1. Network Schedule
• Predominant Network Scheduling
Techniques:
– Critical Path Method (CPM)
– Program Evaluation and Review Technique
(PERT)
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2008, King Saud Dr. Khalid Al-Gahtani

2. Critical Path Method (CPM)
• CPM is a graphical network-based
scheduling techniques that when applied
intelligently and honestly can be an
excellent tool in project management.
• The CPM uses a graphic presentation of
the planned sequence of activities of a
project.
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2008, King Saud Dr. Khalid Al-Gahtani

3. CPM Network
• Diagrammatically illustrates all
interdependencies of the project’s
activities.
• Used as a basis for:
– Scheduling the total project time
– Establishing priorities.
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2008, King Saud Dr. Khalid Al-Gahtani

4. CPM Network
• Can be used for integrating:
– Time
– Cost
– Available resources
• Establishes a critical path for efficient use of
resources
• Determine how much time each of the project
activities may be delayed without affecting the
completion time of the project as determined in
objective number one.
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King Saud University Dr. Khalid Al-Gahtani

5. CPM Network Drawing Schemes
• Arrow Diagramming
(Activity-On-Arrow, AOA).
• Node Diagramming
(Activity-On-Node, AON)
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King Saud University Dr. Khalid Al-Gahtani

6. Activity-On-Arrow Method
• Arrows:
– Original Network Scheduling Technique
– Uses a 2 nodes scheme
– Diagram easily time scaled.
• Nodes:
– Commonly called events
– Mark points in time
– Represent the beginning or end of the time
available for a given activity.
• Links:
– Represent activities
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King Saud University Dr. Khalid Al-Gahtani

7. Activity-On-Arrow Method
• Dummy Activities:
– Dummy Activity is a fictitious activity that has
no time duration and requires no resource
utilization.
– Dummy activities used to develop correct
representation.
– Always break up a dummy activity at the tail,
not at the head of the arrow.
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2008, King Saud Dr. Khalid Al-Gahtani

8. Activity-On-Arrow Method
– Remove redundant dummy activities
– Use unique numbering system for events.
– Allow for addition of future activities
– Try to number events such that the “i” node is
less than the “j” node.
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King Saud University Dr. Khalid Al-Gahtani

9. Drawing AOA Networks
• Prerequisites:
– List of all activities comprising the project
– Order of precedence of each activity
– Duration estimate of each activity
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King Saud University Dr. Khalid Al-Gahtani

10. Drawing AOA Networks
• Basic Rules of Network Logic
1. Before an activity may begin, all activities
preceding it must be completed. (Activities
with no predecessors are self-actuating
when the project begins.)
2. Arrows imply logical precedence only.
Neither the length of the arrow not its
“compass” direction on the drawing have
any significance.
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King Saud University Dr. Khalid Al-Gahtani

11. 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, Arrow Diagramming 11
King Saud University Dr. Khalid Al-Gahtani

12. Bar Chart
14
a
3
b
7
c 18
d
17
e
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King Saud University Dr. Khalid Al-Gahtani

13. Activity on arrow
a
d
b D um m y
c
e
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2008, King Saud Dr. Khalid Al-Gahtani

14. Common Errors in AOA
• Dangling (AOA only).
• Looping.
• Redundancy (AOA only)
• Unique Activity Designation
• Possible of showing Improper Logic
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2008, King Saud Dr. Khalid Al-Gahtani

15. Dangling
8
6 7 10 11 13
9 12
(8) and (9) are left dangling as they are not the last activities.
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King Saud University Dr. Khalid Al-Gahtani

16. Looping
f g
a i
e h
b d
c
Looping error results when an endless loop is shown in the diagram
and you can not progress beyond it.
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King Saud University Dr. Khalid Al-Gahtani

17. Redundancy
2 3
D um m y
4
Dummy 2-4 is unnecessary as it is not needed for network analysis.
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2008, King Saud Dr. Khalid Al-Gahtani

18. Unique Activity Designation
a) 11
10 15
b)
10 15
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King Saud University Dr. Khalid Al-Gahtani

19. Possible of showing improper Logic
A ctivity A A ctivity C
Pla c e C o n cr ete In sta ll pr e finish e d
a) Sla b in ga ra g e sho p ca bin e ts
10 20 25
A ctivity B A ctivity D
In sta ll ga ra ge In sta ll ga ra ge
do or op e n er
15 30
In a) A ctivity D depends on A and B
A ctivity A A ctivity C
Pla c e C o n cr ete In sta ll pr e finish e d
b)
Spring 2008, Sla b in ga ra g e Arrow Diagramming p ca bin e ts
sho 19
10
King Saud University Dr. Khalid0
2 Al-Gahtani 25

20. Possible of showing improper Logic In a) A ctivity D depends on A and B
A ctivity A A ctivity C
Pla c e C o n cr ete In sta ll pr e finish e d
b) Sla b in ga ra g e sho p ca bin e ts
10 20 25
A ctivity B A ctivity D
In sta ll ga ra ge In sta ll ga ra ge
do or op e n er
15 20 30
In b) A ctivity D depends on B only.
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2008, King Saud Dr. Khalid Al-Gahtani

21. Possible of showing improper Logic
A ctivity A
A ctivity D
a) In sta ll W a llb oa rd
10 Pa in t W a ll
25 40
A ctivity B
In sta ll v in yl A ctivity E
flo oring In sta ll ba se trim
15 30 45
A ctivity C A ctivity F
In sta ll C a rp et In sta ll floor r eg ister s
20 35 50
In a) A ctivity F depends on A , B, and C .
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2008, King Saudctivity A
A Dr. Khalid Al-Gahtani
A ctivity D

22. 20 35 50
In a) A ctivity F depends on A , B, and C .
Possible of showing improper Logic
A ctivity A
A ctivity D
b) In sta ll W a llb oa rd
10 Pa in t W a ll
25 40
A ctivity B
In sta ll v in yl A ctivity E
flo orin g In sta ll ba se trim
15 30 31 45
A ctivity C A ctivity F
In sta ll C a rp et In sta ll floor r eg ister s
20 35 50
In b) A ctivity F depends only on B and C .
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King Saud University Dr. Khalid Al-Gahtani

23. Disadvantages of Arrow Notation
• We may need to use “dummy activities”
• Project Management is done on activity
basis
• Does not give all details of the activity on
network diagram
• Arrow would be very long, and don’t
relate to time. The network is not time
scaled
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King Saud University Dr. Khalid Al-Gahtani

24. Disadvantages of Arrow Notation
3 9
A
6
B
C
2
5
Dangling possible if B dos not have successors, B dangles.
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King Saud University Dr. Khalid Al-Gahtani

25. Class work#1:
A ct ivit y D epend s upo n A ct ivit y D epend s upo n
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
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King Saud University Dr. Khalid Al-Gahtani

26. Class work#1:
C E
B D L
A F G N
H I M
J K
Spring 2008, Arrow Diagramming 26
King Saud University Dr. Khalid Al-Gahtani