Download ppt - Project scheduling and control with CPM & PERT

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LARGE SCALE PROJECTSProject scheduling and control with PERT / CPM

The best known and most widely used project scheduling and control method is called PERT, or Program Evaluation and ReviewTechnique. PERT is an analytical method which is designed to aid in the scheduling and control of complex projects which require that certain activities be performed in sequence .

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• PERT has been used for many kinds of construction activities, for building bridge and unusual buildings such as stadiums etc. Project planning method, also called network planning methods, were initially developed independently by two different groups.

• As an internal project for any companies , Critical Path Methods ( CPM ) were developed to plan and control the maintenance of chemical plant, assembly plant or any big projects.

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The immediate success of both the CPM and PERT methodologies may be gauged by the following facts. DuPont’s application of the CPM technique to a maintenance project works resulted in a resulted in a reduction in downtime for maintenance from 125 to 78 hours.

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The PERT technique was widely credited with helping to shorten by two years the time originally estimated for the completion of the engineering and development program.

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PERT and CPM are based substantially on the concepts. As originally developed, PERT was based on probabilistic estimates of activity times that resulted in a probabilistic path through a network of activities and a probabilistic project completion time.

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PERT CHARACTERISTICS AND DEFINITIONSACTIVIT

YAn activity is a part of the total work to be done; it consumes time and resources and has starting and ending points.

EVENT

An event is a “milestone”; it marks the beginning or the end of an activity. In drawing a PERT network, events are symbolized as circle or “nodes”. Events are also numbered, with those at the tail of an activity having lower numbers than events at the head of each activity arrow.

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Activity Time

PERT uses three estimates of the amount of time an activity might take to complete. These estimates are obtained from people who have knowledge about the work and how long it will probably take. They are:

Optimistic Time: The time the activity will take if everything goes well and no delays are encountered.

Or

The shortest time required for completion of the activity assuming that no hurdles or completions are encountered.

• The most likely time or Realistic Time: The time the activity will most likely take under normal conditions, allowing for usual delays.

OR• The time in which the activity is most likely to be

completed .This estimate takes into consideration normal circumstances, making allowance for some unforeseen delays.

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Pessimistic Time The time the activity may take if more than usual delays are encountered.ORThe longest time required to complete the activity assuming that unusual complications and /or unforseen difficulties would arise.PERT weights these three estimates to obtain an “expected time” for an activity by:

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Expected activity time

= Optimistic Time + ( 4 x Realistic Time ) + Pessimistic Time

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Thus if an activity in a PERT network for building a building were “pour the concrete foundation” and it had estimates of 2, 4, and 12 days, its expected duration would be:

2 =Optimistic time,4 =Realistic time and 12 =Pessimistic time

Expected activity time = 2 + (4x4) + 12 / 6 = 5 days.

FLOAT

• Activities that are not critical are called non-critical activities.

• These activities have a certain amount of spare time or float available.

• Thus, non critical activities can be delayed or advanced (depending on the extent of float availability)without affecting the overall completion date.

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• Earliest expected completion time of events (TE)

• Latest allowable time or latest finish time of events

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1 2 3 4 5 6 7 8 9 10Activity Immediate

Precedencerequirements

Event

Begin End

Opti-Mistictime

Real-Istictime

Pesi-Mistictime

Expected

time

Start

ES LS

Finish

EF LF

Totalslack

A None 1 2 3 4 5 4 0 0 4 4 0B A 2 3 4 7 10 7 4 16 11 23 12C B 3 7 2 7 12 7 11 23 18 30 12D A 2 4 3 5 13 6 4 19 10 25 15E D 4 7 1 5 9 5 10 25 15 30 15F A 2 5 7 8 21 10 4 4 14 14 0G F 5 6 1 7 7 6 14 14 20 20 0H G 6 7 --- --- --- --- 20 30 20 30 10I C, E, G 7 8 10 10 10 10 20 30 30 40 10J G 6 8 15 20 25 20 20 20 40 40 0K L, I, J 8 9 2 7 12 7 40 40 47 47 0L A 2 8 10 15 20 15 4 25 19 40 21

PERT data

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PERT DATA WITH EXPECTED TIME

