2. Network Diagrams
A network is a logical and chronological graphic representation of the activities
(and events) composing a project.
Network diagrams are the preferred technique for showing activity sequencing.
2
3. Network Diagrams
3
Three types of information are needed to describe a project.
• Activity information: Break down the project into its individual activities (at
the desired level of detail).
• Precedence relationships: Identify the immediate predecessor(s) for each
activity.
• Time information: Estimate the duration of each activity
The network diagram should convey all this information.
4. Network Diagrams
Two methods: arrow networks and node networks.
4
One type is the activity-on-arc (AOA) project network, where each activity is
represented by an arc. A node is used to separate an activity (an outgoing arc)
from each of its immediate predecessors (an incoming arc). The sequencing of
the arcs thereby shows the precedence relationships between the activities.
The second type is the activity-on-node (AON) project network, where each
activity is represented by a node. Then the arcs are used just to show the
precedence relationships that exist between the activities. In particular, the
node for each activity with immediate predecessors has an arc coming in from
each of these predecessors.
5. Network Diagrams
AON has several advantages over AOA:
◦ AON project networks are considerably easier to construct than AOA project
networks.
◦ AON project networks are easier to understand than AOA project networks
for inexperienced users, including many managers.
◦ AON project networks are easier to revise than AOA project networks when
there are changes in the project.
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6. Network Diagrams
In addition:
◦ There is no need for the use of dummy activities in AON representation.
◦ In AOA, an activity can only start when all it predecessors have finished.
◦ AON allows for overlap/lag representation.
For these reasons, AON are more popular these days.
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8. Arrow Diagramming
Method (ADM)
Also called activity-on-arrow (AOA) network
diagram or (I-J) method (because activities are
defined by the from node, I, and the to node, J)
Activities are represented by arrows.
Nodes or circles are the starting and ending points
of activities.
Can only show finish-to-start dependencies.
8
9. Arrow Diagramming Method (ADM)
9
i j
(a) Basic Activity
Activity Name
Node (Event) i
j > i
Each activity should have a unique i – j value
Node (Event) j
10. Arrow Diagramming Method (ADM)
10
2
A
(b) Independent Activities
4 10
B
12
3
A
6
B
9
(c) Dependent Activities
11. Arrow Diagramming Method (ADM)
11
(f) A Cross
20
18
C
16 D
14
A
12
B
Activities C and D both depend upon the completion of Activities A and B
12. Arrow Diagramming Method (ADM)
Each activity must have a unique i – j numbers, where i (the number at the tail of
the arrow) is smaller than j (the number at the head of the arrow).
It is recommended to have a gap between numbers (i.e., 5, 10, 15, etc.). This will
allow for accommodation of missed activities.
Avoid back arrows.
12
13. Arrow Diagramming Method (ADM)
Draw the arrow network for the following project.
13
*IPA
Activity
-
A
A
B
A
C
B
D
C,D
E
*immediately preceding activity
14. Arrow Diagramming Method (ADM)
Draw the arrow network for the following project.
14
IPA
Activity
-
A
A
B
A
C
B
D
C,D
E
10
30
40
20 50
C
D
A
B
E
15. Arrow Diagramming Method (ADM)
The dummy activity is an activity with zero duration, consumes no resources,
drawn as dashed lines, and used to adjust the network diagram.
◦ When more than one arrow leave the same node and arrive at another node, dummy
activities must be used.
◦ When one activity depends upon two preceding activities and another activity depends only
upon one of these two preceding activities, dummy activities must be used.
15
Dummy Activities (fictitious)
16. Arrow Diagramming Method (ADM)
Used to maintain unique numbering of activities.
Used to complete logic, duration of “0”
The use of dummy to maintain unique numbering of activities.
16
Dummy Activities (fictitious)
17. Arrow Diagramming Method (ADM)
17
4 11
4 11
10
A
B
A
B
Divide node to correct
Dummy
(a) Incorrect Representation
(b) Correct Representation
Dummy Activities (fictitious)
18. Arrow Diagramming Method (ADM)
Draw the arrow network for the following project.
18
Dummy Activities (fictitious)
*IPA
Activity
-
A
A
B
A
C
B,C
D
*immediately preceding activity
19. Arrow Diagramming Method (ADM)
Draw the arrow network for the following project.
19
Dummy Activities (fictitious)
IPA
Activity
-
A
A
B
A
C
B,C
D
10 30
20 40
C
D
A
B
10
30
40
20 50
C
D
A
B
Dummy
Improper solution
Proper solution
20. Arrow Diagramming Method (ADM)
Draw the arrow network for the following project.
20
Dummy Activities (fictitious)
*IPA
Activity
-
A
A
B
A
C
B
D
B,C
E
C
F
*immediately preceding activity
21. Arrow Diagramming Method (ADM)
Draw the arrow network for the following project.
