UNIT-2
Project Management
(PERT/CPM)
INDEX
UNIT 2 PPT SLIDES
S.NO.
1.
2.
3.
4.
5.
6.
TOPIC
LECTURE NO.
Project Management ( PERT/CPM)
Network Analysis
Programme Evaluation and Review Technique (PERT),
Critical Path Method ( CPM ),
Identify Critical Path, Probability of Completing the Project
Within given time, Project Cost Analysis
L1
L2
L3
L5
L6
Project Planning
• Given:
– Statement of work
• written description of goals
• work & time frame of project
– Work Breakdown Structure
• Be able to: develop precedence
relationship diagram which shows
sequential relationship of project activities
3
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.
History
•
•
•
Developed in 1950’s
CPM by DuPont for chemical plants
PERT by U.S. Navy for Polaris missile
CPM 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 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).
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.
The Network construction
• Use of nodes and arrows
 An arrow leads from tail to head directionally
– Indicate ACTIVITY, a time consuming effort that is required to perform
a part of the work.
Arrows
 A node is represented by a circle
- Indicate EVENT, a point in time where one or more activities start
and/or finish.
Nodes
- A dummy shows precedence for two activities with same start & end
nodes
Activity on Node & Activity on Arrow
Activity on Node
Activity on Arrow
Gantt Chart
• A Gantt chart is a type of bar chart, that
illustrates a project schedule.
• Gantt charts illustrate the start and finish
dates of a project. Gantt charts can be
used to show current schedule status
using percent-complete shadings and a
vertical "TODAY" line as shown here.
Gantt Chart
• Popular tool for project scheduling
• Graph with bar representing time for each
task
• Provides visual display of project schedule
• Also shows slack for activities
– (amount of time activity can be delayed
without delaying project)
12
Gantt Chart (continued)
Gantt chart
Originated by H.L.Gantt in 1918
Advantages
Limitations
-
- Do not clearly indicate details regarding
the progress of activities
-
Gantt charts are quite commonly used.
They provide an easy graphical
representation of when activities
(might) take place.
easy to maintain and read.
- Do not give a clear indication of
interrelation ship between the separate
activities
The Project Network
Network consists of branches & nodes
Node
1
2
3
Branch
15
Concurrent Activities
Lay foundation
2
3
Order material
Incorrect
precedence
relationship
3
Lay
foundation
Dummy
2
4
Order material
Correct
precedence
relationship
16
Consider the following table which describes
the activities to be done to build a house
and its sequence
Activity
predecessors Duration
A Design house and obtain financing
3
B Lay foundation
A
2
C Order and receive materials
A
1
D Build house
B,C 3
E Select paint
B,C 1
F Select carpet
E
1
G Finish work
D,F 1
17
Project Network For A House
3
Lay foundation
1
3
Design house
and obtain
financing
2
2
0
1
Order and
receive
materials
Dummy
4
Select
paint
Build
house
1
3
5
6
Finish
work
1
7
1 Select
carpet
18
Critical Path
• A path is a sequence of connected
activities running from the start to the end
node in a network
• The critical path is the path with the
longest duration in the network
• A project cannot be completed in less
than the time of the critical path (under
normal circumstances)
19
All Possible Paths
path1:
1-2-3-4-6-7
3 + 2 + 0 + 3 + 1 = 9 months; the critical path
path2:
1-2-3-4-5-6-7
3 + 2 + 0 + 1 + 1 + 1 = 8 months
path3:
1-2-4-6-7
3 + 1 + 3 + 1 = 8 months
path4:
1-2-4-5-6-7
3 + 1 + 1 + 1 + 1 = 7 months
20
Forward and Backward Pass
• Forward pass is a technique to move forward
through a diagram to calculate activity duration.
Backward pass is its opposite.
• Early Start (ES) and Early Finish (EF) use the
forward pass technique.
• Late Start (LS) and Late Finish(LF) use the
backward pass technique.
