10 14 2 16 A ctivity
K G FS 4 H LS F LF
4 0 9 9 0 10 14 0 16
Spring 2008, Activity on Node 25
King Saud University Dr. Khalid Al-Gahtani