Network Diagrams and Critical Path
ENMGT 5900
R. Newman
Objectives
• To correctly create Network Diagrams
• Forward pass
• Compute project duration
• Backward pass
• Identify Slack
TERMS to KNOW
• AoA
• AoN
• Backword Pass
• Critical Path
• Float
• Forward Pass
• Network Diagram
• Precedence
• Prerequisite
• Slack
PM planning workflow
1. WBS
2. Task list
3. Establish precedence (order of tasks, and interdependencies)
4. Network Diagram &/or GANTT chart
5. Add estimated durations
6. Determine the Critical Path and Project duration
7. Add resources
8. Adjustments to path, resources and duration as
needed or desired
Network Diagrams
(precedence Diagram)
• A graphical representation of tasks for a project
Example Network Diagram for building a tree house project
using Action on Arrow (AoA) method
AoA and AoN
Two common methods for drawing Project Network
Diagrams
1) AoA (Action on Arrow)
2) AoN (Action on Node)
AoA diagrams
• Nodes represent events, milestones, or “gates”
• Arrows represent tasks, work, activities
1 2 53
4
6 7Pick
tree(s)
Design
treehouse
Build and
mount
main
support
Prepare
trees
Purchase
Tools and
materials
Build
platform
and Railing
Dummy arrow indicates
dependency but no activity
AoN diagrams
• Nodes represent tasks, work, activities
• Arrows represent dependencies
Pick Trees
Design
Treehouse
Build and
Mount
Main
Support
Prepare
Trees
Purchase
tools and
materials
Build
Platform
and
Railing
No Dummy arrows Need in
AON diagrams
Example AoA vs AoN
Task prerequisite
A
B
C A, B
D B
53
4
Task A
Task B
Task C
Task D
1
62
CA
B D
AoN
AoA
Example AoA vs AoN
Task prerequisite
A
B A
C A
D B, C
4 5
3
Task A Task B
Task C
Task D
1 2
C
A B D
AoN
AoA
Example AoA vs AoN
Task prerequisite
A
B
C A, B
D A, B
5
3
4Task A
Task B
Task C
Task D
1
2
CA
B D
AoN
AoA
Longer example
C
A B D
AoN
Task prerequisite
A
B A
C A
D B, C
E B
F C
G E, D
H F, G
H
G
F
E
Add Durations
AoN
Task prerequisite Duration
(days)
A 2
B A 5
C A 9
D B, C 6
E B 2
F C 5
G E, D 7
H F, G 3
2
A
9
C
5
B
2
E
6
D
5
F
7
G
3
H
Consider the total duration of each
path (forward pass)
• 19
• 23
2
A
9
C
5
B
2
E
6
D
5
F
7
G
3
H
2
A
9
C
5
B
2
E
6
D
5
F
7
G
3
H
Consider the total duration of each
path
• 27
• 19
2
A
9
C
5
B
2
E
6
D
5
F
7
G
3
H
2
A
9
C
5
B
2
E
6
D
5
F
7
G
3
H
The CRITICAL PATH
• The critical path is 27 days
long
2
A
9
C
5
B
2
E
6
D
5
F
7
G
3
H
Slack (float)
• Items outside of the critical path will have
float, e.g.
• C will be completed on Day 11
• H will be started on day 25 ( after G ends
on day 24)
2
A
9
C
5
B
2
E
6
D
5
F
7
G
3
H
• F, therefore can start on day 12
• But since it only requires 5 days, F could start as late as Day 19
without affecting the schedule
• F has 7 days of FLOAT (aka SLACK) (19-12)
AoN Node Box
Earliest
Start
Duration Earliest
Finish
Task Name
(e.g. buy tools and materials)
Latest
Start
Total
Float
Latest
Finish
Day
12
5 Day
17
TASK F
Day
19
7 Day
24
AoN with Node Boxes
Earliest
Start
Duration Earliest
Finish
Task Name
Latest
Start
Total
Float
Latest
Finish
Day
12
5 Day
16
TASK F
Day
19
7 Day
23
Day
3
9 Day
11
TASK C
Day
3
0 Day
11
Day
1
2 Day 2
TASK A
Day
1
0 Day 2
Day
3
5 Day 7
TASK B
Day
10
7 Day
14
• Critical path typically shown in red
• Items on Critical path have “0” float
MSProject GANTT chart – Critical Path
• If the show critical
path option is
enabled, the critical
path will show in
red
MSProject GANTT chart - Float
• Float can be seen
where tasks off of
the critical path
have a think black
line showing extra
time available
beyond the
duration of the task
Participation exercise
Create your own and compare with teammates before
submitting
1. Create a table for the tasks, precedence and durations
2. build an AoN Network diagram with node boxes, and
answer these questions:
Senior Lecturer, Engineering Management
Robert Newman