CON E 401: Construction
Planning and Scheduling
Activity on Arrow
Part I: Drawing the AOA Network
Part II: Calculating the AOA Network
Learning Objectives
• Part 1:
• Learn to draw AOA networks
• Part 2:
• Learn to calculate the project duration & the Critical
Path
• Learn to calculate the Early and Late Start & Finish of
activities,
• Learn to calculate Total and Free Float
Scheduling Responsibilities
• Develop the project network diagram, based on the activity
information (activities, durations and logic / order).
• Logic Diagrams (Activity on Arrow, Precedence Diagrams)
• Time-scaled diagrams: Bar charts etc.
• Calculate the project duration: Critical Path Method (CPM)
• Identify the critical path
• Identify the total and free float of activities
AOA Diagram [Arrow Networks]
30
F
7
B
12
A
10
20
5
C
8
E
40
60
8
D
6
G
5
70
H
3
50
Precedence Network Diagram [Node Networks]
B
12
A
5
C
8
D
6
F
7
G
5
E
8
H
3
End
Networks and Bar Charts
• Logic networks made bar charts obsolete as a scheduling
method.
• However, bar charts serves now an important role in
scheduling: reporting CPM-based schedule.
• Most industry personnel, especially field people, prefer bar charts
over networks for their simplicity
Time-Scaled Logic Diagrams
Time-Scaled Logic Diagrams cont’d
5
10
15
20
25
30
A5
B -12
F -7
C-8
D-6
A
5
E-8
H-3
Graphical Path Method
B
12
F
7
C
8
D
6
G-5
E
8
H
3
G
5
Time-Scaled Arrow Diagram
Time-Scaled Logic Diagrams
• It was thought of a method that combines the main
advantage of bar charts (time-scaled) with the main
advantage of networks (show logic) in one method
• The main problem is the amount of lines and their
intersections
• A partial solution is to show binding (driving) relationships
only
Networks: A Definition
• Network: A graphical representation of the activities (and
events) comprising the project, in a logical and
chronological depiction
• Network diagrams are basically two types:
• arrow networks and
• node networks:
• Basic node networks
• Precedence networks
Arrow Networks
• Arrow network: A network on which activities are
represented by arrows between nodes (events)
• Also called:
• I-J Method (10-20 for activity A above),
• Activity on Arrow (AOA) Network,
• Arrow Diagramming Method (ADM)
A
10
5
20
13
Arrow Networks
Sched. &
Control S.
Mubarak
- Part 3
• Network schedules were first developed by E. I. Dupont
de Nemours Company in conjunction with the UNIVAC
Applications Research Center of Remington Rand
between 1956 and 1958
• At the beginning, Arrow Networks were the only way to do
CPM schedules
• In the last three decades, Arrow Networks have become
obsolete. They were replaced by Node and Precedence
Networks.
AOA Diagram: Overview
30
F
7
B
12
A
10
5
20
C
8
40
D
E
60
8
H
6
G
5
70
3
50
• The Arrows indicate the Activities.
• The nodes (or Events) indicate Start and Finish
• The sequence shows the logic (predecessors & successors)
• All relationships are Finish to Start
AOA Diagram Representation
Activity Name
(Letter or Description)
Activity 10-20
Mobilize
10
20
5
Node or Event
representing
Activity Start (node i)
Activity Duration
Node or Event
representing
Activity Finish (node j)
• Also called i-j networks
– “i” node marks the beginning
– “j” node marks the end
AoA Diagram
30
F
B
12
7
A
20
10
5
C
8
E
40
60
8
D
G
5
H
6
3
50
• Project has: One Start node, one End node
• All relations are Finish to Start
• Each activity must have a UNIQUE PAIR of start & finish
nodes
• Broken lines indicate “dummy” activities
70
AoA Diagram
F
30
B
7
12
A
20
10
5
C
8
80
E
40
G
60
5
8
70
D
6
50
H
3
One Start node, one End node
90
Unique i-j node pair
30
C
B
Is this network correct?
40
G
Merge
When two or more activities
enter a node, the result is
known as a MERGE
G
10
K
20
M
40
50
L
30
• ALL activities merging to a node MUST
BE COMPLETED before the successor
activities start.
• G, K, L may complete at different times
Burst
When two or more
activities leave one node,
the result is known as
50
BURST
M
30
L
40
N
• ALL activities leaving the same node
will have the SAME Early Start time
• M & N can have the same start time
70
Dummies
• AOA networks use dummy activities
• Dummy activities are represented by dashed lines
• Dummies do not have any duration or
resources
• Two reasons for dummies:
• To show logic
• To ensure that each activity has its own unique
activity i-j node pair
Dummies: Is this the same logic?
Activity Predecessor
C
F
40
E
C
20
G
F
C, E
G
C, E
Activity Predecessor
d1
E
F
40
G
F
C
G
C, E
Typical Problems
• Draw the network (Today’s Learning Objective!)
(Next Lecture!)
• Calculate the Forward Pass The Early Start &
Early Finish of all activities
• The Project Duration
• Calculate the Backward Pass
• The Late Start & Late Finish of all activities
• Then you can find:
• Critical Path: longest path(s)
• Total & Free Float
Draw the Network
• Given information on activities & their
predecessors, create an AOA network
• Guidelines
• One Start, one Finish node
• Unique i-j pair
• No redundancies: avoid unnecessary dummies
• No loops
Loop
30
40
Check your network
• To draw the AOA diagram:
• From table you created the network
• To check logic: Go “backwards”
• From the network create a table showing the actual
predecessors as you drew it.
• The tables should be the same
AOA Limitations
• All relationships Start–Finish
• Difficult to show other relationships
• In many cases you need dummies to show the
relationships
• No time scale
• Not practical for complex networks
Activ
A
B
C
D
E
Practice 1
Dur
5
7
9
6
5
Pred
-A
A
B
C,D
30
B
10
A
5
20
7
D
C
9
6
40
E
5
50
Activ
Practice 2
20
A
10
7
Pred
A
5
--
B
7
--
C
9
A
D
6
A, B
C
d
B
5
Dur
9
40
D
30
6
Practice 3
A
20
C
30
C
D
E
A
B
C
F
G
D
C,D
40
60
D
Predecessor
---
E
10
B
Activity
A
B
50
F
G
70
Practice Problem 4
Predecessor
Activity
A= 4 d
B= 7 d
C= 5 d
D= 8 d
Predecessor
Activity
E= 3 d
F= 8 d
G= 5 d
H=4d
-A
A
A
C
B
E
D
30
B
A
10
20
F
C
E
40
D
60
H
50
G
70
Summary
• Learned the elements of AOA diagrams
• Learned to represent sequence of activities using Activity
on Arrow Diagrams
Next Topic
• Calculate AOA networks
Practice 1
Activity
Duration
Predece
ssor
A
5
--
B
7
A
C
9
A
D
6
B
E
5
C,D
Practice 2
Activ
Dur
Pred
A
5
--
B
7
--
C
9
A
D
6
A, B
Practice 3
Activity
Predecessor
A
--
B
--
C
A
D
B
E
C
F
D
G
C,D
Practice 4
Activ
(days)
Pred
Activ
(days)
Pred
A= 4
--
E= 3
C
B= 7
A
F= 8
B
C= 5
A
G= 5
E
D= 8
A
H=4
D
Practice Problem 4
How long will this project take?
30
B
F
7
A
10
4
20
C
8
E
40
5
3
D
8
60
H
50
4
G
5
70