cpmpertmy (1)

NETWORK TECHNIQUES - CPM & PERT
Presented by
Richa-16173
Divya-16164

Content
• Introduction
• Steps involved in PERT & CPM
• Network principles
• Approaches for network diagram
• Rules for construction of network diagram
• Sample question- CPM & PERT
• Summary

INTRODUCTION
Project
• A project is an interrelated set of activities that has a definite
starting and ending point and that results in a unique product
or service.
Project management
• Project management is a scientific way of planning, implementing,
monitoring & controlling the various aspects of a project such as time,
money, materials, manpower & other resources.
• For proper planning, scheduling and control of activities of given project and
their interrelationship we use network techniques
Technique for project management
 CPM- critical path method.
 PERT-program evaluation review technique.

CPM-CRITICAL PATH METHOD
HISTORY :
• It was developed independently in 1956-57 by Du Pont company in US to
solve trade off cost of project and it over all completion time (scheduling
problems).It was applied to construction of chemical plant
DEFINITION:
Critical path is the sequence of activities between a project’s start and finish
that takes the longest time to complete.
Applied to projects that employ stable technology and relatively risk free
Hence the orientation is “DETERMINISTIC “
.

PERT-PROGRAM EVALUATION REVIEW
TECHNIQUE
HISTORY
• Originally develop to facilitate the planning and scheduling Polaris fleet
Ballistic Missile Project of US government
• Used for risk and uncertain situation
• Used for research and development program, aerospace project
• Project involving new technologies
• Projects with variable completion time
Hence the orientation of PERT is PROBALISTIC

DIFFERENCE BETWEEN
CPM & PERT
CPM PERT
• CPM works with fixed
deterministic time
• PERT works with probabilistic
time
• CPM is useful for repetitive and
non complex projects with a
certain degree of time estimates.
• PERT is useful for non repetitive
and complex projects with
uncertain time estimates.
• CPM includes time-cost trade off. • PERT is restricted to time
variable.
• CPM- for construction projects. • PERT- used for R&D programs.

STEP INVOLVED IN PERT & CPM
Steps involved are :
• Identify the specific activities.
• Determine proper sequence of the activities.
• Construct the network diagram.
• Estimate the time required for each activity.
• Determine the critical path , slack.
• Development of project schedule
• Calculate the variability of project duration and probability of completion in given
time(Update the PERT chart.)

NETWORK PRINCIPLES
ACTIVITY-An activity is a definite task ,job, or function to be performed in a project
E.g. – “Prepare dinner “is an activity
 An activity is represented by an arrow
 The head of the arrow marks the completion of the activity
and the tail of the arrow marks the beginning.
 The length and direction of arrow as no significance.
• Merge activity – an activity which is dependent on two or more preceding activities
• Burst activity- an activity that is followed by two or more activities .
• Path- a path is unbroken chain of activities from initiating node to some other
node(last)
EVENT- describe the start and the completion of the an activity.it is donated by the
number
An event is specific point of time indicating the beginning and the end of one or more
activities.

NETWORK PRINCIPLES
• There can be two format to define the network diagram
 Activity in the Box (AIB)/Activity on the node-
 Activity on arrow (A0A)
Activity in the box (AIB) Activity on arrow(AOA)
Get volunteer
7
Wash car
3
Dry car
4
Collect data
1 2 3
Wash
car
Dry car

APPRAOCHES FOR
NETWORK DIAGRAM
ACTIVITY ON ARROW (AOA):
• Uses arrow to represent activities and nodes to represent events.
• It is Event Oriented.
1 876
54
3
2

• Uses nodes to represent activities indicate precedence relationships
between them.
• It is Activity Oriented.
ACTIVITY ON NODE(AON):

RULES FOR NETWORK DIAGRAM
• Each activity have preceding and
succeeding event.
• Before an activity can begin, it
preceding activity must be completed.
• Each event should have distinct
number in way that head of arrow is
greater than the tail.
• Length and direction of the arrow has
no significance.
• Flow is from left to right
• Arrow should not intersect.
• There should be no loop in the project
network
• Not more than one activity can have
same preceding and succeeding
events. Each activity is represented by
unique numbered arrow
1
2
3 4
Take dinner

TIME ESTIMATES
Once the logic and details of the network has been established time estimates
are assigned-
• Optimistic time(a)-It is the shortest time in which the activity can be
completed.
• Most probable time/likely time (m) -It is the probable time required to
perform the activity.
• Pessimistic time (b)- it is longest estimated time.
• Average time(expected time ) = a+4m*b
6

