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1. Project Networks
Two Approaches
• Activity-on-Arrow (AOA): Uses an arrow to depict an activity
• Activity-on-Node (AON): Uses a node to depict an activity

2. Activity on Arrow (AOR)
Activities are
shown by Arrow
Length of Arrow may show
relative time to complete
tasks
Nodes show where
activities end and
begin in sequence.
The starting node
for an activity is the
activity’s “i-node,”
the ending node is
the “j-node.
Task A Task B Task C
Task D
Each project has
a starting “i-node”
and ending “j-
node”

3. Activity on Arrow (AOR)
Task A Task B Task C
Task D

4. Activity on Node (AON)
Start
Task A
Task B
Task E
Task C
Task D
End

5. Activity on Node (AON)
Activities are show
in nodes or boxes
Start
Task A
Task B
Task E
Task C
Task D
End
Project Has a
Start and an End
Task C is a predecessor to
Task E and a successor to
Task A
Arrow show dependencies.
Task D can’t start until both
Task A and B have completed

6. Project Networks
B
Task
C
Task
D
Task
E
Task
F
Task
A
Task

7. • Networks typically flow from left to right.
• An activity cannot begin until all of its preceding
activities are complete.
• Arrows indicate precedence and can cross over
each other.
• Identify each activity with a unique identifier; this
identifier must increment (1.2.3, A,B,C, etc.) as
the network proceeds.
• Looping is not allowed.
• Conditional statements are not allowed.
• Use start and stop nodes.
Project Networks Rules

8. • Terminology:
A
C
B D
Constructing a Project Network
• Parallel (concurrent)
activities: Activities that can
occur independently and, if
desired, at the same time.
• Merge activity: an activity
that has two or more
preceding
activities on which it depends.
• Activity: an element of the
project that requires time.
Time

9. • Terminology B
D
A C
Constructing a Project Network (cont’d)
• Burst activity: an activity that has
more than one activity immediately
following it (more than one
dependency arrow flowing from it).
• Milestone: a point in time when an
activity is started or completed. It
does not consume time.
Q

10. Project Networks
B
Task
C
Task
D
Task
E
Task
F
Task
A
Task

11. Project Networks
B
Task
C
Task
D
Task
E
Task F
Task
A
Task

12. = Early
Start
ES
Time-Related Task Properties
= Early FinishEF
= Late StartLS
= Late
Finish
LF
= Slack or FloatSL
= DurationDR
A
Task

13. Tasks
ES EF
LS LF
SL
A
DR

14. A
4
Project Networks
C
3
B
8
D
2
E
3
F
10
Critical Path
ES ID EF
SL
LS DR LF

15. Longest Path through the project
network (not the path with the most
number of tasks, but the one that takes
the longest).
=
Any delay of a task on the critical path
will delay the entire project. PM needs
to watch
=
Tasks with zero slack=
Critical Path

16. A
4
Project Networks
C
3
B
8
D
2
E
3
F
10
A-B-D-F 4+8+2+10 = 24
A-C-E-F 4+3+3+10 = 20
ES ID EF
SL
LS DR LF

17. A
4
Project Networks
C
3
B
8
D
2
E
3
F
10
A-B-D-F 4+8+2+10 = 24
A-C-E-F 4+3+3+10 = 20
ES ID EF
SL
LS DR LF