Numericals on Project Crashing


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(Project Crashing)

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1.         For the data given in the table below, draw the network. Crash systematically the activities and determine the optimal project duration and cost. Indirect cost is ` 70 per day.  (April 2003)

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

 

2.         The following is a table showing details of a project : Indirect cost is ` 200 per week.

NODES

Normal

Crash

Time (weeks)

Cost (`)

Time (weeks)

Cost (`)

1 – 2

8

1500

6

2000

1 – 4

10

2000

7

3000

2 – 4

5

800

4

1400

2 – 3

6

1100

4

1500

2 – 5

8

900

5

1500

3 – 4

0

0

0

0

4 – 6

12

300

8

400

5 – 6

5

500

4

800

(a)     Construct the project network and identify the critical path. What is the normal duration and corresponding total cost of the project?

(b)     Crash the project systematically and find out minimum cost and optimal time and also find out the additional cost required to reach the optimal time.

                        (April, 10)

3.         The time and cost estimates and precedence relationship of different activities constituting a project are given.

Activity

A

B

C

D

E

F

G

H

I

Predecessor

B

B

A

A

F

C,E,G

F

Time         (in weeks)

Normal Crash

3

8

6

5

13

4

2

6

2

2

6

4

2

10

4

1

4

1

Cost

(in `)

Normal

Crash

80

6

100

40

30

150

12

35

70

190

10

120

100

90

150

14

45

80

 

4.         Following 7 activities are involved in completion of a small project.

Activity

Preceding Activity

Time (Hrs.)

Crash cost

 

 

Normal

Crash

` / Hour

A

3

1

40

B

4

2

50

C

B

0

0

ZERO (Nil)

D

A & C

5

3

20

E

B

3

2

30

F

D

3

2

10

G

E

2

1

20

Determine which is the quickest possible time in which the project can be completed and how much is the additional cost for this purpose.

Normal project cost is ` 1500.

 

5.         The time and cost estimate of different activities of a project and their precedence relationship are given below :                                                                                                        (Oct. 2007)

Activity

Preceding Activity

Time in Weeks

Cost in `

 

 

Normal

Crash

` / Hour

A

6

4

10,000

14,000

B

4

3

5,000

8,000

C

A

3

2

4,000

5,000

D

B

8

3

1,000

6,000

E

B

14

6

9,000

13,000

F

C, D

8

4

7,000

8,000

Overhead costs amount to ` 1,000 per week. Answer the following questions :

(i)      Crash the project to optimal extent. What will be the optimum project duration and total minimum cost?

(ii)     What will be the critical activities after such crashing?

(iii)    What will be the minimum project duration and corresponding total project costs?

6.         Following are the various activities involved in a project. The cost and time information for these activities is given below :

Activity

Immediately

Proceeding Activity

Normal

Crash

Time (days)

Cost (`)

Time (days)

Cost (`)

A

3

140

2

210

B

6

215

5

275

C

2

160

1

240

D

A

4

130

3

180

E

A

2

170

1

250

F

A

7

165

4

285

G

B, D

4

210

3

290

H

C, E

3

110

2

160

(a)     Draw the PERT network.

(b)     Find out the critical path and the expected project completion time.

(c)     What is the minimum possible project completion time after crashing the activities involved in the project and the associated cost of completing the project?     (Oct. 2009)

 

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