CPM & PERT – sample Question

1- IDENTIFY THE ACTIVITIES
2- ESTIMATE THE EXPECTED TIME by using = a+4m+b/6

Start
A B
C D
E
F
Level 1 Level2 Level 3
G
H I J
end
Level4 Level 5 level6
Each activity have preceding and succeeding
event.
Before an activity can begin, it preceding
activity must be completed.
Each event should have distinct number in
way that head of arrow is greater than the tail.
Length and direction of the arrow has no
significance.
Flow is from left to right
Arrow should not intersect.
There should be no loop in the project
network
Not more than one activity can have same
preceding and succeeding events. Each activity
is represented by unique numbered arrow
3- construction of network diagram

KEY
 It defines what format we are using
 It act has reference
A
ES EF
D
SLACK
LS LF
ES- earliest start time
EF-earliest finish time
LS-latest start
LF latest finish
D-duration

4-ESTIMATING TIME OF COMPLETION
Planning the schedule of the project
Time estimates include:
1) D-Total time for completion( we already have)
2) ES- Earliest start time: the earliest time at which the activity
can start given that its precedent activities must be completed first.
3) EF-Earliest finish time: equals to the earliest start time for the activity
plus the time required to complete the activity.
4) LF- Latest finish time: the latest time in which the activity can be
completed without delaying the project.
5) LS- Latest start time: equal to the latest finish time minus the time
required to complete the activity.

6) FORWARD PASS:
The early start and early finish times are calculated by moving forward through
the network considering the predecessor activities .
Considers maximum
7) BACKWARD PASS:
The latest start and finish times are calculated by moving backward through the
network.
Considers minimum
8) SLACK TIME:
Slack time for an activity is the difference between its earliest and latest start time
or between the earliest and latest finish time.
9) Critical path- is the path of activities having zero Slack time.

A
F
J
G
D
H
EB
C
I
s
t
a
r
t
E
n
d
PERT DIAGRAM & KEY

6
A
4
F
4
J
3
G
10
D
8
H
6
E
6
B
3
C
4
I
s
t
a
r
t
E
n
d
FILLING OF DURATION or
EXPECTED TIME(D)

0 6 6
A
9 4 13
F
24 4 28
J
19 3 22
G
9 10 19
D
12 8 20
H
12 6 18
E
6 6 12
B
6 3 9
C
20 4 24
I
s
t
a
r
t
E
n
d
Moving alphabetically
Forward pass deals with
Earliest start and earliest finish
Can B start
on 5th day
We pick maximum value
28
days
EF= ES+ expected time

0 6 6
A
9 4 13
F
24 4 28
J
24 28
19 3 22
G
9 10 19
D
12 8 20
H
12 6 18
E
6 6 12
B
6 3 9
C
20 4 24
I
s
t
a
r
t
E
n
d
28
days
Backward pass
Latest start & latest finish
We pick the minimum value
Move Alphabetically backward
Last
activity
What is the latest finish for J
that would still allow the
project to finish on the 28th
day?
So 28-4 would give us the
latest start which is 24

0 6 6
A
9 4 13
F
24 4 28
J
24 28
19 3 22
G
9 10 19
D
12 8 20
H
12 6 18
E
6 6 12
B
6 3 9
C
20 4 24
I
20 24
s
t
a
r
t
E
n
d
28
days
Backward pass
Now we go backwards
So , its J and I
We look at the right hand side of I
What is the latest finish time for I
Since it is coming only from J ,
it will be 24
Latest finish time of one
activity is equivalent to latest
start time of the next activity.

0 6 6
A
9 4 13
F
24 28
24 4 28
J
24 28
19 3 22
G
21 24
9 10 19
D
11 21
12 8 20
H
12 20
12 6 18
E
15 21
6 6 12
B
6 3 9
C
20 4 24
I
20 24
s
t
a
r
t
E
n
d
28
days
Backward pass
Similarly we can calculate
for the activities H,E,G,D,F

0 6 6
A
9 4 13
F
24 28
24 4 28
J
24 28
19 3 22
G
21 24
9 10 19
D
11 21
12 8 20
H
12 20
12 6 18
E
15 21
6 6 12
B
6 3 9
C
8 11
20 4 24
I
20 24
s
t
a
r
t
E
n
d
28
days
RULE FOR BACKWARD PASS
We pick the minimum value,
the smallest value.
C has two values , on the right
hand side, there are two arrows
coming out of C.
One value is going to 11 and one
is 24
This is the latest
finish time for C
which will still allow
the project to
happen on 28th day.
If we use
24, it will
change the
whole
schedule.

SCHEDULING WHEN RESOURCES ARE LIMITED
• The early start schedule refers to the schedule in which all activities start
as early as possible. The late start schedule reflects a desire to commit
resources late – as late as possible.
• In real life situations there may be restrictions on the availability of
resources . In the face of these , various schedules may have to be
considered to find out which one is most appropriate in the light of these
restrictions.

