Network Analysis CPM & Pert

By,
Ankit Mahindrakar
Dhananjay Patil
Gaurang Panigrahi
Santosh Shelke
Rohit Bhopi
Javed
Project
A project is a series of activities directed to

accomplishment of a desired objective.
Plan your work first..then work

your plan
Network Analysis
Introduction
Network analysis is the general name given to certain specific
techniques which can be used for the planning, management and
control of projects.
One definition of a project:
A project is a temporary endeavour undertaken to create a
"unique" product or service
NETWORK TECHNIQUES
Developed in 1950s
CPM by DuPont for chemical plants
PERT by U.S. Navy for Polaris missile
CPM = Critical Path Method was developed by Du Pont and

the emphasis was on the trade-off between the cost of the
project and its overall completion time (e.g. for certain
activities it may be possible to decrease their completion times
by spending more money - how does this affect the overall
completion time of the project?)
PERT = Program Evaluation Review Technique was developed by

the US Navy for the planning and control of the Polaris missile
program and the emphasis was on completing the program in the
shortest possible time. In addition PERT had the ability to cope with
uncertain activity completion times (e.g. for a particular activity the
most likely completion time is 4 weeks but it could be anywhere
between 3 weeks and 8 weeks).
NETWORK TECHNIQUES
PERT
-Program Evaluation and
Review Technique
- developed by the US
Navy with Booz
Hamilton Lockheed
- on the Polaris
Missile/Submarine
program 1958
CPM
Critical Path Method
Developed by El Dupont
for Chemical Plant
Shutdown Project- about
same time as PERT
Both use same calculations, almost similar

Main difference is probabilistic and deterministic in time
estimation
5
CPM - Critical Path Method
Definition: In CPM activities are shown as a network of precedence

relationships using activity-on-node network construction
Single estimate of activity time
Deterministic activity times
USED IN : Production management - for the jobs of repetitive in

nature where the activity time estimates can be predicted with
considerable certainty due to the existence of past experience.
PERT Project Evaluation & Review Techniques

Definition: In PERT activities are shown as a network of precedence
relationships using activity-on-arrow network construction
Multiple time estimates
Probabilistic activity times
USED IN : Project management - for non-repetitive jobs (research and

development work), where the time and cost estimates tend to be
quite uncertain. This technique uses probabilistic time estimates.
Activity on Node & Activity on Arrow
Activity on Node
Activity on Arrow
- A completion of an activity is
represented by a node
- An arrow represents a task,

while a node is the completion
of a task
- Arrows represent order of events
Activity Slack
Each event has two important times associated with it :
- Earliest time ET , which is a calendar time when a event can occur when all
the predecessor events completed at the earliest possible times
- Latest time LT , which is the latest time the event can occur with out
delaying the subsequent events and completion of project.
Difference between the latest time and the earliest time of an event is the
slack time for that event
Positive slack : Slack is the amount of time an event can be delayed without
delaying the project completion
9
Benefits of CPM/PERT
Useful at many stages of project management

Mathematically simple
Give critical path and slack time
Provide project documentation
Useful in monitoring costs
10
Questions Answered by CPM & PERT
Completion date?
On Schedule?
Within Budget?
Critical Activities?
How can the project be finished early at the least cost?
11
Example 1- A simple network

Consider the list of four activities for making a simple product:
Activity
Description
Immediate
predecessors
Buy Plastic Body
Design Component
Make Component
Assemble product
A,C
Immediate predecessors for a particular activity

are the activities that, when completed, enable
12
the start of the activity in question.
Sequence of activities
Can start work on activities A and B anytime, since
neither of these activities depends upon the
completion of prior activities.
Activity C cannot be started until activity B has been
completed
Activity D cannot be started until both activities A and
C have been completed.
The graphical representation (next slide) is referred to

as the PERT/CPM network
16
Network of Four Activities

Arcs indicate project activities
A
2
Nodes correspond to the beginning
and ending of activities
14
Scheduling with activity time

Activity
A
B
C
D
E
F
G
H
I
Immediate
predecessors
A
A
A
E
D,F
B,C
G,H
Completion
Time (week)
5
6
4
3
1
4
14
12
2
Total
51
This information indicates that the total time required
to complete activities is 51 weeks. However, we can see

from the network that several of the activities can be
conducted simultaneously (A and B, for example).
12
Arc with ES & EF time

EF = earliest finish time
ES = earliest start time
Activity
2
16
t = expected activity
time
Earliest start & earliest finish time

We are interested in the longest path through the
network, i.e., the critical path.
Starting at the networks origin (node 1) and using a
starting time of 0, we compute an earliest start (ES) and
earliest finish (EF) time for each activity in the network.
The expression EF = ES + t can be used to find the earliest
finish time for a given activity.
For example, for activity A, ES = 0 and t = 5; thus the
earliest finish time for activity A is
EF = 0 + 5 = 5
17
Network with ES & EF time

5
4
1
3
Earliest start time rule:
The earliest start time for an activity leaving a
particular node is equal to the largest of the earliest
finish times for all activities entering the node.
18
Activity, duration, ES, EF, LS, LF

