Pert Network

8/11/2019 Pert Network

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PERT NETWORK


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CPM : CRITICAL PATH METHOD

PERT : USED FOR PROJECT PLANNING & MONITORING

GANTT CHART

EVENT

ACTIVITY

NETWORK

AOAACTIVITY ON ARROW

AONACTIVITY ON NODE

SLACK/FLOAT

CRITICAL PATH

t= Duration of activity

1 2

EF = ES + t LF = LS + t

LS = LFt Slack = LSES or LF - EF

ES LS EF LF


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EXPECTED COMPLETION TIME =+4+

6

STANDARD DEVIATION, = [ (b a)/6]2

NETWORK CONVENTION :

1. AOAACTIVITY ON ARROW

2

1 43

2. AON - ACTIVITY ON NODE

B

A

C

D


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RULES FOR COMPUTING EF(EARLIEST FINISH TIME) & LF(LATEST FINISH

TIME) IN NETWORK :

1.MOVING FORWARD FIND EF TIME (CHOOSING THE MAXIMUM AT ACTIVITY

INTERSECTION.

2.AT LAST NODE, MAXIMUM EF = LF

3.USE RETURN PATH TO FIND LF (CHOOSING MINIMUM AT EVERY

INTERSECTION.


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b

Problem 1. Project with following data are to be completed. Draw the network

and critical path.

(a)What is the minimum duration of the project?

(b)Draw the Gantt Chart for early start schedule

(c) Determine the peak requirement of money and day on which it occurs in

above schedule

ACTIVITY PREDECE-

SSORS

DURATION

(DAYS)

COST

(RS/DAY)

A - 2 50

B - 4 50

C A 1 40D B 2 100

E A,B 3 100

F E 2 60


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EF LF

EF LF

EF LF C=1

A=2 EF LF

t=0 E=3 F=2

B=4

D=2

EF LF

EF LF

4 4

7 7

1

3

4

5

2

0 0

9 9

4 4


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Activity Duration(t)

EF ES =

EF - t

LF LS =

LF - t

Event

Slack =

LSES

or

LF - EF

On

critical

path

A 2 2 0 4 2 2 No

B 4 4 0 4 0 0 Yes

C 1 5 4 9 8 4 No

D 2 6 4 9 7 3 No

E 3 7 4 7 4 0 Yes

F 2 9 7 9 7 0 Yes


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(c)

Peak requirement of money on 5thand 6thday for Rs.200/- Ans.

Day Activity Requirement of money(Rupees)

1 A + B 50 +50=100

2 A + B 50 + 50=100

3 B + C 50 + 40=90

4 B 50

5 D + E 100+100=200

6 D + E 100 + 100=200

7 E 100

8 F 60

9 F 60


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#2 (a)Draw the network using AON system and find critical path for the

project.

Activity Designation Predecessor Time in weeks

Design A - 21

Built prototype B A 5

Evaluate C A 7

Test prototype D B 2

Write

equipment

report

E C,D 5

Write method

report

F C,D 8

Write final

report

G E,F 2


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(b)Using 3 time estimates of activities, find probability of completing project

in 35 weeks.

Activity Time estimation

a=Most

optimistic time

b=Pessimistic

time

m=Most likely

time

A 10 12 28

B 4 4 10

C 4 6 14

D 1 2 3

E 1 5 9

F 7 8 9

G 2 2 2


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EF LF

EF LF

EF LF

EF LF

EF LF

EF LF

28 2836 36

38 38

33 36

28 28

26 26

21 21

A,21

C,7F,8

G,2

E,5D,2

B,5


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Activity Duration

(t)

EF ES=

EF - t

LF LS= LF -t Slack=

LS-ES

On

critical

pathA 21 21 O 21 0 0 Yes

B 5 26 21 26 21 0 Yes

C 7 28 21 28 21 0 Yes

D 2 28 26 28 26 0 Yes

E 5 33 28 36 31 3 No

F 8 36 28 36 28 0 Yes

G 2 38 36 38 36 0 Yes


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CRITICAL PATH :

THERE ARE TWO CRITICAL PATHS THROUGHOUT THE NETWORK :

ACFG and ABDFG

(b) Time Estimate

Activity a b m Expected

Project completion time

Te=(a+4m+b)/6

A 10 12 28 22.33B 4 4 10 8

C 4 6 14 11

D 1 2 3 2.5

E 1 5 9 7

F 7 8 9 8.16

G 2 2 2 2

Total expected completion time = 60.99 weeks


16/18

#3 A project has following time schedule :

(a)Construct a PERT network

(b) Compute critical path and its duration

(c) Total Float for each activity

Activity : 1-2 1-3 1-4 2-5 3-6 3-7 4-6 5-8 6-9 7-8 8-9Time

(Months)

2 2 1 4 8 5 3 1 5 4 3


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EF LF EF LF

4

1

ES LS 2 EF LF EF LF EF LF

2 5 4

1 8 3

EF LF EF LF EF LF

3 5

(a) PERT network is shown above

2 7 6 11

0 0 2 2 7 8 11 12

1 710 10 15 15

1

2

3

4

7

5

8

96


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(b & c) Critical path : 136 - 9 with duration of 15 months

Activity Duration EF ES=

EF - t

LF LS =

LF - t

Total

Float =

LF - EF

1-2 2 2 0 7 5 5

1-3 2 2 0 2 0 0

1-4 1 1 0 7 6 6

2-5 4 6 2 11 7 5

3-6 8 10 2 10 2 03-7 5 7 2 8 3 1

4-6 3 4 1 10 5 6

5-8 1 7 6 12 11 5

6-9 5 15 10 15 10 0

7-8 4 11 7 12 8 1

8-9 3 14 11 15 12 1

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