(1)

Activity

(2) Immediate

precedence requirement

(3) Events

Begins End

(4) Optimistic time

(5) Realistic time

(6) Pessimistic time

(7) Expected time

(8)

Start

ES LS

(9)

Finish

EF LF

(10)

Total slack

A B C D E F G H I J K L

None A B A D A F G

CEG G LIJ

A

1 2 3 2 4 2 5 6 7 6 8 2

2 3 7 4 7 5 6 7 8 8 9 8

3 4 2 3 1 7 1 -- 10 15 2 10

4 7 7 5 5 8 7 --- 10 20 7 15

5 10 12 13 9 21 7 ---- 10 25 12 20Expected time

= Optimistic Time + ( 4 x Realistic Time ) + Pessimistic Time

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4 7 7 6 5 10 6 --- 10 20 7 15

4 7 7 6 5 10 6 --- 10 20 7 15

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PROJECT SCHEDULING

Data on the activities in the Print Project

ACTIVITY DESCRIPTION TIMEREQD.

PREDECESSORS

A Widen access door 3 -----B Build compressor housing 3 AC Remove old printing press 1 -----D Move other machines to create

more space2 C

E Re-lay concrete floor 8 A,DF Upgrade factory power supply 4 -----G Lay new electrical cabling 1 FH Update and adjust pre-press

equipment4 ----

I Operators go on training course 12 CJ Install new printing press 6 B,E,F,G,K Commission new press 4 H,I,J,

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NETWORK DIAGRAM FOR PRINTING PRESS PROJECT

Nodes with activity

0

A

C D

H

B

3

3

1

F

K

E

G

8

4

6

1

1

4

J

I12

86

6

2

6

4

4

4

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NETWORK DIAGRAM FOR PRINTING PRESS PROJECT

Priority activity

0

1

3 4

8

2

A3

B3

6

12

5

7

E8

F4

J6

C1

G1

H4

11

10I12

E8J6

J6

D2

J6

K4

K4

K4

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FLOW OF CALCULATION FOR EARLY START, ES, AND EARLY FINISH, EF, TIMES.

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EARLY FINISH

Priority Activities

0

1

3 4

8

2

A3

B3

6

12

5

7

E8

F4

J6

C1

G1

H4

11

10I12

E8 J6

J6

D2

J6

K4

K4

K4

40

84

30

10 31

113

113

63

131

1711

1713

126

40

54

104

115

2117

2121

EARLY START

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Precedence Chart Showing Activities Their Required Sequence, and Time Requirements for the New Product

Introduction ProjectActivityCode

Description ImmediateProcessor

Activity

Timeweeks

A Organize Sales Office ------ 6

B Hire Sales people A 4

C Train Sales People B 7

D Select advertising agency A 2

E Plan Advertising Campaign D 4

F Conduct Advertising Campaign E 10

G Design Package ---- 2H Set Up Packaging Facilities G 10

I Package initial Stocks H, J 6

J Order Stock from Manufacturer ---- 13

K Select Distributors A 9

L Sell Distributors C, K 3

M Ship Stock to Distributors I,L 5

Table

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Network Diagram for New Product Introduction Project

0

A

CB

6

47

D E

H

J

F

G

24 10

2

10

13

K

L

I

6

6

93

3

5

M

5

Nodes with activity

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Network Diagramming

A network is developed that takes account of the precedence relationships among the activities; it must be based on a complete, verified, and approved activity list.

The important information required for these network diagrams is generated by the following three questions:

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• Which activities must be completed before each activity can be started.

• Which activities can be carried out in parallel.

• Which activities immediately succeed other activities.

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ARCS NETWORK DIAGRAM FOR THE NEW PRODUCT INTRODUCTION PROJECT.

0 1

2

Start (0)A (6

)

3B (4) 4

C(7)

8D(2)

5

G(2)

6H(10)

J(13)

7

I(6)

K(9)L(3) 10

M(5)

9E(4)

F(10)

11FINISH(0)

Priority Activity

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FLOW OF CALCULATION FOR EARLY START, ES, AND EARLY FINISH, EF, TIMES.

