6.         For the data given in the table below, draw the network. Crash systematically the activities and determine the optional project duration and cost :

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Activity

1 – 2

1 – 3

2 – 4

2 – 5

3 – 4

4 – 5

Normal Time (days)

8

4

2

10

5

3

Normal Cost (`)

100

150

50

100

100

80

Crash Time (days)

6

2

1

5

1

1

Crash Cost (`)

200

350

90

400

200

100

Indirect cost is ` 70/- per day.

 

7.         The following table gives the activities and other relevant data for a project :

Activity

Normal

Time (Days)

Crash Time

(Days)

Normal Cost

(`)

Crash Cost

(`)

1 – 2

4

3

600

800

1 – 3

2

2

400

400

1 – 4

5

4

750

900

2 – 3

7

5

400

600

2 – 5

7

6

800

100

3 – 5

2

1

500

650

4 – 5

5

4

600

850

(a)     Draw the network of the project.

(b)     Find the normal duration and cost of the project.

(c)     Find the duration with minimum cost.

 

8.         A project consists of activities A, B, C, D, E & F. Following table provides the details about these activities. On the basis of Network diagram drawn using these data the Project Manager wants to take certain decision of so as to save the project’s time and cost. The direct Project Cost is ` 580 and the indirect cost is ` 70 per day.

Activity

Preceding

Activity

Activity duration

In days

Shortest

Time / day

Cost reduction

Per day

A

8

6

50

B

4

2

100

C

A

2

1

40

D

B

10

5

60

E

A

5

1

25

F

C, D

3

1

10

(a)     Draw the Network diagram and find project’s duration.

(b)     Find Critical Path.

(c)     Identify the lowest cost and associated time.

(d)     Determine the optimum project length and optimum cost after crashing.

(e)     Calculate the shortest time and associated cost.

 

9.         A small marketing project consists of jobs in the table given below. With each job is listed its normal time and crash time in days.  The cost in ` per day of crashing each job is also given.

Activity

Normal duration in days

Crash duration in days

Crashing cost        (` Per day)

1 —–> J

1 – 2

9

6

20

1 – 3

8

5

25

1 – 4

15

10

30

2 – 4

5

3

10

3 – 4

10

6

15

4 – 5

2

1

40

(a)     Draw the network diagram and find the normal project length.

(b)     If overhead costs are ` 60 per day and assuming normal projects costs as      ` 1000/-, what is the optimal project length and minimum total cost?

 

10.       A project consists of five activities. Relevant details about activities duration, crash time, normal and crash costs are as given in the following table.

Activity

Normal time (days)

Crash time (days)

Normal Cost (`)

Crash Cost   (`)

1 – 2

5

4

170

240

1 – 3

9

6

310

550

2 – 3

6

4

80

200

2 – 4

10

8

130

230

3 – 4

6

4

110

290

The indirect cost is estimate at ` 120 per day of project duration.

What is the optimal project duration i.e. duration at total minimum cost?

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