0 6 6
A
0 6
9 4 13
F
24 28
24 4 28
J
24 28
19 3 22
G
21 24
9 10 19
D
11 21
12 8 20
H
12 20
12 6 18
E
15 21
6 6 12
B
6 12
6 3 9
C
8 11
20 4 24
I
20 24
s
t
a
r
t
E
n
d
28
days
Backward pass
Similarly we can calculate
for the activities B , A

0 6 6
A
0 0 6
9 4 13
F
24 15 28
24 4 28
J
24 0 28
19 3 22
G
21 2 24
9 10 19
D
11 2 21
12 8 20
H
12 0 20
12 6 18
E
15 3 21
6 6 12
B
6 0 12
6 3 9
C
8 2 11
20 4 24
I
20 0 24
s
t
a
r
t
E
n
d
28
days
Backward pass
SLACK TIME
Bottom- top =Slack time, i.e.,
Latest finish time – earliest finish time
or
Latest start time – earliest start time
6-6=0

0 6 6
A
0 0 6
9 4 13
F
24 15 28
24 4 28
J
24 0 28
19 3 22
G
21 2 24
9 10 19
D
11 2 21
12 8 20
H
12 0 20
12 6 18
E
15 3 21
6 6 12
B
6 0 12
6 3 9
C
8 2 11
20 4 24
I
20 0 24
s
t
a
r
t
E
n
d
28
days
Critical Path Activities
Those activities which have a slag
zero, that means no slack.
Map the path from start to end
Which activity has
zero slack from
start?
there is only one
activity from start
which has slack
zero i.e. activity A
Critical path is
A-B-H-I-J
It is possible sometimes to
have more than one critical
path in a project.

CPM MODEL
The usual assumptions underlying CPM analysis are :
 The costs associated with a project can be divided into two
components : direct costs and indirect costs .
 Activities of the project can be expedited by crashing which involves
employing more resources.
 Indirect costs associated with the project increases linearly with
project duration.
Given the above assumptions , CPM analysis seeks to examine the
consequence of crashing on total cost . The procedure used in this respect
is generally as follows:
 Examine the cost – time slope of activities on the critical path obtained
and crash the activity which has the least slope .
 Construct the new critical path after crashing as per step.
 Determine project duration and cost .
 Repeat steps, till all activities on the critical path are crashed .

PERT MODEL
 Variability in PERT analysis is measured by variance or its square root ,
standard deviation.
The steps involved in calculating the standard deviation of the duration of the
critical path are as follows :
 Determine the standard deviation of the duration of each activity on
the critical path.
 Determine the standard deviation of the total duration of the
critical path on the basis of information obtained in the step.
 Armed with information about the mean and standard deviation of
critical path duration.

QUES.: Given that the variance for the project is
9.1, what is the probability that the project
would be completed in 27 days?
In order to do this question , the first thing is to
draw a normal distribution curve

Expected time for completing the project is 28 days.
This means that it is the expected time or mean time.
It means that there is 50-50 chance that the project will be completed in 28 days.
µ = 28X= 27
In order to know
the probability of
the project to be
completed in 27
days ,
we need to know
this area
σ2 ( variance)
= 9.11
So, σ= √9.11
= 3.02
FORMULA
Z= X- µ
σ , so Z= 27-28
3.02
= -0.33
Look for the value of Z= -0.33 in the Z
distribution table.
area for standard distribution table shows
that the value (area) is 0.1293.

0.50
0.1293
0.5-0.1293=0.3707
= 37.07%
We know that there is 0.5 chance of
project being completed in 28 days
By looking at Z table we have
found this.
What this is telling us is that the probability of the project being completed in
27 days is 37.07%.
Remember that the probability for 28 days is 50%

NETWORK COST SYSTEM
 To provide a vehicle for cost planning and control of projects , the
network cost system was developed . This represents a very useful
supplement to the traditional time – oriented network analysis .
 The basic principle of network cost system is fairly simple : costs
are planned , measured , analysed , and controlled in
terms of project activities.
 As the project progresses , the following may be measured /
estimated periodically for purposes of monitoring and control :
 Costs incurred to – date ,
 Budgeted costs to – date ,
 Value of work done to – date ,
 Cost over – run to – date , and
 Time over – run to – date .

CONCLUSION
The techniques of PERT and CPM discussed here are essentially
time – oriented . They seek to answer questions like :
What is the most desirable time schedule of activities ?
How much time would it take , on an average , to
complete the project ?
What is the probability of completing the project in a
specified time ?

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