Transcript NETWORK MODELS – CPM AND PERT Quantitative Techniques for Decision Making M.P. Gupta & R.B.

NETWORK MODELS –
CPM AND PERT
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
CHAPTER
13
Learning Objectives
• Draw a network
• Calculate floats
• Identify critical activities and critical path
• Cost crashing
• Resource levelling
• PERT network
• Calculation of probability of completing project in
certain time.
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 2
PROJECT COST AND TIME OVER-RUNS
• The problem is so acute in India that a Ministry of Statistics and Programme
Implementation has been set up. A flash report of the ministry, dealing with
projects of Rs 100 Crores and above, for July 2009 reveals the following
statistics:
•
•
•
•
•
•
•
•
•
•
•
No of projects monitored 602
Original estimate Rs 544656.88 Crores
Anticipated cost Rs 600414.11 Crores
Cost overrun
Rs 55757.23 Crores
Projects ahead of schedule 13
Projects on schedule
145
Projects delayed
370
Projects with no fixed date of commissioning 74
Delay ranges from 1 – 51 months.
Percentage of cost overruns in delayed projects 10.24%
Considering the magnitude of the problem, it is imperative that projects are
managed properly
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 3
Definitions
•
•
•
•
Activity. It is a clearly defined project element, a job or a
task which requires the consumption of resources
including time. It is denoted by an arrow.
Event. An event describes the start or completion of an
activity. It is denoted by a numbered circle.
Path. A path is an unbroken chain of activities from the
initiating node to some other node, generally to the last
node indicating the end or completion of the project.
Dummy Activity. A dummy activity is that activity which
has a logical function only and consumes no time or
resources. It is denoted by a dotted arrow. There are two
types of dummies:
– Identity Dummy. It helps to keep the designation of
each activity unique or different from another.
– Dependency Dummy. It helps to keep the logic correct.
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 4
Rules and Conventions
• Activity arrows should be drawn from left to right
indicating progressive approach towards the ultimate
objective or the final event.
• Crossing of activity arrows should be avoided. Arrows
should be drawn as straight or bent lines but not
curved lines.
• Avoid use of unnecessary dummies.
• Activities are set in the order of their execution. Events
are set in the order of their occurrence.
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 5
Rules and Conventions
• Head event number should be greater than tail
event number. No event is numbered until the
tail event of each activity arrow ending into that
event has been numbered.
• There should be no danglers or loops.
Danglers are activities which lead no where. All
activities must be connected to events and the
finishing activities must be connected to the
finish event of the project.
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 6
Critical Path Method
• It is used where activity duration is known
with certainty.
• Activities are identified.
• Dependency of activities is determined
• Network is drawn
• Earliest start times and latest finish times are
calculated
• Critical path and critical activities are
identified
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 7
Example
• Rasoi Appliances wants to launch a
newly designed microwave oven.
• Activities required for the launch have
been identified. Their relationship with
each other and the activity duration
have also been determined.
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 8
Activity
Symbol
Activity Description
Predecessor
Time
(days)
A
Develop advertising plan
-
6
B
Develop promotion and training
materials plan
-
7
C
Develop training plan
-
8
D
Schedule Radio,TV and print media
advertising
A
20
E
Develop advertising copy
A
18
F
Prepare promotional material for instore introduction
B
9
G
Prepare material for training of
stores representatives
B
8
H
Conduct pre-introduction advertising
campaign
D, E
7
I
Select store representatives for
training
C
2
J
Conduct training
G, I
14
K
Final in-store launch of product
F, H and J
10
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 9
If dummy
the from
dummy
LNetwork.
hadLand
not
been
put,
then
node
5is
Start
the
left
number
the
nodes
as
we
move
Consider
Activity
A
Hthe
is
activity
dependent
activities
haswhich
on
been
the
can
drawn.
completion
follow
This
only
ofwould
an
A
Activities
oridentity
Bhave
or
•••••Drawing
a
We
can
start
with
