Cpm
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SEMINOR ON CRITICAL PATH METHOD FOR PROJECT MANAGEMENT Presentation By GANGADHAR JADI (07IM6008)
CONTENTS:CONTENTS INTRODUCTION. STEPS IN CRITICAL PATH METHOD. NETWORK REPRSENTATION. NUMBERING OF EVENTS. TIME ANALYSIS. SLACK. DRAWING OF CRITICAL PATH. EXAMPLE . CONCLUSION. REFERENCES .
INTRODUCTION:A project defines a combination of interrelated activities which must be executed in a certain order before the entire task can be completed. the activities are interrelated in a logical sequence. it is essential to manage effectively the project through proper planning ,scheduling ,and control. network scheduling is a technique used for planning and scheduling large projects. CPM, PERT are the basic planning and control techniques.
STEPS IN CRITICAL PATH METHOD:Planning. Scheduling. Controlling.
NETWORK REPRESENTATION:
(A) ACTIVITY:- An activity is a physically identifiable part of the project.
Tail
Head
NETWORK REPRESENTATI0N (condt….)
(B) EVENT:- An event represents the start or the completion of an activity. EVENT ACTIVITY
BRUST EVENT MERGE EVENT
NETWORK REPRESENTATI0N (condt….)
(C) PREDECESSOR AND SUCCESSOR ACTIVITIES: Predecessor activity: Activities that must be completed immediately before the start of another activity. Successor activities: activities which have to follow the activity under consideration.
NETWORK REPRESENTATI0N (condt….)
D
B A
F C
E
NETWORK REPRESENTATI0N (condt….)
(D) DUMMY ACTIVITY: An activity depicts the dependency or relationship over the other but does not consume the time or resource. C
A A B
C D
O B
D
NETWORK REPRESENTATI0N (condt….) (E)Numbering of events(Fulkerson I-J rule): The Initial event which has all outgoing arrows no incoming arrow is numbered 1 Delete the all arrows coming out from one node this will converts some more nodes into initial events number 2,3…….
NETWORK REPRESENTATI0N (contd….)
Numbering of events 3
B 1
A
2
D 5
C
E 4
F
6
TIME ANALYSIS IN CRITICAL PATH METHOD:The time analysis in network is done for:
Determine the completion time of project Earliest time when each activity can start Latest time when each activity can start without delaying the total project Determining slack for each activity Identification of critical activities and critical path
TIME ANALYSIS IN CRITICAL PATH METHOD(CONTD….) Forward pass computations (earliest event time): Earliest occurrence Ei=earliest time of event I time for each event (Es)ij=earliest starting time of activity i,j Step1: the computations begins from start node Dij=duration time of activity i,j and move towards the end node. Assume (Ef)ij=earliest finish time of activity i,j earliest occurrence time for initial event is Ej=earliest time of event j zero Step2:(Es)ij=Ei (Ef)ij=Ei+Dij Ej=max(Ei+Dij)
TIME ANALYSIS IN CRITICAL PATH METHOD (Contd….) Backward pass computation (latest event time): Latest event time indicates the time by which all activities (Lj)=Latest time of event entering into that event j must be completed without delaying the total (Lf)ij= Latest finish time of activity I,j project completion time (Ls)ij= Latest starting Step1:for ending event assume E=L time of activity I,j Step2:(Lf)ij=Lj (Li)= Latest time of Step3:(Ls)ij=Lj-Dij event i Step4:(Li)=min((Lf)ij-Dij)
SLACK:
Slack of an event is difference between the latest time and earliest time of an event slack=Li-Ei (for tail event) slack=Lj-Ej (for head event)
DRAWING OF CRITICAL PATH:
Draw the path which is connected all the zero slack events. The activities in the critical path is critical activities. Delay in the critical activity affect the total completion time of the project.
EXAMPLE:Activity A B C D E F G
Predecessors Duration(Weeks) _ 4 A 3 A 2 B 5 B 3 C,D 4 E,F 3
Example (contd…..) Network diagram: 3
B 1 0 o
A 4
2 4 4
7 7 3
C 2
D 5 D1 4 6 12
E 3 6 12 12
5 10 16 D2
F 4
7
8 G 16 16 3 19 19
Example (contd…..) Computation of slack:
activity duration Es Ef A B C D E F G
4 3 2 5 3 4 3
0 4 4 7 7 12 16
4 7 6 12 12 16 19
Ls
Lf
slack
0 4 10 7 13 12 16
4 7 12 12 16 16 19
0 0 6 0 6 0 0
Example (contd…..) Critical path: 3
B 1 0 0
A 4
2 4 4
7 7 3
C 2
Critical path: A-B-D-F-G
D 5
E 3 6 12 12
4 6 12
D1
5 10 16
F 4
D2 7
8 G 16 16 3 19 19
CONCLUSION:
Graphically displays project activities Estimates how long the project will take Indicates most critical activities Show where delays will not affect project
REFERENCES:
S.D.SHARMA ”Operations research” Kedar Nath Ram Nath&co,meerut,2006,pp-316-329. MARTAND TELSANG” Industrial engineering and production management” S.Chand, 2005, pp-285292. A.TAHA ”Operations Research” Macmillan Publishing co.,1982,pp-458-468. http://en.wikipedia.org/wiki/Critical_path._28_Aug07 .
