SPM-UNIT II

ACTIVITY PLANNING

Prof. Kanchana Devi

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

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.

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.

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

Fragment of precedence Network

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Install Program

Test

Data

Take-on

Code

A loop represents an impossible

sequence

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Code

Program

Release

Program

Test

Program

Diagnose

Errors

Correct

Errors

A Dangle

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Design

Program

Install

Program Test Program

Code

Program

Write User

Manual

Resolving the Dangle

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Design

Program

Install

Program

Test

Program

Code

Program

Write

User

Manual

Sign-Off

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.

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.

Project Specification

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Project Activity Network

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Project Activity Network

represented as CPM Network

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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

Using Dummy Activities

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…….

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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.

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

CPM Network

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A CPM Network after forward

pass

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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

Backward Pass

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CPM Network after the backward

pass

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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.

Critical Path

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Event

Number

Latest

Date

Earliest

Date

Slack

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)

Activity Schedule showing total

float for each activity

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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

Activity Network Diagram

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1

2

3 5

4

7

6

8

10 9

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

Problem 1

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Draw activity network of the project.

Find total float of each activity.

Activity Time in Weeks

1-2 20

1-3 25

2-3 10

2-4 12

3-4 5

3-5 10

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