21
Dummy Activities (fictitious)
IPA
Activity
-
A
A
B
A
C
B
D
B,C
E
C
F
10
30
40
20 60
C
E
A
B
Dummy 1
50
Dummy 2
D
F
22. Arrow Diagramming Method (ADM)
Removal of Redundant Activities
22
A
A
A
A
B
B
B
B
C C
Original Diagram Diagram after removal of
redundant dummies
(a)
(b)
23. Arrow Diagramming Method (ADM)
Removal of Redundant Activities
23
Original Diagram Diagram after removal of
redundant dummies
A
A
A
A
C
C
B
C
B B
(c)
(d)
B E
C
E
E E
24. Arrow Diagramming Method (ADM)
Removal of Redundant Activities
24
Immediately Preceding
Activity (IPA)
Depends Upon
Activity
-----
A
B
-----
A
A, B
A
B
C
B C
A
Redundant
Relationship
25. Arrow Diagramming Method (ADM)
Removal of Redundant Activities
25
Depends Upon
Description
Activity
-----
-----
A
A, B, C
A, B, C
B, C, J, M
B, C, D, E, K
D, E, F, G, L
-----
-----
-----
-----
Site Clearing
Removal of Trees
Excavation for Foundations
Site Grading
Excavation for Utility Trenches
Placing formwork & Reinforcement
Installing sewer lines
Pouring concrete
Obtain formwork & reinforcing
steel
Obtain sewer lines
Obtain concrete
Steelworker availability
A
B
C
D
E
F
G
H
J
K
L
M
26. Arrow Diagramming Method (ADM)
Removal of Redundant Activities
26
H
40
G
45
C
F
D
35
15
10
5
B
A
20
M
25
J
30
E
L
K
28. Node Networks Method (AON)
This method is also called the precedence diagram method (PDM).
The nodes represent activities and the arrows represent logical relationships among the
activities.
AON representation allows the overlap or lag representation on the relationship arrows
connecting activities.
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29. Node Networks Method (AON)
29
a) Independent Activities
10
A
20
B
Activity number
Activity name
b) Dependent Activities
20
B
10
A
Link
Link
B depends on A
30. Node Networks Method (AON)
30
30
C
10
A
20
B
40
D
c) A Merge Relationship
C depends on A & B
D depends on C
d) A Burst Relationship
20
B
30
C
40
D
10
A
B depends on A
C depends on B
D depends on B
31. Node Networks Method (AON)
31
e) Start & Finish Dummy Activities
A
C
B
E
D
A
Start
Dummy
Finish
Dummy
C
B
E
D
32. Node Networks Method (AON)
Draw the node network for the following project.
32
*IPA
Activity
-
A
A
B
A
C
B
D
C,D
E
*immediately preceding activity
33. Node Networks Method (AON)
Draw the node network for the following project.
33
IPA
Activity
-
A
A
B
A
C
B
D
C,D
E
A E
C
D
B
34. Node Networks Method (AON)
Draw the node network for the following project.
34
*IPA
Activity
-
A
A
B
A
C
B,C
D
*immediately preceding activity
35. Node Networks Method (AON)
Draw the node network for the following project.
35
IPA
Activity
-
A
A
B
A
C
B,C
D
A
C
D
B
36. Node Networks Method (AON)
Draw the node network for the following project.
36
*IPA
Activity
-
A
A
B
A
C
B
D
B,C
E
C
F
*immediately preceding activity
37. Node Networks Method (AON)
Draw the node network for the following project.
37
IPA
Activity
-
A
A
B
A
C
B
D
B,C
E
C
F
A PF
C
D
B
E
F
42. Node Networks Method (AON)
42
Improper Proper
A
B
C
A
B
C
PS
Do not start a network with more than one node
Recommendations for Proper Node Diagram Drawing
43. Node Networks Method (AON)
43
Improper Proper
Do not end a network with more than one node
A
B
C
A
B
C
PF
Recommendations for Proper Node Diagram Drawing
45. Lags and Leads
In some situations, an activity cannot start until a certain time after the end of its Predecessor.
Lag is defined as a minimum waiting period between the finish (or start) of an activity and the
start (or finish) of its successor.
Arrow networks cannot accommodate lags. The only solution in such networks is to treat it as a
real activity with a real duration, no resources, and a $0 budget.
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46. Lags and Leads
The term lead simply means a negative lag. It is seldom used in construction.
In simple language: A positive time gap (lag) means ‘‘after’’ and a negative time gap (lead)
means ‘‘before.’’
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47. Lags and Leads
Lag describes delay. It means addition of time so it is denoted by “+” sign in the network
diagram.
Lead always describes advancement. This means reduction in time taken so it is denoted by
“-” sign in the network diagram.
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48. Lags and Leads
48
Place Concrete
3
Strip Forms
2
3
A lag in a node network
Place Concrete Strip Forms
Cure Concrete
A lag in an arrow network
50. AOA and AON Networks
Construct an AOA and AON networks for the activities listed in Table below
50
IPA
Activity
-
A
-
B
A, B
C
C
D
C
E
D
F
D, E
G
51. AOA and AON Networks
For the network below, prepare a table showing a list of immediate predecessors and immediate
successors for each of the activities. Use the i - j node notation for activities.
51
5
7
4
3
1
2
6