2. Network Planning Models
Prof. Kanchana Devi
2
Scheduling techniques model the project’s activ ities and
their relationships as a “Network”.
In network time flows from left to right
These techniques were developed in 1950’s
There are two best techniques:
CPM (Critical Path Method)
PERT (Program Evaluation Review Technique)
Both uses an “activity-on-arrow” approach
Activities are drawn as arrows joining circles, or nodes
Which show the start and completion time of the activities
3. Precedence Network
Prof. Kanchana Devi
3
Recently used , Popular one
It uses “activity-on-node” networks
Where activities are represented as nodes
Links between the nodes are represented as
sequencing requirements.
4. Formulating a Network Model
Prof. Kanchana Devi
4
First stage:
Representing the activities and their
relationships as graph.
In “Activity-on-node”
Representing the activities as nodes(boxes) and
the lines between nodes represent the
dependencies.
5. Rules:Constructing Precedence
Network
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5
A project network should have only one start
node
A project network should have only one end
node
A node has a duration
Links normally have no duration
Precedents are the immediate preceding
activities
Time moves from left to right
A network may not contain loops
A network should not contain dangles
6. Fragment of precedence Network
Prof. Kanchana Devi
6
Install
Program
Test
Data
Take-on
Code
7. A loop represents an impossible
sequence
Prof. Kanchana Devi
7
Code
Program
Release
Program
Test
Program
Diagnose
Errors
Correct
Errors
8. A Dangle
Prof. Kanchana Devi
8
Design
Program
Install
Program
Test Program
Code
Program
Write User
Manual
9. Resolving the Dangle
Prof. Kanchana Devi
9
Design
Program
Install
Program
Test
Program
Code
Program
Write
User
Manual
Sign-Off
10. Representing Lagged Activities
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10
Undertake two activities in parallel as there
is a lag between two.
Activities are lagged because a stage in one
activity must be completed before the other
may proceed.
Show each stage as separate activity.
11. Adding Time Dimension
Prof. Kanchana Devi
11
Each activity have an estimate of its duration.
Forward pass – Earliest dates at which
activities may commence and project be
completed.
Backward pass – Latest start dates for
activities and critical path.
15. Dummy activities
15
When two paths within a network have a
common event to occur.
It is incorrect to require both hardware
specification and data structure design
17. …….
Prof. Kanchana Devi
17
Dummy activities shown as dotted lines have
a zero duration and use no resources.
Use of dummy activity where two activities
share the same start and end nodes makes it
easier to distinguish activity end points.
18. Forward Pass
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18
Activity Duration
(Weeks)
Earliest Start
Date (Weeks)
Earliest Finish
Date(Weeks)
A 6 0 6
B 4 0 4
C 3 6 9
D 4 4 8
E 3 4 7
F 10 0 10
G 3 10 13
H 2 9 11
20. A CPM Network after forward
pass
Prof. Kanchana Devi
20
21. Activity table for forward pass
Prof. Kanchana Devi
21
Activity Duration
(weeks)
Earliest
Start
Date
Latest
Start
Date
Earliest
Finish
Date
Latest
Finish
Date
Total
Float
A 6 0 6
B 4 0 4
C 3 6 9
D 4 4 8
E 3 4 7
F 10 0 10
G 3 10 13
H 2 9 11
24. Identifying the Critical Path
Prof. Kanchana Devi
24
Any delay on the critical path will delay the
project.
Difference between earliest and latest date
for an event is known as slack.
Event with slack of zero is critical as any
delay in achieving that event will delay the
completion date of the project.
26. Activity Float
Prof. Kanchana Devi
26
As events have slack, activities possess float.
Total float is the difference between earliest
start and latest start ( or difference between
earliest finish and latest finish)
28. Activity Schedule
Prof. Kanchana Devi
28
Actvity Name Time Actvity Name Time
1-2 A 4 5-6 G 4
1-3 B 1 5-7 H 8
2-4 C 1 6-8 I 1
3-4 D 1 7-8 J 2
3-5 E 6 8-10 K 5
4-9 F 5 9-10 L 7
30. Solution
Prof. Kanchana Devi
30
Activity Activity
Name
Normal
Time
E.S E.F L.S L.F Total
Float
1-2 A 4 0 4 5 9 5
1-3 B 1 0 1 0 1 0
2-4 C 1 4 5 9 10 5
3-4 D 1 1 2 9 10 8
3-5 E 6 1 7 1 7 0
4-9 F 5 5 10 10 15 5
5-6 G 4 7 11 12 16 5
5-7 H 8 7 15 7 15 0
6-8 I 1 11 12 16 17 5
7-8 J 2 15 17 15 17 0
8-10 K 5 17 22 17 22 0
9-10 L 7 10 17 15 22 5
31. Problem 1
Prof. Kanchana Devi
31
Draw activity network of the project.
Find total float of each activity.
Activity Time inWeeks
1-2 20
1-3 25
2-3 10
2-4 12
3-4 5
3-5 10
32. Problem 2
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32
Find out the critical path and total float.
Activity Immediate
Predecessor
Time
A 3
B 8
C 5
D A 9
E C 2
F B,E 6
H B,E 12
G D 11