The document discusses network planning models for project scheduling. It describes two main techniques: CPM (Critical Path Method) and PERT (Program Evaluation Review Technique). Both use an "activity-on-arrow" approach where activities are drawn as arrows between nodes representing start and end times. More recently, precedence networks use an "activity-on-node" approach where activities are represented as nodes and dependencies as lines between nodes. The document provides examples of constructing precedence networks and performing forward and backward passes to determine the critical path and calculate total float for activities.

1. SPM-UNIT II
ACTIVITY PLANNING
Prof. Kanchana Devi

2. Network Planning Models
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 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
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 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
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 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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 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
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Install
Program
Test
Data
Take-on
Code

7. A loop represents an impossible
sequence
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Code
Program
Release
Program
Test
Program
Diagnose
Errors
Correct
Errors

8. A Dangle
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Design
Program
Install
Program
Test Program
Code
Program
Write User
Manual

9. Resolving the Dangle
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Design
Program
Install
Program
Test
Program
Code
Program
Write
User
Manual
Sign-Off

10. Representing Lagged Activities
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 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
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 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.

12. Project Specification
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13. Project Activity Network
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14. Project Activity Network
represented as CPM Network
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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

16. Using Dummy Activities
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17. …….
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 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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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

19. CPM Network
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20. A CPM Network after forward
pass
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21. Activity table for forward pass
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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

22. Backward Pass
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23. CPM Network after the backward
pass
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24. Identifying the Critical Path
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 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.

25. Critical Path
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Event
Number
Latest
Date
Earliest
Date
Slack

26. Activity Float
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 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)

27. Activity Schedule showing total
float for each activity
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28. Activity Schedule
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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

29. Activity Network Diagram
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1
2
3
5
4
7
6
8
109

30. Solution
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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
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 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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 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