THANK YOU…
CONTENTS:CONTENTS INTRODUCTION. STEPS IN CRITICAL PATH METHOD. NETWORK REPRSENTATION. NUMBERING OF EVENTS. TIME ANALYSIS. SLACK. DRAWING OF CRITICAL PATH. EXAMPLE . CONCLUSION. REFERENCES .
INTRODUCTION:A project defines a combination of interrelated activities which must be executed in a certain order before the entire task can be completed. the activities are interrelated in a logical sequence. it is essential to manage effectively the project through proper planning ,scheduling ,and control. network scheduling is a technique used for planning and scheduling large projects. CPM, PERT are the basic planning and control techniques.
STEPS IN CRITICAL PATH METHOD:Planning. Scheduling. Controlling.
NETWORK REPRESENTATION:
(A) ACTIVITY:- An activity is a physically identifiable part of the project.
Tail
Head
NETWORK REPRESENTATI0N (condt….)
(B) EVENT:- An event represents the start or the completion of an activity. EVENT ACTIVITY
BRUST EVENT MERGE EVENT
NETWORK REPRESENTATI0N (condt….)
(C) PREDECESSOR AND SUCCESSOR ACTIVITIES: Predecessor activity: Activities that must be completed immediately before the start of another activity. Successor activities: activities which have to follow the activity under consideration.
NETWORK REPRESENTATI0N (condt….)
D
B A
F C
E
NETWORK REPRESENTATI0N (condt….)
(D) DUMMY ACTIVITY: An activity depicts the dependency or relationship over the other but does not consume the time or resource. C
A A B
C D
O B
D
NETWORK REPRESENTATI0N (condt….) (E)Numbering of events(Fulkerson I-J rule): The Initial event which has all outgoing arrows no incoming arrow is numbered 1 Delete the all arrows coming out from one node this will converts some more nodes into initial events number 2,3…….
NETWORK REPRESENTATI0N (contd….)
Numbering of events 3
B 1
A
2
D 5
C
E 4
F
6
TIME ANALYSIS IN CRITICAL PATH METHOD:The time analysis in network is done for:
Determine the completion time of project Earliest time when each activity can start Latest time when each activity can start without delaying the total project Determining slack for each activity Identification of critical activities and critical path
TIME ANALYSIS IN CRITICAL PATH METHOD(CONTD….) Forward pass computations (earliest event time): Earliest occurrence Ei=earliest time of event I time for each event (Es)ij=earliest starting time of activity i,j Step1: the computations begins from start node Dij=duration time of activity i,j and move towards the end node. Assume (Ef)ij=earliest finish time of activity i,j earliest occurrence time for initial event is Ej=earliest time of event j zero Step2:(Es)ij=Ei (Ef)ij=Ei+Dij Ej=max(Ei+Dij)
TIME ANALYSIS IN CRITICAL PATH METHOD (Contd….) Backward pass computation (latest event time): Latest event time indicates the time by which all activities (Lj)=Latest time of event entering into that event j must be completed without delaying the total (Lf)ij= Latest finish time of activity I,j project completion time (Ls)ij= Latest starting Step1:for ending event assume E=L time of activity I,j Step2:(Lf)ij=Lj (Li)= Latest time of Step3:(Ls)ij=Lj-Dij event i Step4:(Li)=min((Lf)ij-Dij)
SLACK:
Slack of an event is difference between the latest time and earliest time of an event slack=Li-Ei (for tail event) slack=Lj-Ej (for head event)
DRAWING OF CRITICAL PATH:
Draw the path which is connected all the zero slack events. The activities in the critical path is critical activities. Delay in the critical activity affect the total completion time of the project.
EXAMPLE:Activity A B C D E F G
Predecessors Duration(Weeks) _ 4 A 3 A 2 B 5 B 3 C,D 4 E,F 3
Example (contd…..) Network diagram: 3
B 1 0 o
A 4
2 4 4
7 7 3
C 2
D 5 D1 4 6 12
E 3 6 12 12
5 10 16 D2
F 4
7
8 G 16 16 3 19 19
Example (contd…..) Computation of slack:
activity duration Es Ef A B C D E F G
4 3 2 5 3 4 3
0 4 4 7 7 12 16
4 7 6 12 12 16 19
Ls
Lf
slack
0 4 10 7 13 12 16
4 7 12 12 16 16 19
0 0 6 0 6 0 0
Example (contd…..) Critical path: 3
B 1 0 0
A 4
2 4 4
7 7 3
C 2
Critical path: A-B-D-F-G
D 5
E 3 6 12 12
4 6 12
D1
5 10 16
F 4
D2 7
8 G 16 16 3 19 19
CONCLUSION:
Graphically displays project activities Estimates how long the project will take Indicates most critical activities Show where delays will not affect project
REFERENCES:
S.D.SHARMA ”Operations research” Kedar Nath Ram Nath&co,meerut,2006,pp-316-329. MARTAND TELSANG” Industrial engineering and production management” S.Chand, 2005, pp-285292. A.TAHA ”Operations Research” Macmillan Publishing co.,1982,pp-458-468. http://en.wikipedia.org/wiki/Critical_path._28_Aug07 .
THANK YOU…
