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Critical Path Method
1. Chapter –6
Critical 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
2. Content…
•Introduction to CPM
•Difference between CPM and PERT
•Terms and Definitions
•Calculation of Float
•Critical Path
3. 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.
4. Difference between CPM and PERT
CPM
PERT
Activity Oriented network
Event oriented network
The time estimatesare of a fair degree of accuracy
Time estimates are not that accurate andthere is an uncertainty attached to it
Follows deterministic approach
Followsprobabilistic approach
Cost is governingfactor
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 thatpath which joins the critical activities
Criticalpath is the path which joins the critical events
5. 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= TEi + tEij
6. 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= TLj -tEij
7. 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
8. 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
9. 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 –TEj
10. 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–TEi
11. 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 –TEj = 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
12. 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
13. 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
14. 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
15. 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
16. CPM Analysis
F
1
2
4
3
5
6
7
8
A
B
C
D
E
H
K
J
I
10
8
12
8
10
6
5
12
6
12
8
Aprojectconsistsof11activities,representedbythe
networkshownbelowinfigureandalsothenormal
durationsrequiredtoperformvariousactivitiesofthe
projectaregiveninnetwork.Compute(a)Eventtimes
(b)activitytimesandtotalfloat.Alsodetermine
thecriticalpath.
17. a. Computation of Event times Event No. PredecessorSuccessorEventEvent12345678Earliest Expected Time (↓ )Latest occurrence Time ( ↑ ) tETETE (Max)tETLTL (Min)
18. b. Computation of activity times and floats
Activity
Duration
Earliest (Units)
Latest (Units)
Total Float
Free Float
Independent 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
19. 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
E
H
K
J
I
10
8
12
8
10
6
5
12
6
12
8
20. Problem –2
F
1
2
4
3
5
6
7
8
A
B
G
E
D
I
L
J
5
4
4
6
2
6
7
8
0
6
7
C
K
3
Networkshownbelowinfigureandalsothenormaldurationsrequiredtoperformvariousactivitiesoftheprojectaregiveninnetwork.Compute(a)Eventtimes(b) activitytimes(c)totalfloatforeachactivityandestablishthecriticalpath.Alsodeterminethefreefloatandindependentfloat.
21. Problem –2
1
2
3
6
4
5
A
B
E
D
G
H
3
5
3
1
14
4
C
F
4
Networkshownbelowinfigureandalsothenormaldurationsrequiredtoperformvariousactivitiesoftheprojectaregiveninnetwork.Compute(a)Eventtimes(b) activitytimes(c)totalfloatforeachactivityandestablishthecriticalpath.Alsodeterminethefreefloatandindependentfloat.
6
1
I