0 1

2

Start (0)A (6

)

3

B (4)

4C(7)

8D(2)

5

G(2)

6H(10)

J(13) 7

I(6)

K(9)

L(3) 10M(5)

9E(4)

F(10)

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FINISH(0)00

20122

130 1913

60

86

128

2212

106 1710

156

2017

2520 2525

EARLY

0;00;0

EARLY

Priority Activities

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FLOW OF CALCULATION FOR LATE START, LS, AND LATE FINISH, LF, TIMES.

0 1

2

Start (0)A (6

)

3

B (4)

4C(7)

8D(2)

5

G(2)

6H(10)

J(13) 7

I(6)

K(9)

L(3) 10M(5)

9E(4)

F(10)

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FINISH(0)0;00;0

2;40;2

0;00;0

LATEEARLY

Start Finish

EARLY LATE

12;142;4

13;140;1

6;60;0

10;106;6

14;1410;10

8;116;9

12;158;11

15;176;8

22;2512;15

25;2525;25

20;2017;17

25;2520;20

19;2013;14

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PROJECT GRAPH OF ACTIVITIES ON NODES

A,6 B,4 C,7 L,3 M,5

K,9

D,2 E,4 F,10

J,13

G,2 H,10

I,6Finish,0

A,6

Critical Path

Activity Code

Time, Weeks

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1 2

3

4

7

5

6

89

A 4

B 7

C 7

D 6

E 5

F 10 G 6

H 0

I 10

J 20

K 7

PERT NETWORK WITH ACTIVITY TIME

Continue from slide # 38

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PERT data

(1)

Activity

(2) Immediate


(3) Events

Begins End

(4) Optimistic time

(5) Realistic time


(7) Expected time

(8)

Start

ES LS

(9)

Finish

EF LF

(10)

Total slack


None A B A D A F G

CEG G LIJ

A

1 2 3 2 4 2 5 6 7 6 8 2

2 3 7 4 7 5 6 7 8 8 9 8

3 4 2 3 1 7 1 -- 10 15 2 10

4 7 7 5 5 8 7 --- 10 20 7 15

5 10 12 13 9 21 7 ---- 10 25 12 20

4 7 7 6 5 10 6 --- 10 20 7 15

4 7 7 6 5 10 6 --- 10 20 7 15

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1 2

3

4

7

5

6

89

A 4

B 7

C 7

D 6

E 5

F 10 G 6

H 0

I 10

J 20

K 7

PERT NETWORK WITH EARLY START ( ES )

ES 0 ES 4

ES 11

ES1 0

ES 14

ES 20

ES 20

ES 40ES 47

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(1)

Activity

(2) Immediate


(3) Events

Begins End

(4) Optimistic time

(5) Realistic time


(7) Expected time

(8)

Start

ES LS

(9)

Finish

EF LF

(10)

Total slack


None A B A D A F G

CEG G LIJ

A

1 2 3 2 4 2 5 6 7 6 8 2

2 3 7 4 7 5 6 7 8 8 9 8

3 4 2 3 1 7 1 -- 10 15 2 10

4 7 7 5 5 8 7 --- 10 20 7 15

5 10 12 13 9 21 7 ---- 10 25 12 20

4 7 7 6 5 10 6 --- 10 20 7 15

ES0 4 11 4 10 4 14 20 20 20 40 4

PERT DATA WITH EARLY START ( ES )

0 4 11 4 10 4 14 20 20 20 40 4

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(1)

Activity

(2) Immediate


(3) Events

Begins End

(4) Optimistic time

(5) Realistic time


(7) Expected time

(8)

Start

ES LS

(9)

Finish

EF LF

(10)

Total slack


None A B A D A F G

CEG G LIJ

A

1 2 3 2 4 2 5 6 7 6 8 2

2 3 7 4 7 5 6 7 8 8 9 8

3 4 2 3 1 7 1 -- 10 15 2 10

4 7 7 5 5 8 7 --- 10 20 7 15

5 10 12 13 9 21 7 ---- 10 25 12 20

4 7 7 6 5 10 6 --- 10 20 7 15

ES0 4 11 4 10 4 14 20 20 20 40 4

PERT DATA WITH EARLY START / EARLY FINISH ( ES ) / (EF )