been
eliminated
and
activity
E the
also
would
have
ended
atF
to
thethese
right
ofactivity
the
network
in
order
of
their
C
D
dummy.
as
and
E.
Add
Activity
have
been
J
is
K
dependent
completed.
which
can
on
start
D
completion
and
only
E
follow
when
of
A,
activities
A,Ifcase,
B
and
C as
they
have
no
node 7. In that
a reference
to activity
between
nodes
appearance.
two
or
more
nodes
are
on
the
same
and
Activities
activities
G
follow
H,
G
and
F
B
and
and
I.
Add
J
I
are
follows
these
completed.
C.
activities
Add
these
to
the
activities
network.
to
2-7
would
refer
to
both
D
and
E
causing
problems
of
predecessors.
the
work. from top to bottom.
line,net
number
unique reference.
D
H
6
L
20
A
7
E
2
5
6
18
F
K
8
1
B
7
G
3
4
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
10
9
8
C
8
9
I
2
7
J
14
Page 10
Calculating Earliest Start Time
(EST)
• The earliest that the project can start is
at time zero.
• The earliest finish time for an activity is
the earliest start time + activity duration.
• The earliest start time of an activity
which is dependent on two or more
activities is the time at which all the
preceding activities are completed.
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 11
At
get
Node
7 is8,
starting
event
forat
activity
J.2
J can
startKonly when
9,the
EST
= is
EST
at Node
8 + duration
of
activity
At
AtNode
Node
Node
5,
4,
2,we
3,
6,
EST
EST
is =
= EST
EST
at
Node
Node
12Activity
++ Activity
Activity
Duration
Duration
of
of E
B
A
D=
activities
Ito
and
G
are
completed.
Activity
I 8,
can7 be
completed
earliest by 8 + 2
From
7
8,
26
+
7
=
33.
From
3
to
+
9
=
16
=
33
+
10
=
43
+ 20
= 26,
and
==earliest
6
0 ++ Node
18
87
6 on
==87
6724
Node
7) 24
0 = 24.
=610,
while
G can
end(from
+58to
= 15.
Hence
the +
earliest
thatEarliest
J can
From
6 toend
8,isof
15
+ 14day.
= 29. Earliest K can start is 33.
H
can
start
26.
start
is the
15th
26
D
20
6
A
6
E
18
2
0
1
B
7
7
C
8
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
G
8
3
H
7
6
L
24
5
33
K
8
10
F
9
43
9
15
8
4
I
2
7
J
14
Page 12
Latest Finish Time
• The project will take 43 days.
• Start form Node 9 as 43 days and work backward
to find out the latest time when the starting event
of an activity must occur, or the latest time by
which all preceding activities must finish so that
the project is not delayed
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 13
At
Node
3, LFT
is = LFT
at Node
6–
Activity Duration
Duration of of
G or
At
Node
2,
LFT
at
Node
5
–
Activity
E or
8,
6,
LFT
at
9
Duration
5,
7
L
4,
6
At
Node
7,
is
=
LFT
Node
8
–Activity
of K
JIH
At Node 1, LST = 0
LFT at Node 8 – Activity Duration of F
LFT at Node
7 –10
Duration of D.
33
733Activity
26
0
=–=17
26
19
2
19
= 19 –=8 43
=11 –
or14
933
= 24
smallest
value.
Node
LFT
is = 6LFT is = 11
IfTake
eventthe
3 occurs
at 24 then
theAt
project
will2,get
delayed.
26
6
A
6
E
18
2
6
0
1
0
D
20
B
7
11
7
C
G
8
3
L
24
5
26
F
9
33
K
8 10
33
43
9
43
15
8
4
8
6
26
H
7
I
2
7
J
14
17
19
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 14
Floats
• Spare time in an activity is called float. It
is used to economise on resources
without affecting the overall duration of
the project.
• Types of floats
– Total float
– Free float
– Interference float
– Independent float
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 15
4
26
G
3
8
30
Total
Float.
==30
– 4–the
–43–spare
=323= 23
• •• Total
TotalFloat.
Float.
It30
is
time available on any given
Free
Float.
==26
–30
4
––
activity
if the
tail
Total
Float.
=
3
• ••Free
Float.
26
–event
434
–=–
319occurred
==
1923 at its earliest time
• Interference Float. = 23 – 19 = 4
Freethe
Float.
The
spare
time
available
on less
an activity
and
head
event
at equal
its
latest
time.float
• •Interference
Float.
It is
to total
free if
• Independent Float. The spare time available in an activity which
bothIfthe
tail
the
headat
events
occur
their at
float.
this
float
is
anbyactivity,
itatwill
Total
Float
= and
Time
Latest
Head
– Time
Earliest
is neither
affected
by used
the
useup
of in
float
preceding
activities nor
earliest
time.
Iffloat
this
spare time
is used
up during
interfere
with
the
availability
floats
available
for the
does
it affect
the
inof
subsequent
activities.
Tail
–available
Activity
Duration.
execution of
this activity,
it will have no effect on
activities.
• subsequent
Independent
Float
= 30= –Time
4 –Earliest
3 = 23Head – Time
subsequentFloat
activities.
Latest
– Duration.
• Interference
=
TotalTail
Float
– Free Float
= 26Earliest
– 8 – 3 = 15
Free Float = Time
= 23 – 19 Head
= 4 – Time Earliest Tail
– Activity Duration
= 26 – 4 – 3 = 19