21
Early Times
(House building example)
• ES - earliest time activity can start
• Forward pass starts at beginning of
network to determine ES times
• EF = ES + activity time
– ESij = maximum (EFi)
i
– EFij = ESij + tij
– ES12 = 0
– EF12 = ES12 + t12 = 0 + 3 = 3 months
j
22
Computing Early Times
-ES23 = max (EF2) = 3 months
- ES46 = max (EF4) = max (5,4) = 5 months
- EF46 = ES46 + t46 = 5 + 3 = 8 months
- EF67 =9 months, the project duration
23
Late Times
• LS - latest time activity can be started
without delaying the project
• Backward pass starts at end of network to
determine LS times
• LF - latest time activity can be completed
without delaying the project
– LSij = LFij - tij
– LFij = minimum (LSj)
24
Computing Late Times
– If a deadline is not given take LF of the
project to be EF of the last activity
– LF67 = 9 months
– LS67 = LF67 - t67 = 9 - 1 = 8 months
– LF56 = minimum (LS6) = 8 months
– LS56 = LF56 - t56 = 8 - 1 = 7 months
– LF24 = minimum (LS4) = min(5, 6) = 5 months
– LS24 = LF24 - t24 = 5 - 1 = 4 months
25
Project cost analysis:ES=5, EF=5
ES=3, EF=5
LS=3, LF=5
1
3
ES=0, EF=3
LS=0, LF=3
2
3
2
LS=5, LF=5
0
1
ES=3, EF=4
4
ES=5, EF=8
ES=8, EF=9
LS=5, LF=8
LS=8, LF=9
LS=4, LF=5
1
ES=5, EF=6
LS=6, LF=7
3
1
5
6
1
7
ES=6, EF=7
LS=7, LF=8
26
Activity Slack
• Slack is defined as the LS-ES or LF-EF
• Activities on critical path have ES = LS &
EF = LF (slack is 0)
• Activities not on critical path have slack
–
Sij = LSij - ESij
–
Sij = LFij - EFij
– S24 = LS24 - ES24 = 4 - 3 = 1 month
27
Total slack/float or Slack of an activity
• Total slack/ float means the amount of
time that an activity can be delayed
without affecting the entire project
completion time.
• The activity on a given path share the
maximum possible slack of the activity
along that path according to its share.
• Sum of the possible slacks of the activities
can not exceed the maximum slack along
that path.
28
Free slack of an activity
• This is the maximum possible delay of
an activity which does not affect its
immediate successors.
• This is evaluated as
• FSij = ESj – EFij
29
Activity Slack Data
Activity
1-2*
2-3
2-4
3-4*
4-5
4-6*
5-6
6-7*
ES
0
3
3
5
5
5
6
8
LS
0
3
4
5
6
5
7
8
EF
3
5
4
5
6
8
7
9
LF
3
5
5
5
7
8
8
9
Slack (S)
0
0
1
0
1
0
1
0
Free slack
0
0
1
0
0
0
1
0
* Critical path
30
Probability of completing the
project within given time:0
•
Activity
•
•
Design house and
obtain financing
•
Lay foundation
•
•
Order and receive
materials
•
Build house
•
Select paint
•
Select carpet
•
Finish work
2
1
4
3
6
5
8
7
10
9
31
Probabilistic Time Estimates
• Reflect uncertainty of activity times
• Beta distribution is used in PERT
a + 4m + b
Mean (expected time): t =
6
2
b
a
Variance: s = (
)
6
2
where,
a = optimistic estimate
m = most likely time estimate
b = pessimistic time estimate
32
P (time)
P (time)
Example Beta Distributions
a
b
a
t
m
b
P (time)
m
t
a
m=t
b
33
Activity Information
Activity
1–2A
1–3B
1–4C
2–5D
2-6 E
3-5 F
4–5G
4–7H
5–8I
5–7J
7–8K
6–9L
8–9M
Time estimates (wks)
a
m
b
6
8 10
3
6
9
1
3
5
0
0
0
2
4 12
2
3
4
3
4
5
2
2
2
3
7 11
2
4
6
0
0
0
1
4
7
1
10 13
Mean Time
t
Variance
s2
34
Activity Information
Activity
1 – 2A
1 – 3B
1 – 4C
