5 Practice Questions on Network Analysis (Part 1)


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1.         The time and the cost estimates and precedence relationship of different activities constituting a project are given below :

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Activity

Intermediate

Predecessor

Time (in weeks)

Direct Cost (in `)

Normal

Crash

Normal

Crash

A

4

3

60

90

B

6

4

150

250

C

2

1

38

60

D

A

5

3

150

250

E

C

2

2

100

100

F

A

7

5

115

175

G

D, E, B

4

2

100

240

Indirect cost varies as follows :

Days

15

14

13

12

11

10

9

8

7

6

Cost (`)

600

500

400

250

175

100

75

50

5

25

(a)     Draw an arrow diagram for the project.

(b)     Determine the project duration which will return in minimum total project cost.

2.         The time and cost estimates and precedence relationship of the different activities constituting a project are given below :

Activity

Predecessor

Time (in weeks)

Direct Cost (in `)

Normal

Crash

Normal

Crash

A

3

2

80

190

B

8

6

6

10

C

B

6

4

100

120

D

B

5

2

40

100

E

A

13

10

30

90

F

A

4

4

150

150

G

F

2

1

12

14

H

C, E, G

6

4

35

45

I

F

2

1

70

80

(a)     Draw a project network diagram and find the critical path.

(b)     If a deal line of 17 weeks is imposed for completion of the project which activities will be crashed, what should be the additional cost and what would be the critical activities of the crashed network after crashing?

3.         The following tab le gives the activities in a construction project and other relevant information.

Activity

Preceding

Activity

Normal Time

(Days)

Crash Time

(Days)

Normal

Cost (`)

Crash

Cost (`)

1 – 2

20

17

600

720

1 – 3

25

25

200

200

2 – 3

1 – 2

10

8

300

440

2 – 4

1 – 2

12

6

400

700

3 – 4

1 – 3, 2 – 3

5

2

300

420

4 – 5

2 – 4, 3 – 4

10

5

300

600

(i)      Draw the activity network of the project.

(ii)     Find the critical Path

(iii)    Using the above information, Crash or Shorten the activity step by step until the shortest duration is reached.

 

4.         For an activity in a network the normal duration is 12 days and the normal cost is    ` 2000/-, For the same activity the crash duration is 8 days with crashing cost as     ` 3,200/-. Find the cost slope of this activity.

 

5.         The table below provides cost and time estimates of seven activities of a project.

Activity

Time estimates  (in weeks)

Direct Cost estimates  (` In 000)

Normal

Crash

Normal

Crash

1 – 2

2

1

10

15

1 – 3

8

5

15

21

2 – 4

4

3

20

24

3 – 4

1

1

7

7

3 – 5

2

1

8

15

4 – 6

5

3

10

16

5 – 6

6

2

12

36

(i)      Draw the project network corresponding to normal time.

(ii)     Determine the critical path and the normal duration and normal cost of the project.

(iii)    Crash the activities so that the project completion time reduces to 9 weeks with minimum additional cost.

 

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