Question

There are four critical paths in a network. A-B-C-D-E, A-F-E, A-B-H-J-K-E and A-S-T-E. Each activity in this network can be crashed by a maximum of 2 weeks. The crashing cost (per week), for the first week, for activity A is: $540, E is $545 and all other activities is : $135 (per week per activity). The crashing cost, second week and onwards, for activity A is $1080 per week, E is $1350 per week and for all other activities is $405 per activity per week. You have a maximum crashing budget of $2300. The maximum possible reduction in the project duration will be:

Select one:

a. 3 weeks

b. 4 weeks

c. 5 weeks

d. 1 week

e. 2 weeks

Answer 1

Trick is we can crash only one activity per path per week here. We crash that event first which has low crashing cost.

1. For first week:- ​​​​​​​

Case-a: We crash only A, since A is common for all paths. So the crashing cost would be 540.

Case-b: We crash only E, since E is common for all paths. So the crashing cost would be 545.

Case-c: We crash B(B is common for 1st and 3rd paths), F(in second path), S(in 4th path). So the crashing cost is 135+135+135=405.

Since in Case-c, crashing cost is lower, we opt that crash.

So crash cost for first crash is 405.

2. For second week:-

The logical approach for second week also would be same as above and here also we crash B(B is common for 1st and 3rd paths), F(in second path), S(in 4th path). So the crashing cost is 405+405+405=1215.

Now since each activity can be crashed only twice, we have exhausted the crashing potential of B,F& S.

Till now we used 405+1215=1620 for crashing.

3. For third week:-

If we think about taking activity C in the first path, we need to choose from A and E(since F is exhausted) in the second path(and since if we choose A or E in the second path, they are common to all paths so we mandatorily have to choose A or E from first path also)which is exceeding our crashing budget i.e if we choose A from all paths, cost becomes 1620+1080=2700 which is not in our budget.

So it is possible to crash for only two weeks.

Please comment if any doubt.