Cpm

SEMINORON

CRITICAL PATH METHOD FOR

PROJECT MANAGEMENT

Presentation ByGANGADHAR JADI

(07IM6008)

CONTENTS

INTRODUCTION.STEPS IN CRITICAL PATH METHOD. NETWORK REPRSENTATION.NUMBERING OF EVENTS.TIME ANALYSIS.SLACK.DRAWING OF CRITICAL PATH.EXAMPLE .CONCLUSION.REFERENCES .

CONTENTS:-

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.

EVENTACTIVITY

MERGE EVENT

BRUST EVENT

(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….)

A

B

C

D

E

F

NETWORK REPRESENTATI0N (condt….)

(D) DUMMY ACTIVITY: An activity depicts the dependency or relationship over the other but does not consume the time or resource.

A

B

C

D

A

B D

C

O

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 (condt….)

Numbering of events

4

2

3

651 A

B

C

D

E

F

NETWORK REPRESENTATI0N (contd….)

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….)

Earliest occurrence time for each event

Step1: the computations begins from start node and move towards the end node. Assume earliest occurrence time for initial event is zero

Step2:(Es)ij=Ei

(Ef)ij=Ei+Dij

Ej=max(Ei+Dij)

Ei=earliest time of event I(Es)ij=earliest starting

time of activity i,j Dij=duration time of

activity i,j(Ef)ij=earliest finish time

of activity i,jEj=earliest time of event j

Forward pass computations (earliest event time):

TIME ANALYSIS IN CRITICAL PATH METHOD (Contd….)

Latest event time indicates the time by which all activities entering into that event must be completed without delaying the total project completion time

Step1:for ending event assume E=L

Step2:(Lf)ij=Lj

Step3:(Ls)ij=Lj-Dij

Step4:(Li)=min((Lf)ij-Dij)

(Lj)=Latest time of event j

(Lf)ij= Latest finish time of activity I,j

(Ls)ij= Latest starting time of activity I,j

(Li)= Latest time of event i

Backward pass computation (latest event time):-

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 Predecessors Duration(Weeks)

A _ 4

B A 3

C A 2

D B 5

E B 3

F C,D 4

G E,F 3

A

B

C

D

F

E

G1 2

6

3

4

5

7 8

0 4

7

6

12

10

16 19 1916

7

12

12

16

44

3

2

5

3

4 3

Example (contd…..)

o

D2

D1

Network diagram:

Example (contd…..)

activity duration Es Ef Ls Lf slack

A 4 0 4 0 4 0

B 3 4 7 4 7 0

C 2 4 6 10 12 6

D 5 7 12 7 12 0

E 3 7 12 13 16 6

F 4 12 16 12 16 0

G 3 16 19 16 19 0

Computation of slack:

Critical path: A-B-D-F-G

A

B

C

DF

E

G1 2

6

3

4

5

7 8

0 4

7

6

12

10

16 19 1916

7

12

12

16

44

3

2

5

3

4 3

Example (contd…..)

0

D2

D1

Critical path:

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-285-292.

A.TAHA ”Operations Research” Macmillan Publishing co.,1982,pp-458-468.

http://en.wikipedia.org/wiki/Critical_path._28_Aug07.

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