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 16
Calculation of floats
Activity
Total Float
(TL Head – TE
Tail – Duration)
Free Float
(TE Head – TE
Tail – Duration )
Interference
Float
(Total Float –
Free Float)
Independent
Float
(TE Head – TL
Tail – Duration)
A
6 – 0 – 6 =0
B
11-0-7=4
7-0-7=0
4-0=4
7-0-7=0
C
17-0-8=9
8-0-8=0
9-0=9
8-0-8=0
D
26-6-20=0
E
26-6-18=2
24-6-18=0
2-0=2
24-6-18=0
F
33-7-9=17
33-7-9=17
17-17=0
33-11-9=13
G
19-7-8=4
15-7-8=0
4-0=4
15-11-8 (0)
H
33-26-7=0
I
19-8-2=9
15-8-2=5
9-5=4
15-17-2 (0)
J
33-15-14=4
33-15-14=4
4-4=0
33-19-14=0
K
43-33-10=0
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 17
Identifying Critical Activities and
Critical Path
• All activities whose floats are zero are called
critical activities. They are critical as they
have no spare time available for their
execution. Critical activities have the same
EFT and LST at their start and finish nodes
and have no float.
• Management must exercise strict control to
ensure that critical activities are executed as
per schedule.
• The path through these activities is called
critical path.
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 18
26
D
6
20
6
6
0
1
24
5
33
26
11
B
G
8
3
7
8
9
33
4
8
10
9
43
15
8
C
43
K
F
7
0
E
18
2
7
L
6
A
26
H
J
I
2
7
14
17
19
A,D,H and K are critical activities. Critical Path is 1 -2 – 7- 8 - 9
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 19
Cost Crashing
• Some activities in a project can be completed in
shorter time by employing extra resources. But the
duration of all activities cannot be reduced by
increasing resources because of their nature or
because of the restrictions on employment due to
space constraints and so on.
• If an activity can be completed earlier, extra cost on
extra resources will have to be incurred, but if this
reduces the overall duration of the project this will
result in reduction of the overhead costs.
• Completing an activity in a shorter time than normal
is referred to as activity crashing and the additional
cost is called crash cost.
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 20
Example
Activity Dependency
Normal
Time
Crash
Time
Normal Crash Cost
Cost
(Increase per day)
A
START
4
4
4000
-
B
START
8
6
8000
1500
C
F, D, FINISH
3
3
600
-
D
B
6
5
900
150
E
START
7
5
350
100
F
A
15
12
9000
900
G
B
12
10
1200
200
H
G, FINISH
10
8
1000
150
J
L, FINISH
5
4
1000
300
K
E
9
7
900
150
8
2200
350
L
G&K
11
Fixed cost is Rs 500 per day.
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 21
Solution
• Draw the network.
• Calculate EST and LFT using normal times of activity
duration.
• Identify critical activities and path.
• The duration of the project will reduce only if activities
on critical path are crashed.
• Crash the activity which is cheapest to crash.
• After crashing any activity, recompute the timings and
identify critical path. The path may change causing
the critical activities to change.
• Continue crashing activities in this manner till the
objective has been achieved, i.e. lowest cost of
project or minimum time.
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 22
Total cost Rs 47150
Direct cost Rs 29150
Indirect cost Rs 18000
A
4
19
2
4
F18
15
0
33
6
B
8
3
8
0
G
12
7
E
7
5
D
8
1
C
3
4
11
20
6
I
9
H
20
10
20
31
L
K
9
36
7
20
11
J
8
5
36
31
B, G, L and J are critical activities and should be
considered for crashing
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 23
Activity
Crash
Days
by Cost of crashing per
day
B
2
1500
G
2
200
L
3
350
J
1
300
• Activity G is the cheapest to crash. Crash G by 2 days.
• Recompute the timings and identify the critical path.
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 24
Total cost Rs 46550
Direct cost Rs 29550
Indirect cost Rs 17000
A
4
19
2
4
F16
15
0
5
31
6
B
8
3
8
0
G
10
7
E
7
C
3
D
8
1
Cost reduced by Rs 600
Time reduced by 2 days
4
18
6
I
9
H
18
10
18
29
L
K
9
34
7
11
J
8
5
34
9
18
29
B, G, L and J are still critical activities. B, L and J should be
considered for crashing
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 25
Activity
Crash
Days
by Cost of crashing per
day
B
2
1500
L
3
350
J
1
300
• Activity J is the cheapest to crash. Crash J by 1 days.
• Recompute the timings and identify the critical path.
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 26
Total cost Rs 46350
Direct cost Rs 29850
Indirect cost Rs 16500
A
4
19
2
4
F15
15
0
5
30
6
B
8
3
8
0
G
10
7
E
7
C
3
D
8
1
Cost reduced by Rs 800
Time reduced by 3 days
4
18
6
I
9
H
18
10
18
29
L
K
9
33
7
11
J
8
4
33
9
18
29
B, G, L and J are still critical activities. B, and L should be
considered for crashing
