Article on Network Analysis

8/6/2019 Article on Network Analysis

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Software Project Management

Network Ana lys i s

Network analysis is a vital technique in PROJECT MANAGEMENT. It enables us to

take a systematic quantitative structured approachto the problem of managing aproject through to successful completion. Moreover, it has a graphical

representation which means it can be understood and used by any individual who

has less technical background.

TERMS

Project A project has a start date and an end date.

Task - A Task has a def in ite start, a def in ite end, consumes human or

material resources and which produces something.

Event An Event is a snapshot in time, does not consume resources. An

event occurs.

Predecessor A Predecessor is a task that should be completed before atask can be scheduled

Successor A Successor is a task that can be scheduled only after a task

is completed.

Dummy Task A Dummy Task is a task that has no definite start, definite

end does not consume resources. A Dummy Task depicts a dependency

between any two tasks.

Early Start The Earliest when a task can be scheduled

Latest Start The Latest when a task can be scheduled

Early Finish The Earliest when a task can be completed

Latest Finish The Latest when a task can be completed

Article by Gayathri Kumar Pg : 1


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Network Ana lys i s

Free Float Everybody before a task gives as early as possible; everybody

after that task, start as early as possible

Total F loat Everybody before a task g ives a s ear ly a s pos sible;

everybody after that task start as late as possible. Total Float is always

>= Free Float

Critical Task A Critical Task is a task that has no Total Float.

Crit ica l Path A Cr it ica l Path i s a path which inc ludes one or more

Critical Tasks. A project has at least one Critical Path. There can be more

than one Critical Path for a Project.

NOTATIONS

A task is represented by an arrow

An event is represented by a circle

A dummy task is represented by a dotted arrow

All Early times are represented in blue colour

All Late times are represented in red colour

NETWORK DIAGRAMS

TABLE 1

TASK PREDECESSOR

A -

B -

C A



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Network Ana lys i s

From the above diagram, the following are statements of fact:

1. Task A and Task B have no predecessors

2. Task C has Task A as the predecessor

3. Task A has Task C as the successor

4. A project i s not complete unti l Task B and Task C are completed.

5 . Task C can star t as soon as Event 2 has occurred

6. Event 2 can occur as soon as Task A has been completed

7. Every task is identif ied uniquely as I ,J where I i s str ictly less than J.

This was found by Dr. Fulkerson. So in the above diagram,

a . Tas k A 1 ,2

b . Tas k B 1 ,3

c . Tas k C 2 ,3

TABLE 2

TASK PREDECESSOR

A -

B -

C -


1 3

2

B

AC


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Network Ana lys i s

The above is theoretical ly incorrect as Tasks A, B and C have I = J. So the

other way of drawing the diagram would be

Now Tasks can be identified as follows:

a . Tas k A 1 ,2

b . Tas k B 1 ,4

c . Tas k C 1 ,3

TABLE 3

TASK PREDECESSOR

A -

B A

C D,A

D B

E D


1 2

A

B

C

1 4

A

B

C

2A

3


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Network Ana lys i s

The above d iagram i ll us trates a cyclic dependency - Task C can be

scheduled as soon as Event 2 occurs. Event 2 can occur as soon as Task A and

Task D are completed. Task B can be scheduled as soon as Event 2 occurs. If

we have to identify the tasks, it would be like this:

a . Tas k A 1 ,2

b . Tas k B 2 ,3

c . Tas k C 2 ,5

d. Task D 4,2 Here I is > than J

e . Tas k E 4 ,5

Looking at the above network d iagram, i t can be concluded that such a

project can never be completed.

Another example of a cyclic dependency -

Example: - If a house is locked and if the master key and the duplicate key

are both inside the house, how would we represent the network diagram for

the following tasks:

Task A Find Key

Task B Open Door

Task C Go Inside


1 3

2

C

AB

D

4E5


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Network Ana lys i s

To find the key(Task A), one has to go inside (Task C) ; to go inside (Task C),

one has to open door(Task B); to open door, one has to find the key(Task A).

Such a project can never end. It is an infeasible project.

Going back to where we left, the above network diagram can be drawn in a

different way as follows:

This network diagram also explains that a Tool is preferred than to people.

The Tool requires us to only feed the Network Table correctly and it would

draw the network diagram. What would seem as an infeasible Project could

actually have a solution.

TABLE 4

TASK PREDECESSOR

A -

B C

C -

D A

E A,C


1 3

2

C

AB

D

54

6

E

D


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Network Ana lys i s

TABLE 5

TASK PREDECESSOR DURATION

A - 2

B - 6

C A 1

D C,B 3

E D 9

F B,C 5

TOTAL 26

Find ES, EF, LS, LF, FF, TF


1

2

C

AD

E

5

4

B

3

2 5


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Network Ana lys i s

TASK PREDECESSOR DURATION ES EF LS LF FF TF

A - 2 0 2 3 5 0 3

B - 6 0 6 0 6 0 0

C A 1 2 3 5 6 3 3

D C,B 3 6 9 6 9 0 0

E D 9 9 18 9 18 0 0

F B,C 5 6 11 13 18 7 7

TOTAL 26

CRITICAL TASKS B, D, E

CRITICAL PATH BDE 18

TABLE 6


B

A

C

4 D

E

F2

6

1

3

95

6

0

4

1

3

0

6 9

18

2

6

2

3

9

9

11

18

18

9

6

13

0

5

3

2 5


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Network Ana lys i s


A - 1

B A 2

C - 4

D A 7

E B,C 3

F E,D 11

G - 6

H G 4

TOTAL 38



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Network Ana lys i s


6 15

4 5

0 0

1 1

8 8

A

1

1

0

C

44

1

G6

6

9

B2

3

3

E

3

7

5

D

7

5

8

F

11

1

1

8

H

4

10

15

2

1

3

4

6

5

19 19


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Network Ana lys i s


A - 1 0 1 0 1 0 0

B A 2 1 3 3 5 1 2

C - 4 0 4 1 5 0 1

D A 7 1 8 1 8 0 0

E B,C 3 4 7 5 8 1 1

F E,D 11 8 19 8 19 0 0

G - 6 0 6 9 15 0 9

H G 4 6 10 15 19 9 9

TOTAL 38

CRITICAL TASKS A,D,F

CRITICAL PATH ADF 19

TABLE 7


A - 5

B A 11

C A 3

D A 6

E B,D 4

F E,C 7

G F 2



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Network Ana lys i s


H G 10

TOTAL 48


A

B

D

16 16

3

4

5 5

2

0 0

1

5

0

115

10

16

11


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Network Ana lys i s


A - 5 0 5 0 5 0 0

B A 11 5 16 5 16 0 0

C A 3 5 8 17 20 12 12

D A 6 5 11 10 16 5 5


C

E

F

G

H

1616

20 20

5

39 39

8

29 29

7

27 27

6

5

3

6

4

7

2

10

8

20

27

29

39

29

27

20

16

17


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Network Ana lys i s


E B,D 4 16 20 16 20 0 0

F E,C 7 20 27 20 27 0 0

G F 2 27 29 27 29 0 0

H G 10 29 39 29 39 0 0

TOTAL 48

CRITICAL TASKS A,B,E,F,G,H

CRITICAL PATH ADF 39

*** End of Document ***


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Article on Network Analysis