4 11 18 10 15 14 20 20 30 40 47 19

EARLY FINISH (EF) = ES + Expected time

4 7 7 6 5 10 6 --- 10 20 7 15

0 4 11 4 10 4 14 20 20 20 40 4

4 11 18 10 15 14 20 20 30 40 47 19

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1 2

3

4

7

5

6

89

A 4

B 7

C 7

D 6

E 5

F 10 G 6

H 0

I 10

J 20

K 74747

4040

30202311

2020

2510

1414

4 4

0 0

ES LF

PERT NETWORK WITH EARLY START / LATE FINISH ( ES ) / ( LF )

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(1)

Activity

(2) Immediate


(3) Events

Begins End

(4) Optimistic time

(5) Realistic time


(7) Expected time

(8)

Start

ES LS

(9)

Finish

EF LF

(10)

Total slack


None A B A D A F G

CEG G LIJ

A

1 2 3 2 4 2 5 6 7 6 8 2

2 3 7 4 7 5 6 7 8 8 9 8

3 4 2 3 1 7 1 -- 10 15 2 10

4 7 7 5 5 8 7 --- 10 20 7 15

5 10 12 13 9 21 7 ---- 10 25 12 20

4 7 7 6 5 10 6 --- 10 20 7 15

LF0 4 11 4 10 4 14 20 20 20 40 4

PERT DATA WITH EARLY START / EARLY FINISH LATE FINISH ( ES ) / (EF ) / ( LF )

LATE FINISH (LF) = From the end time

4 11 18 10 15 14 20 20 30 40 47 19

4 23 30 25 30 14 20 30 40 40 47 40

4 7 7 6 5 10 6 --- 10 20 7 15

0 4 11 4 10 4 14 20 20 20 40 4

4 11 18 10 15 14 20 20 30 40 47 19

4 23 30 25 30 14 20 30 40 40 47 40

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(1)

Activity

(2) Immediate


(3) Events

Begins End

(4) Optimistic time

(5) Realistic time


(7) Expected time

(8)

Start

ES LS

(9)

Finish

EF LF

(10)

Total slack


None A B A D A F G

CEG G LIJ

A

1 2 3 2 4 2 5 6 7 6 8 2

2 3 7 4 7 5 6 7 8 8 9 8

3 4 2 3 1 7 1 -- 10 15 2 10

4 7 7 5 5 8 7 --- 10 20 7 15

5 10 12 13 9 21 7 ---- 10 25 12 20

4 7 7 6 5 10 6 --- 10 20 7 15

0 4 11 4 10 4 14 20 20 20 40 4

PERT DATA WITH EARLY START / EARLY FINISH / LATE FINISH / TOTAL SLACK ( ES ) / (EF ) / ( LF ) ( TS)

Slack time = LF - Expected Time - ES

4 11 18 10 15 14 20 20 30 40 47 19

4 23 30 25 30 14 20 30 40 40 47 40

4 - 4 - 0 = 0 23- 7 - 4 = 12 30- 7-11 = 12

25-6-4 = 15

30-5-10 = 15 14-10-4 = 0 20-6-14 = 0 30-0-20 = 10

40-10-20 = 10 40-20-20 = 0 47-7-40 = 0 40-15-4 = 21

0 12 12 15 15 0 0 10 10 0 0 21

4 7 7 6 5 10 6 --- 10 20 7 15

0 4 11 4 10 4 14 20 20 20 40 4

4 11 18 10 15 14 20 20 30 40 47 19

4 23 30 25 30 14 20 30 40 40 47 40

0 12 12 15 15 0 0 10 10 0 0 21

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(1)

Activity

(2) Immediate


(3) Events

Begins End

(4) Optimistic time

(5) Realistic time


(7) Expected time

(8)

Start

ES LS

(9)

Finish

EF LF

(10)