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 27
Activity
Crash
Days
by Cost of crashing per
day
B
2
1500
L
3
350
• Activity L is the cheapest to crash. Crash L by 3 days.
• Recompute the timings and identify the critical path.
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 28
Total cost Rs 45900
Direct cost Rs 30900
Indirect cost Rs 15000
A
4
19
2
4
F12
15
0
5
27
6
B
8
3
8
0
G
10
7
E
7
C
3
D
8
1
Cost reduced by Rs 1250
Time reduced by 6 days
4
18
6
I
9
H
18
10
18
26
L
K
9
30
7
8
J
8
4
30
9
18
26
B, G, L and J are still critical activities. B should be
considered for crashing
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 29
Activity
B
Crash
Days
2
by Cost of crashing per
day
1500
• Crash activity B by 2 days
• Recompute the timings and identify the critical path.
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 30
Total cost Rs 47900
Direct cost Rs 33900
Indirect cost Rs 14000
A
4
19
2
4
F12
15
0
5
27
6
B
6
3
6
0
G
10
7
E
7
C
3
D
6
1
Cost increased by Rs 750
Time reduced by 8 days
4
16
6
I
9
H
16
10
16
24
L
K
9
28
7
8
J
8
4
28
7
16
24 Even if we
B, G, L, J, E and K are now critical activities.
crash E or K the duration on path B – G – L – J cannot be
reduced any further. No further crashing is necessary
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 31
Activity
Crashed
Crashed by
(Days)
Duration of
Project
Direct
Costs
Indirect
Costs
Total
Cost
Normal
-
36
29150
18000
47150
G
2
34
29550
17000
46550
J
1
33
29850
16500
46350
L
3
30
30900
15000
45950
B
2
28
33900
14000
47900
• The project can be completed in 30 days at a least
cost of Rs 45950.
• The minimum time required to complete the project is
28 days at a cost of Rs 47900
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 32
Resource Levelling
• All activities can start at the earliest time only
if there are enough resources to perform all
the work defined by the activities.
• Often this may not be the case. It may also
not be possible to follow a policy of ‘hire and
fire’ always.
• A reasonably steady level of resources
throughout the project duration can be
achieved by adjusting the start time of
activities which have float available in them.
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 33
Resource Levelling - Example
Activity
Preceded By
Duration
Manpower
Required
A
Start
3
3
B
Start
2
2
C
B
2
3
D
A
4
2
E
B
3
3
F
D, C
3
3
G
F, E, Finish
4
3
H
Start, Finish
8
1
I
D, C
6
2
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 34
• Draw the network. Calculate EST and LFT.
Identify critical activities.
3
A
3
7
D
4
2
C
2
2
3
0
1
B
2
0
3
5
7
I
6
4
F
3
10
E
3
5
10
14
G
4
6
14
H
8
A, D, F and G are critical activities.
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 35
• Make a table, listing the activities in the descending order of their latest finish
times.
• Plot the activities on a time graph
Activ EST
-ity
LFT
Days
Men
A
0
3
3
3
B
0
5
2
2
C
2
7
2
3
D
3
7
4
2
E
2
10
3
3
F
7
10
3
3
G
10
14
4
3
H
0
14
8
1
I
7
14
6
2
1 2
3
4 5 6 7 8
9 10
11
12
13
14
• Red lines indicate critical activities schedule
• Green lines indicate schedule of other activities if started
earliest
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 36
Plot labour requirements on a time graph.
Activ EST
-ity
LFT
Days
Men
A
0
3
3
3
B
0
5
2
2
C
2
7
2
3
D
3
7
4
2
E
2
10
3
3
F
7
10
3
3
G
10
14
4
3
H
0
14
8
1
I
7
14
6
2
1 2
3
4 5 6 7 8
9 10
11
12
13
14
•
Red line shows labour
10
required for critical activities
• Green line indicates
requirements if all activities are 5
started earliest
• Blue shows levelled resources.
1
E and H are started later.
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Labour
Page 37
PERT Network
• PERT – Programme Evaluation and Review
Technique – is used in probabilistic situations
when the duration of activities is not known
with certainty.
• Three time estimates are used for activity
duration – pessimistic time, optimistic time
and most likely time.
• Mean time for each activity is calculated.
• Network is drawn as for CPM with mean
times as activity durations
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 38
PERT Network
• Critical activities are identified.
• Standard deviation on the critical path is
calculated.
• Using the standard deviation and the
mean and assuming normal distribution,
project duration with different levels of
confidence or vice versa can be
computed.
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 39
PERT - Network
•
•
M e a n T im e 
to  4tm  t p
6
S ta n d a rd D e v ia tio n 
t p  to
6
• Standard deviation cannot be added. Variance can
be added. Standard deviation on the critical path is

Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
 S D A    S D B   ...
2
2

Page 40
PERT - Example
Activity
Predecessor
Optimistic Time
(to)
Most likely
Time (tm)
Pessimistic
Time (tp)
A
-
1
2
3
B
-
1
2
3
C
-
1
2
3
D
A
1
2
9
E
A
2
3
10
F
B
3
6
15
G
B
2
5
14
H
D, E
1
4
7
J
C
4
9
20
K
J, G
1
2
9
L
H, F, K,
Finish
4
4
4
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 41
Solution
Activity
Optimistic
Time (to)
Most
likely
Time (tm)
Pessimistic
Time (tp)
Mean
Time
Standard
Deviation
A
1
2
3
2
0.33
B
1
2
3
2
0.33
C
1
2
3
2
0.33
D
1
2
9
3
1.33
E
2
3
10
4
1.33
F
3
6
15
7
2.00
G
2
5
14
6
2.00
H
1
4
7
4
1.00
J
4
9
20
10
2.67
K
1
2
9
3
1.33
L
4
4
4
4
0
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 42
• Draw the network and find critical activities
2
A
2
5
D
3
5
E
4
2
1
1 6
6
7
0
1
1
1
2
B
2
G
6
6
C
2
2
4
2
15
F
7
3
0
H
4
J
10
8
12
7
K
3
1
5
19
L
4
9
1
9
1
Critical2
C, J, K and L are critical activities.
path is 1 – 4 – 7 – 8 – 9
Project will be completed in 19 days or less with 50% confidence.
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 43
Activity
Optimistic
Time (to)
Most
likely
Time (tm)
Pessimistic
Time (tp)
Mean
Time
Standard
Deviation
C
1
2
3
2
0.33
J
4
9
20
10
2.67
K
1
2
9
3
1.33
L
4
4
4
4
0
S. D. 

 
  0 .3 3 
 S DC
2
2
 S DJ

 S DK
2

2
 S DL 
  2 .6 7    1 .3 3    0 
2
2
2
2


3
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 44
• With 84% level of confidence how much time would the
project take?
• PERT assumes that the distribution of the total project
completion time is normal. 84% represents Mean + 1
standard deviation. We can say with 84% level of
confidence that the project will finish in 22 weeks.
• What are the chances that the project will finish in 20
weeks?
z 

x
0.33 SD

20  19
 0.33
3
19 20
From normal distribution tables the probability when z =0.33 is 0.6290.
There is a 63% chance that the project will finish in 20 weeks.
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 45
Differences – PERT and CPM
• PERT is a probabilistic model and is based on three
time estimates. It is used mainly for projects where
the activity durations are uncertain, like research and
development projects. Levels of confidence and
probabilities can be associated with the completion
date of a project.
• CPM is based on certainty of the activity durations. It
is used for projects where there is certainty about the
time that each activity would take. The project
completion duration is not probabilistic but is certain.
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 46
Summary
• PERT and CPM are network analysis techniques that
help in planning, monitoring and controlling projects.
• PERT is a probabilistic model and deals with the
uncertainty of activity durations. It is based on three
time estimates – optimistic time, most likely time and
pessimistic time.
• CPM is a deterministic technique and activity duration
is known with certainty.
• Critical activities have no time slacks and it is vital
that they completed as per schedule, else the project
will be delayed causing time and cost over runs.
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 47
Summary
• Management should monitor the critical activities
closely in order to ensure timely completion of
projects.
• The slacks of time available in activities are called
floats. These are used for levelling resources.
• A time cost trade off can be calculated for a network
by crashing critical activities.
• Networks are a useful tool only if they are regularly
updated.
• Computer software packages exist that update and
redraw the network once the progress on the
activities is fed in.
Quantitative Techniques for Decision Making
M.P. Gupta & R.B. Khanna
© Prentice Hall India
Page 48