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RS Management Consulting House


TimeTime

RevisionRevision According to PMBOK Third Edition


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Arrow Network Techniques

Case 1:

A < C, B & B < D & C < D

Dummy Activity (Dashed Arrow)Dummy Activity (Dashed Arrow)

(2 3) = activity C(2 3) = activity C

(2 3) = activity B(2 3) = activity B

1 2 3 4AA CC DD

BB


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Ca se 1

T he Right:

E is Dummy Activity (Duration = 0)

A < C, B & B < D & C < D

AA CC DD

BB EE


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Ca se 2A < C & B < E & C < D, E

Because B is not < DBecause B is not < D

AA CC DDBB

EE


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Ca se 2

A < C & B < E & C < D, E

AA CC DD

BBEE


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Ca se 3

A < D, E & B < E, F & C < F

A is not < FA is not < F

AA

CC

DD

BB

FF

EE


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RS Management Consulting HouseRS Management Consulting House

Ca se 3

AA

CC

DD

BB

FF

EE1 3 6

2

4

5

A < D, E & B < E, F & C < F


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Ca se 4

A < C & B < D & C < D

1 2 4 5AA CC DD

BB 3 XX

Dummy x is unnecessaryDummy x is unnecessary


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Ca se 5:

A < C & B < C, D, E & C < E

CC

1 5

4AA

DDBB

2

3

EE

xx zz

B is a redundant restriction on EB is a redundant restriction on E


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Ca se 5

No need for Dummy Z

1

54AA

CC

DDBB

2

3 6

EE

xx

A < C & B < C, D, E & C < E


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Example:Given the data for a small project.


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Solution:

Critical Path = A, C, D, F & GProject Duration = 24 days

A0 0 5

0 5 5

B5 5 11

10 6 16

C

5 0 9

5 4 9D

9 0 16

9 7 16

E9 3 18

12 9 21

F16 0 21

16 5 21

G21 0 24

21 3 24


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Example

Consider the simplified activity-on-arrow description of a project network given in the table:

(a) Draw the CPM network for this task structure.(b) Determine the project duration.


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DurationyA (1,2) 8B (2,3) 10C (2,4) 2

D (3,4) 16E (3,5) 4F (4,5) 8G (3,6) 7H (4,6) 12I (5,7) 3J (6,7) 8K (7,8) 2

ask Activity


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Solution:

Project Duration = 56 days

Critical Path = A, B, D, H, J & K

6

4

7 83

E

4

J

8

H 128

32 1034

C

2

34

34

D

16

1 2

5

0 A 8

0 8 8

8 B 18

8 10 18 54 B 56

54 2 56

18

39

G

7

2546

2251

1847 34

43 F8 4251

4646 54

5446 46

34 3418

18

4251

4554

I

3


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Ex. (3):Ex. (3):

A project consists of the activities shown in the table. The durationsA project consists of the activities shown in the table. The durationsrepresent the optimisticrepresent the optimistic ( a), ( a), most likely (m). and pessimistic (b)most likely (m). and pessimistic (b)times (days) for each activity. Find the critical path for this PERTtimes (days) for each activity. Find the critical path for this PERT

Network. Network.

a m b(1,2) 5 8 10(1,3) 18 20 22(1,4) 26 33 40(2,5) 16 18 20

(2,6) 15 20 25(3,6) 6 9 12(4,7) 7 10 12(5, 7) 5 7 8(6, 7) 3 4 5

ActivityDuration (days)

a m bA (1,2) 5 8 10 8B (1,3) 18 20 22 20C (1,4) 26 33 40 33D (2,5) 16 18 20 18

E (2,6) 15 20 25 20F (3,6) 6 9 12 9G (4,7) 7 10 12 8H (5,7) 5 7 8 7M (6,7) 3 4 5 4

Activity Duration


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S olution For Ex. ( 3 ):


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Examp le:Activity

duration(weeks)

PrecedingActive

Overlap

A 5 - -

B 4 A -

C 5 A Lag 1

D 5 A -

E 5 B Overlap 2

F 4 B,C -

G 6 D -

H 4 E Overlap 1

I 3 F, G - , overlap 2

j 2 H,A,I -


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Examp le:

Draw the network for above project.

Calculate the total project duration &indicate the C.P.

Calculate total Flout & Free flout for eachactivity.


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