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