PERT:Programme Evaluation and Review Technique”. and CPM

PERT:Programme Evaluation and Review Technique”.

And

CPM : Critical Path Method

PERT was developed by US Navy Engineers to plan and control the huge Polaris Submarine Programme. AND Du Pont and Remington Rand Companies CPM to help the process of scheduling

1.When is each individual phase of the project scheduled to start and finish?

2.How soon will the project be completed?

3.Which are the independent activities?

4.Which are inter-related activities?

5.What is total project time?

PERT AND CPM ????

7.Which are the critical phases of the project to be finished on time and required close managerial attention to avoid delay?

8.Can project time be curtailed?

9.At what cost?

10.Can resources reduced and then the cost?

6.What are different resources required for completion of the project?

2 TERMINOLOGY USED IN PERT AND CPM

ACTIVITY :

At HEAD / RHSTAIL / LHS

TYPES

1. PARALLEL / CONCURRENT / INDEPENDENT ACTIVITY

2, PRECEEDING ACTIVITY

3.SUCCEEDING ACTIVITY

CONSUME RESOURCES AND TIME

EVENT / NODE

DO NOT CONSUME RESOUCES AND TIME

2

AB

C

DE

F

BURSTING EVENT

MERGING EVENT

4

Rules of Network Construction

1.In network diagram, arrows represent activities and circles (or nodes) the events. The length of an arrow is of no significance.

2.Each activity must start and end in a node The tail of an activity represents the start and head, the completion of work.

3.The event numbered 0 or 1 denotes start of the project and is acted initial node (or event). All activities emerging (or taking off) from event 1 should not be preceded by any other activity or activities Events carrying the highest number denote the completion event.

4.Events should be numbered such that for each activity (i, J), i < j

5.An event number should not get repeated or duplicated,

6.The same starting and completion events should not identify two activities.

7.The logical sequence (or inter relationship) between activities must follow the following rules:

i)An event cannot occur until all the incoming activities into it have been completed.

ii)An activity cannot start unless all the proceeding activities, on which it depends, have been completed.

DUMMY ACTIVITY

1 2

A

B

NOT ALLOWED

LOOP / LOOPING

Though a dummy activity does not consume either resources or time, even then it has to follow the rules (1) and 7(ii).

Activity Immediate Predecessors

A -

B -

C A

D A

E C, B

Activity Immediate Predecessors

A -

B -

C A

D B

Activity Immediate Predecessors

A -

B -

C A

D B

E C, D

F D

G E

H F

1

2

3

5

4

6

7

8

A

B

C

D

E

F

G

H

Dummy Activity

Beginning Event

Ending Event Activity

1 2 1-2

1 3 1-3

2 4 2-4

3 4 3-4

3 5 3-5

4 6 4-6

5 6 5-6

Q1.Draw the network for the following activities.

Acitivity Duration( Days)

1-2 20

1-3 25

2-3 10

2-4 12

3-4 5

4-5 10

Activity Time Activity Time

1-2 4 5-6 4

1-3 1 5-7 8

2-4 1 6-8 1

3-4 1 7-8 2

3-5 6 8-10 5

4-9 5 9-10 7

Q2.Draw the network for the following activities.

Acitivity Duration( Days)

1-2 13

2-3 8

3-4 10

3-5 11

4-6

9

5-6 10

5-7 6

6-8 8

7-8 7

8-9 14

9-10 18

Q3.Draw the network for the following activities.

Activity Duration

1-2 10

1-3 4

1-4 6

2-3 5

2-5 12

2-6 9

3-7 12

4-5 15

5-6 6

6-7 5

6-8 4

Activity Predecessor Activity

A Open work order None

B Get material for a A

C Get material for B A

D Turn A on lathe B

E Turn B on lathe B, C

F Polish B E

G Assemble A and B D, F

H pack G

An assembly is to be made from two parts A and B. Both parts must be turned on a lathe and B must be polished whereas, A need not be polished The sequence of activities together with their predecessors is given below. Construct a PERT diagram.