Total slack


None A B A D A F G

CEG G LIJ

A

1 2 3 2 4 2 5 6 7 6 8 2

2 3 7 4 7 5 6 7 8 8 9 8

3 4 2 3 1 7 1 -- 10 15 2 10

4 7 7 5 5 8 7 --- 10 20 7 15

5 10 12 13 9 21 7 ---- 10 25 12 20

4 7 7 6 5 10 6 --- 10 20 7 15

0 4 11 4 10 4 14 20 20 20 40 4

PERT DATA WITH EARLY START / EARLY FINISH / LATE FINISH / TOTAL SLACK LATE START ( ES ) / (EF ) / ( LF ) / ( TS) / ( LS )

LATE START ( LS ) = Total Slack + ES

4 11 18 10 15 14 20 20 30 40 47 19

4 23 30 25 30 14 20 30 40 40 47 40

0 12 12 15 15 0 0 10 10 0 0 21

0 16 23 19 25 4 14 30 30 20 40 25

4 7 7 6 5 10 6 --- 10 20 7 15

0 4 11 4 10 4 14 20 20 20 40 4

4 11 18 10 15 14 20 20 30 40 47 19

4 23 30 25 30 14 20 30 40 40 47 40

0 12 12 15 15 0 0 10 10 0 0 21

0 16 23 19 25 4 14 30 30 20 40 25

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CRITICAL PATHThe critical path is the largest through the network.

1, 2, 8, 9 4 + 15 + 7 = 26

1, 2, 3, 7, 8, 9, 4 + 7 + 7 + 10 + 7 = 35

1, 2, 4, 7, 8, 9 4 + 6 + 5 + 10 + 7 = 32

1, 2, 5, 6, 7, 8, 9, 4 + 10 + 6 + 0 + 10 + 7 = 37

1, 2, 5, 6, 8, 9, 4 + 10 + 6 + 20 + 7 = 47

The critical path will be 1, 2, 5, 6, 8, 9 = 47

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1 2

3

4

7

5

6

89

A 4

B 7

C 7

D 6

E 5

F 10 G 6

H 0

I 10

J 20

K 74747

4040

30202311

2020

2510

1414

4 4

0 0

ES LF

CRITICAL PATH NETWORK

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EXAMPLE : In this example the finish-start (F-S) links have zero duration. A network will be developed for the project represented by the data in table:

Activity Duration (wks) Precursor activity (ies)A 4 ---B 3 ---C 6 A,BD 1 BE 7 DF 2 CG 5 C,E,H 8 EJ 4 GK 5 F,G,L 6 J,H,M 3 L,K,

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START

E

H FINISH

L M

J

F

G

KC

B

A

D

0 4 26

3

5

1

5

7

4

8 0

6 3

Duration

31

40

0 0

0 0START

4 11

E

11 19

H29 29FINISH

20 26

L26 29

M

16 20J

10 12

F

11 16

G

16 21

K4 10

C

0 3

B

0 4

+ A

3 4

D

0 4 26

3

5

1

5

7

4

8 0

6 3

Duration

Early Start

32

Early Finish

41

0 0

0 0START

4 11

4 11E

11 19

12 20 H

29 29

29 29FINISH

20 26

20 26L

26 29

26 29M

16 20

16 20J

10 12

19 21F

11 16

11 16G

16 21

21 26K

4 10

5 11C

0 3

0 3B

0 4

1 5 A

3 4

3 4D

0 4 26

3

5

1

5

7

4

8 0

6 3

Duration

Early Start

33

Early Finish

Late Start

Late Finish

42

Path with maximum duration or Critical Path Mean ( CPM )

Start + A+C+F+K+M = 4+6+2+5+3 = 20

Start + A+C+G+J+L+M = 4+6+5+4+6+3 = 28

Start + B+C+G+K+M = 3+6+5+5+3 = 22

Start + B+C+G+J+L+M = 3+6+5+4+6+3 = 27

Start + B+D+E+G+K+M = 3+1+7+5+5+3 = 24

Start + B+D+E+G+J+L+M = 3+1+7+5+4+6+3 = 29 ( CPM )

Start + B+D+E+H+L+M = 3+1+7+8+6+3 = 28

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0 0

0 0START

4 11

4 11E

11 19

12 20H 29 29

29 29FINISH

20 26

20 26L

26 29

26 29M

16 20

16 20J

10 12

19 21F

11 16

11 16G

16 21

21 26K

4 10

5 11C

0 3

0 3B

0 4

1 5 A

3 4

3 4D

0 4 26

3

5

1

5

7

4

80

6 3

Duration

Early Start

35

Early Finish

Late Start

Late Finish

44

Activity-on-node diagrams in which finish-to-start (F-S) links have duration's, and in which there are start-to-start (S-S) and finish-to-finish (F-F) links will now be considered.