2 – 5D
2 – 6E
3-5F
4 – 5G
4 – 7H
5 – 8I
5 – 7J
7 – 8K
6 – 9L
8 – 9M
Time estimates (wks)
a
m
b
6
8 10
3
6
9
1
3
5
0
0
0
2
4 12
2
3
4
3
4
5
2
2
2
3
7 11
2
4
6
0
0
0
1
4
7
1
10 13
Mean Time
t
8
6
3
0
5
3
4
2
7
4
0
4
9
Variance
s2
.44
1.00
.44
.00
2.78
.11
.11
.00
1.78
.44
.00
1.00
4.00
35
Network With Times
2
6
E
5
A 8
L
4
D0
1
3
B6
5
F
3
G4
C3
4
H
2
8
I
7
9
M
9
K
0
J
4
7
36
PERT Example
Equipment testing
and modification
2
Final
debugging
Dummy
Equipment
installation
1
6
System
development
3
Manual
Testing
Job
training
Position
recruiting
4
Orientation
5
System
Training
8
System
Testing
9
System
changeover
Dummy
7
37
Early And Late Times
Activity
t
s2
ES
1-2
1-3
1-4
2-5
2-6
3-5
4-5
4-7
5-8
5-7
7-8
6-9
8-9
8
6
3
0
5
3
4
2
7
4
0
4
9
0.44
1.00
0.44
0.00
2.78
0.11
0.11
0.00
1.78
0.44
0.00
1.00
4.00
0
0
0
8
8
6
3
3
9
9
13
13
16
EF
8
6
3
8
13
9
7
5
16
13
13
17
25
LS
1
0
2
9
16
6
5
14
9
12
16
21
16
LF
9
6
5
9
21
9
9
16
16
16
16
25
25
S
1
0
2
1
8
0
2
11
0
3
3
8
0
38
Network With Times
ES=8, EF=13
2
ES=0, EF=8
(LS=1, LF=9 )
( LS=16 LF=21 )
6
5
8
0
(LS=0, LF=6 )
6
(LS=9, LF=9 )
4
ES=9, EF=16
3
ES=0, EF=3
3
( LS=21 LF=25 )
ES=8, EF=8
ES=0, EF=6
1
ES=13, EF=17
(LS=2, LF=5 )
4
3
( LS=9, LF=16 )
5
ES=6, EF=9
(LS=6, LF=9 )
8
7
ES=9, EF=13
4
ES=3, EF=7
(LS=5, LF=9 )
( LS=12, LF=16)
2
ES=3, EF=5
( LS=14, LF=16)
0
9
ES=16, EF=25
( LS=16 LF=25 )
ES=13, EF=13
( LS=16 LF=16 )
4
9
7
39
Project Variance
Project variance is the sum of the variances
along the critical path
s2 = s2 13 + s2 35 + s2 58 + s2 89
= s2 B + s2 F + s2 I + s2 M
= 1.00 +0.11 + 1.78 + 4.00
= 6.89 weeks
40
Probabilistic Network Analysis
Determine the probability that a project is
completed (project completion time is )
within a specified period of time
x-m
Z =
where
s
m = tp = project mean time
s = project standard deviation
x = project time (random variable)
Z = number of standard deviations of x from
the mean (standardized random variable) 
41
Normal Distribution Of Project Time
X ~ N (m ,s 2 )
z=
Probability
xm
s
Zs
m = tp
x
Time
42
Standard Normal Distribution Of
transformed Project Time
Probability
Z ~ N (0,1 )
Z
m =0
z
Time
43
Probabilistic Analysis Example
What is the probability that the project is
completed within 30 weeks?
P(X 30) = ?
s2 = 6.89 weeks
s = 6.89
= 2.62 weeks
Z = x - m =30 - 25 = 1.91
2.62
s
P(Z  1.91) = ?
44
Determining Probability
From Z Value
Z
0.00
..
1.1
.
..
0.3643
.
1.9
0.4713
0.01 ..
04
..
0.3665
0.3729
.
+0.4719
…
…
0.09
0.4767
P( x < 30 weeks) = 0.50+ 04719
= 0.9719
m = 25
x = 30
Time (weeks)
45
What is the probability that the project will
be completed within 22 weeks?
22 - 25 = -3
= -1.14
Z=
2.62
2.62
P(Z< -1.14) = 0.1271
x = 22 m = 25 x=28
Time (weeks)
P( x< 22 weeks) = 0.1271
46
Benefits of PERT/CPM
• Useful at many stages of project
management
• Mathematically simple
• Uses graphical displays
• Gives critical path & slack time
• Provides project documentation
• Useful in monitoring costs
47
Limitations of PERT/CPM
• Assumes clearly defined, independent,
& stable activities
• Specified precedence relationships
• Activity times (PERT) follow
beta distribution
• Subjective time estimates
• Over-emphasis on critical path
48