Chapter – 6Critical Path Method (CPM)
Course Code - CIE 403
Mr. Ramesh Nayaka, (M.Tech. – IIT Madras)
Assistant Professor
Department of Civil Engineering
Manipal Institute of Technology, Manipal - 576104
Karnataka, India
Content…
• Introduction to CPM
• Difference between CPM and PERT
• Terms and Definitions
• Calculation of Float
• Critical Path
Introduction to CPM
CPM network are usually used for repetitive type of projects,
where fairly accurate estimates of time can be made for the
activities of the project.
The activities of these projects are characteristically subject
to relatively small amount of variation. Hence CPM is not
suitable for research and development type of projects.
Examples from fairly diverse field where application of CPM
can be made:
Building a new bridge across river ganga, Constructing a
multi-storeyed building, extension of a factory building, shifting a
manufacturing unit to other site and manufacturing of a new car
etc.
Difference between CPM and PERT
CPM PERT
Activity Oriented network Event oriented network
The time estimates are of a fair
degree of accuracy
Time estimates are not that
accurate and there is an
uncertainty attached to it
Follows deterministic approach Follows probabilistic approach
Cost is governing factor Time is governing factor
Project duration is so fixed such
that the cost is minimum
Assumed that cost is directly
proportional to time so time is
reduced maximum possible to
enjoy least cost
Critical path is that path which
joins the critical activities
Critical path is the path which
joins the critical events
Terms and Definitions
Activity Times
Forward Passing :
Earliest Start Time (EST) : earliest time by which an
activity start
EST = earliest event time of tail event = TEi
Earliest Finish Time (EFT) : Earliest time by which an
activity can be completed
EFT = EST + tEij = TE
i + tEij
Terms and Definitions
Activity Times
Backward Passing :
Latest Finish Time (LFT) : latest time by which an activity
can completed without delaying the completion of the
project
LFT = Latest Finish Time of head event = TLj
Latest Start Time (LST) : latest time by which an activity
can start without delaying the completion of the project
LST = LFT - tEij = TL
j - tEij
Terms and Definitions
FLOATS
Similar to slack in PERT
Associated with activity times
Denotes flexibility range within which the activity start
and finish time may fluctuate without affecting the total
duration of the project
Terms and Definitions
TYPES OF FLOATS
Total Float (FT) : timespan by which starting or finishing
of an activity can be delayed without affecting the overall
completion time of the project.
It refers to the amount of time by which the completion of
activity could be delayed beyond earliest expected
completion time without affecting overall project duration
time
FT= LST – EST or LFT - EFT
Terms and Definitions
TYPES OF FLOATS
Free Float (FF) : duration by which an activity can be
delayed without delaying any other succeeding activity.
It refers to the amount of time by which the completion of
an activity can be delayed beyond the earliest finish time
without affecting the earliest start time of a subsequent
succeeding activity.
This float is concerned with the commencement of
subsequent activity
FF = FT – Sj , Sj= Slack of head event = TLj – TE
j
Terms and Definitions
TYPES OF FLOATS
Independent Float (FID): It is excess time available if the
preceding activity ends as late as possible and the
succeeding activity starts as early as possible
It is refers to that the amount of time by which the start of
an activity can be delayed, without affecting earliest start
time of any immediately following activities
This float concerned with prior and subsequent activities
FID= FF – Si
Si = slack of tail event =TLi– TE
i
Terms and Definitions
TYPES OF FLOATS
Interfering Float (FIT) : Another name for head event slack
(Sj), it is the difference between total float and free float
FIT = FT – FF = TLj – TE
j = Sj
Note : if the total float (FT) for any activity is zero then such
activity is called critical activity
Critical Activity : an activity is said to be critical, if a delay in
its start cause a further delay in the completion of the entire
project
Terms and Definitions
Critical Path : The sequence of critical activities in a network
which determines the duration of a project is called critical
path.
• It is the longest path in the network from the starting event to
the ending event
• For activities lies on critical path
EST =LST , EFT = LFT and EST –EFT = LST – LFT
Sub critical activity : When total float (FT ) is positive
Critical Activity :When total float (FT ) is zero
Super critical activity : When total float (FT ) is negative
Calculating Critical Path & Float for a
Network Diagram
Find out the length of all the paths in the
network diagram
The longest path is the critical path
Float = EF – LF = ES - LS
Terms and Definitions
Critical Path : The sequence of critical activities in a network
which determines the duration of a project is called critical
path.
• It is the longest path in the network from the starting event to
the ending event
• For activities lies on critical path
EST =LST , EFT = LFT and EST –EFT = LST – LFT
Sub critical activity : When total float (FT ) is positive
Critical Activity :When total float (FT ) is zero
Super critical activity : When total float (FT ) is negative
Terms and Definitions
Critical Path : The sequence of critical activities in a network
which determines the duration of a project is called critical
path.
• It is the longest path in the network from the starting event to
the ending event
• For activities lies on critical path
EST =LST , EFT = LFT and EST –EFT = LST – LFT
Sub critical activity : When total float (FT ) is positive
Critical Activity :When total float (FT ) is zero
Super critical activity : When total float (FT ) is negative
CPM Analysis
F
1
2
4
3
5
6
7 8
A
B
C
D
EH
K
J
I
10 8 12
8 10
6
5
126
12
8
A project consists of 11 activities, represented by the
network shown below in figure and also the normal
durations required to perform various activities of the
project are given in network. Compute (a) Event times
(b) activity times and total float. Also determine
the critical path.
a. Computation of Event times
Event
No.
PredecessorSucces
sor
Event Event
1
2
3
4
5
6
7
8
Earliest Expected Time (↓ ) Latest occurrence Time ( ↑ )
tE TE TE (Max) tE TL TL (Min)
b. Computation of activity times and floats
Activity Duration Earliest (Units) Latest (Units)Total
Float
Free
Float
Independe
nt Float
(i - j) tEij EST EFT LST LFT FT
FF FID
1 - 2
1 - 3
2 – 5
2 – 7
3 – 4
3 – 6
4 – 5
5 - 6
5 - 7
6 - 7
7 - 8
c. Location of Critical path
• 1- 3 – 4 – 5 – 6 – 7 = 52 units
F
1
2
4
3
5
6
7 8
A
B
C
D
EH
K
J
I
10 8 12
8 10
6
5
126
12
8
Problem – 2
F
1
2
4
3
5
6
7
8
A
B
G
E
D I L
J
54
4
6 2
6
7
8
0
6
7C
K
3
Network shown below in figure and also the normal
durations required to perform various activities of the
project are given in network. Compute (a) Event times (b)
activity times (c) total float for each activity and establish
the critical path. Also determine the free float and
independent float .
Problem – 2
1
2
3
6
4
5
A
B
E
D
G
H
3
5
3
114
4
C
F
4
Network shown below in figure and also the normal
durations required to perform various activities of the
project are given in network. Compute (a) Event times (b)
activity times (c) total float for each activity and establish
the critical path. Also determine the free float and
independent float .
6 1I