The nature and duration of each links will be shown against each arrow. Showing in the figure illustrates the case in which activity F cannot start until one week after the finish to activity X, and activity C cannot commence until two weeks after the completion of activity F.

X0

F CF - S (1) F - S (2)

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EXAMPLE A project consists of activities A, B and C with links as shown in the tables

Activity DurationWeeks

PrecursorActivity

Link Type Link Duration

A 4 ------B 24 A F - S 0C 12 B S –S 6

F - F 3

0

A4

4

4

B28

24

10

C31

12

F - S (0)

S - S (6)

F - F (3)

Start for B (4) plus S - S(6) = 10

Finish for B(28) plus F-F(3)=31

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0

0 4A

4

4

4

4 28B

28

24

10

19 31C

31

12

F - S (0)

S - S (6)

F - F (3)

Block B and Block C are independent with Late finish and Late start

Late Finish

Late Start

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EXAMPLE A project data are given to find out all the respectful information for every individual block.

Activity Duration weeks Precursor activity Link type Link DurationA 4 ------ F--S 0B 3 ------ F--S 0C 6 A,B F--S 0D 1 B F--S 6E 12 D S--S 4F 2 C F--S 0G 5 E,F F--S 0H 8 E S--S 3

F--F 2J 4 G F--S 1K 5 F,G F--S 0L 6 J,K F--S 0M 3 L,K F--S 0

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START0

A4

C6

F2

K5

B3

G5

J4

M3

L6 E

12 D

1

S-S (4)

H8

S-S (3)

F-F (2)

F-S (1)

F-S (6)

FINISH0

49

PERT DATA WITH DURATION

ACTIVITY

DURATION(WEEK)

PRECURSORACTIVITY

ABCDEFGH

JKLM

4361

12258

4563

--------

A,B,BDC

E,F,E

GF,G,J,H,L,K,

ES LSSTART

EF LF

FINISH

SLACK

TOTAL

50

0 0

START0

0 4

A4

4 10

C6

10 12

F2

30 35

K5

0 3

B3

25 30

G5

31 35

J4

41 44

M3

35 41

L6

13 25

E129 10

D1

S-S (4)

16 27

H8

S-S (3)

F-F (2)

F-S (1)

F-S (6)

44 44

FINISH0

Early Start

EarlyFinish

51

PERT DATA WITH ES & EF

ACTIVITY

DURATION(WEEK)

PRECURSORACTIVITY

ABCDEFGH

JKLM

4361

12258

4563

--------

A,B,BDC

E,F,E

GF,G,J,H,L,K,

ES

0049

13102516

31302541

LSSTART

EF LF

FINISH

43

101025123027

35354144

SLACK

TOTAL

52

0 0

0 0START

0

0 4

13 17 A

4

4 10

17 23 C

6

10 12

23 25 F

2

30 35

36 41 K

5

0 3

0 3 B

3

25 30

25 30 G

5

31 35

31 35 J

4

41 44

41 44 M

3

35 41

35 41 L

613 25

13 25 E

129 10

9 10 D

1

S-S (4)

16 27

27 35 H

8

S-S (3)

F-F (2)

F-S (1)

F-S (6)

44 44

44 44FINISH

0

Late Start

LateFinish

53

PERT DATA WITH LS & LF

ACTIVITY

DURATION(WEEK)

PRECURSORACTIVITY

ABCDEFGH

JKLM

4361

12258

4563

--------

A,B,BDC

E,F,E

GF,G,J,H,L,K,

ES

0049

13102516

31302541

LSSTART

130

179

13232527

31363541

EF LF

FINISH

43

101025123027

35354144

173

231025253035

35414144

SLACK

TOTAL

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PERT DATA WITH TOTAL SLACK

ACTIVITY

DURATION(WEEK)