Optimistic Time (a)– The shortest possible time for completion of activity is called as Optimistic time. This is represented as ‘a’.

Pessimistic Time (b) – The longest of maximum possible time for completion of an activity is called as Pessimistic time and denoted as ‘b’.

Most likely Time (m) - If the same activity is done repeatedly then the most repeated time taken to complete the activity is called as Most likely time and it is denoted by ‘m’.

TIME ESTIMATES

Expected Time (te) - This is practical workable time for completion of a activity & calculated as:

a + 4m + b te = -------------------

6

VARIANCES OF ACTIVITIES ON CRITICAL PATH

=

CRITICAL PATH

THE LONGEST TIME PATH THROUGH A NETWORK IS CALLED THE CRITCAL PATH.IT IS DENOTED BY DOUBLE LINES IN THE NETWORK.

1.IDENTIFIES SET OF ACTIVITIES AND EVENTS WHICH ARE CRITICAL AND HENCE NEED TO CONTROLL AND MONITOR.

2.TO SHRTEN PROJECT TIME,SOME OF THE ACTIVITIES ON THE CRITICAL PATH MUST BE SHORTENED.

3.CRITICAL PATH IDENTIFIES ACTIVIES FOR PREFERNCES IN RESOURCE ALLOCATION.

4.CRITICAL PATH IMPLIES “CONTROL BY EXCEPTION”

Esj = Efj + tij

Forward pass computation:

BACKWARD PASS COMPUTATION

Efi = Efj – tis

EARLIST START ( Es ) AND FINISH TIMES (Ef)

LET ZERO BE THE STRATING TIME FOR THE PROJECT.THEN THIS WILL BE THE EARLIEST START TIME,Es,FOR THIS ACTIVITY.

GIVEN Es FOR AN ACTIVITY,THE EARLIST FINISH TIME. Ef, OF THAT ACTIVITY IS Es PLUS THE ACTIVITY TIME t.

Ef = Es + t

LATEST START ( Ls ) AND FINISH TIMES (Lf)

SUPPOSE A TARGET TIME IS GIVEN FOR COMPLETING A PROJECT THEN THIS TIME IS CALLED THE LATEST FINISH TIME (Lf) FOR THE FINAL ACTIVITY.

THE LATEST START TIME (Ls) IS THE LATEST TIME AT WHICH AN ACTIVITY CAN START IF THE TARGET IS TO BE MAINTAINED.

Ls = Lf - t

FOR CRITICAL PATH

Es = Ef

a) Draw networkb) Calculate expected time of each activityc) Identify Critical Pathd) State Project Duratione)Find variances of activities on critical path and its standard deviation

Activity Optimistic Most Likely Pessimistic

1-2 6 7 8

1-3 4 5 12

1-4 2 10 12

2-5 3 7 11

3-6 10 20 48

3-7 6 9 18

4-6 3 3 9

5-8 3 3 9

6-9 8 18 40

7-8 2 6 10

8-9 2 5 14

a) Draw networkb) Calculate expected time of each activityc) Identify Critical Pathd) State Project Duratione)Find variances of activities on critical path and its standard deviation

ActivityOptimistic Most Likely Pessimistic

1-2 2 5 8

1-3 4 10 16

1-4 1 7 13

2-5 5 8 11

3-5 2 8 14

4-6 6 9 12

5-6 4 7 10

a) Draw networkb) Calculate expected time of each activityc) Identify Critical Pathd) State Project Duration

Activity Optimistic Most Likely Pessimistic

1-2 2 5 8

1-3 6 6 6

1-4 1 7 13

2-5 3 9 13

3-5 2 8 14

4-6 6 9 12

5-6 4 7 10

Activity Predecessor activity Time (weeks)A - 2B - 6

C - 4D A 6E B 8F C 7