EF = earliest finish time
ES = earliest start time
Activity
3
2
LS = latest start
time
19
LF = latest finish time
Latest start & latest finish time

To find the critical path we need a backward pass calculation.
Starting at the completion point (node 7) and using a latest
finish time (LF) of 26 for activity I, we trace back through the
network computing a latest start (LS) and latest finish time
for each activity
The expression LS = LF t can be used to calculate latest start
time for each activity. For example, for activity I, LF = 26 and t
= 2, thus the latest start time for activity I is
LS = 26 2 = 24
20
Network with LS & LF time

D[5,8]
3[7,10]
5
7
4
1
3
Latest finish time rule:
The latest finish time for an activity entering a
particular node is equal to the smallest of the latest
start times for all activities leaving the node.
21
Slack or Free Time or Float

Slack is the length of time an activity can be delayed without affecting the
completion date for the entire project.
For example, slack for C = 3 weeks, i.e. Activity C can be delayed up to 3
weeks
3
(start anywhere between weeks 5 and 8).
2
ES
5
LS
8
EF
9
EF
12
LF-EF = 12 9 =3
LS-ES = 8 5 = 3
LF-ES-t = 12-5-4 = 3
22
Activity schedule for our example

Activity
A
B
C
D
E
F
G
H
I
23
Earliest
start (ES)
0
0
5
5
5
6
10
9
24
Latest
start (LS)
0
6
8
7
5
6
10
12
24
Earliest
Latest
finish (EF) finish (LF)
5
6
9
8
6
10
24
21
26
5
12
12
10
6
10
24
24
26
Slack
(LS-ES)
0
6
3
2
0
0
0
3
0
Critical
path
Yes
Yes
Yes
Yes
Yes
IMPORTANT QUESTIONS
What is the total time to complete the project?

26 weeks if the individual activities are completed on schedule.
What are the scheduled start and completion times for each activity?
ES, EF, LS, LF are given for each activity.
What activities are critical and must be completed as scheduled in order to

keep the project on time?
Critical path activities: A, E, F, G, and I.
How long can non-critical activities be delayed before they cause a delay in
the projects completion time
Slack time available for all activities are given.
24
Importance of Float (Slack) and Critical Path
1.
Slack or Float shows how much allowance each activity has, i.e. how
long it can be delayed without affecting completion date of project
2.
Critical path is a sequence of activities from start to finish with zero

slack. Critical activities are activities on the critical path.
3.
Critical path identifies the minimum time to complete project
4.
If any activity on the critical path is shortened or extended, project

time will be shortened or extended accordingly
25
Importance of Float (Slack) and Critical Path (cont)

5.
So, a lot of effort should be put in trying to control activities along

this path, so that project can meet due date. If any activity is
lengthened, be aware that project will not meet deadline and some
action needs to be taken.
6.
If one can spend resources to speed up some activity, do so only for

critical activities.
7.
Dont waste resources on non-critical activity, it will not shorten the

project time.
8.
If resources can be saved by lengthening some activities, do so for

non-critical activities, up to limit of float.
9.
Total Float belongs to the path
26
Limitations to CPM/PERT
Clearly defined, independent and stable activities

Specified precedence relationships
Over emphasis on critical paths
Thank you

Network Analysis CPM & Pert

Uploaded by

Copyright:

Available Formats

Network Analysis CPM & Pert

Uploaded by

Document Information

Original Description:

Original Title

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

Network Analysis CPM & Pert

Uploaded by

Copyright:

Available Formats

By,

A project is a series of activities directed to

Plan your work first..then work

CPM = Critical Path Method was developed by Du Pont and

PERT = Program Evaluation Review Technique was developed by

Both use same calculations, almost similar

CPM - Critical Path Method

Definition: In CPM activities are shown as a network of precedence

USED IN : Production management - for the jobs of repetitive in

PERT Project Evaluation & Review Techniques

USED IN : Project management - for non-repetitive jobs (research and

Activity on Node & Activity on Arrow

- An arrow represents a task,

Useful at many stages of project management

Questions Answered by CPM & PERT

Example 1- A simple network

Buy Plastic Body

Immediate predecessors for a particular activity

the start of the activity in question.

The graphical representation (next slide) is referred to

Network of Four Activities

Scheduling with activity time

This information indicates that the total time required

to complete activities is 51 weeks. However, we can see

Arc with ES & EF time

Earliest start & earliest finish time

Network with ES & EF time

Activity, duration, ES, EF, LS, LF

LF = latest finish time

Latest start & latest finish time

Network with LS & LF time

Slack or Free Time or Float

Activity schedule for our example

What is the total time to complete the project?

What activities are critical and must be completed as scheduled in order to

Importance of Float (Slack) and Critical Path

Critical path is a sequence of activities from start to finish with zero

Critical path identifies the minimum time to complete project

If any activity on the critical path is shortened or extended, project

Importance of Float (Slack) and Critical Path (cont)

So, a lot of effort should be put in trying to control activities along

If one can spend resources to speed up some activity, do so only for

Dont waste resources on non-critical activity, it will not shorten the

If resources can be saved by lengthening some activities, do so for

Total Float belongs to the path

Clearly defined, independent and stable activities

You might also like