PRECURSORACTIVITY

ABCDEFGH

JKLM

4361

12258

4563

--------

A,B,BDC

E,F,E

GF,G,J,H,L,K,

ES

0049

13102516

31302541

LSSTART

130

179

13232527

31363541

EF LF

FINISH

43

101025123027

35354144

173

231025253035

35414144

SLACK

TOTAL

130

1300

130

11

06

100

Total Slack = LS - ES

55

A+C+F+K+M = 4+6+2+5+3 = 20

A+C+F+G+J+L+M =4+6+2+5+4+6+3 = 30

A+C+F+G+K+M = 4+6+2+5+5+3 = 25

B+C+F+K+M = 3+6+2+5+3 = 19

B+C+F+G+J+L+M = 3+6+2+5+4+6+3 = 29

B+C+F+G+K+M = 3+6+2+5+5+3 = 24

B+C+F+G+J+L+M = 3+6+2+5+4+6+3 = 30

B+D+E+G+J+L+M = 3+1+12+5+4+6+3 = 34

B+D+E+G+K+M =3+1+12+5+5+3 = 29

B+D+E+G+J+L+M = 3+1+15+5+4+6+3 = 37

B+D+E+H+L+M = 3+1+12+8+6+3 = 33

CRITICAL PATH MEAN (CPM)

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THE BAR CHARTThe bar chart can be drawn. All activities with float have been shown as starting at their earliest start time.

A B C D F E H G K J L

M

0 10 20 30 40 50Weeks

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EXAMPLEAs part of a large computer net work system project of MAN (Metropolitan Area Network) is to be installed in the city. Cabling and work station will be carried out by a civil engineering group. Setting out the networking with cabling for communication which connect one or more telephones and computers and associated devices. Installation of networking was carried out by Computer Engineering group. Non destructive testing (NDT) for the networking will be carried out by independent assessors for statuary purpose, and once this has been finishes, the Civil Engineering group will place for constructing the building as required according to the networking. The different groups have been asked to provide estimates of their rates of progress . The area covering is 120 km square. Each group assumes that it has one team working, starting at one end and proceeding to the other.The initial plan provides for all operation to be at least 4 km apart. The following data are given on the next slide.

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Group Activity Estimated rate ofworking (km/day)

Duration(days)

Civil Engg. X-Building 2 60

Suppliers P-Placing 4 30Computer

Engg.W-Network

setup1 120

NDTassessors

N-NDT 2 60

Civil Engg. B-Sub-bldg. 4 30

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0 0

0 0START

0

0 60

0 118 X

60

2 61

2 119 P

30

S-S (2)

F-F(1)

3 123

3 123 W

120

S-S(1)

7 125

65 125 N

60

S-S(4)

F-F(2)

9 126

96 126 B

30S-S(2)

F-F(1)

126 126

126 126FINISH

0

F-F (4)

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PROBLEMS # 1The following information covers part of a large PERT :

Starting Event Following event Expected timeweeks

A C 11A D 6B D 5C E 7C F 5D F 9D G 10D H 12E F 2F H 8F I 12G H 4H I 8

What is the critical path and how many weeks will it take to complete this work. Also construct a data for ES, LS, EF, LF and slack weeks.

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KEY POINTS

• Straight lines connecting circles represent tasks that take time or resources; these lines are called activities.

• The circles are called events and represent a point in time .

• A dotted line is called a dummy activity.

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• The critical path through a network is the chain of activities whose times determine the overall duration of the project.

• Activities on the critical path are known as critical activities.

• The top right of each event records its earliest finish time.

• The bottom right of the event records the latest finish time.

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• Events whose earliest time equals their latest time are on the critical path.

• Spare time for an activity is called a float.• Total float=latest finish time-earliest start

time-activity duration.• The float is used to identify whether any

delay in starting or carrying out an activity will cause a delay in the project completion time.

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• The latest finish time for each of the previous events is obtained by subtracting the activity durations from the preceding events along the backward route, taking the minimum value where there is more than one route back into an event.

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Data Flow Diagrams – Relationship Grid