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
Activity on Arrow (AOR)Activities are
shown by ArrowLength 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 DTask
E
Each project has a starting “i-node” and
ending “j-node”
Activity on Arrow (AOR)
Task A Task B Task C
Task DTask
E
Activity on Node (AON)
Start
Task A
Task B
Task E
Task C
Task D
End
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
Project Networks
BTask
CTask
DTask
ETask
FTask
ATask
• 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
• 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 theproject that requires time.
Time
• 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
Project Networks
BTask
CTask
DTask
ETask
FTask
ATask
Project Networks
BTask
CTask
DTask
ETask FTask
ATask
= Early StartES
Time-Related Task Properties
= Early FinishEF = Late StartLS = Late FinishLF = Slack or FloatSL
= Duration
DRATask
Tasks
ES EF
LS LF
SLA
DR
A
4
Project Networks
C
3
B
8
D
2
E
3
F
10
Critical PathES ID EFSLLS DR LF
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
A
4
Project Networks
C
3
B
8
D
2
E
3
F
10
A-B-D-F 4+8+2+10 = 24A-C-E-F 4+3+3+10 = 20
ES ID EFSLLS DR LF
A
4
Project Networks
C
3
B
8
D
2
E
3
F
10
A-B-D-F 4+8+2+10 = 24A-C-E-F 4+3+3+10 = 20
ES ID EFSLLS DR LF