The following is a table of activities associated with a project at Rafay Ishfaq

Question

The following is a table of activities associated with a project at Rafay Ishfaq's software firm in Chicago, their durations, what activities each must precede and the crash cost to reduce duration per week:

Activity

Duration (weeks)

Precedes

Crash Cost/Week

A (start)

2

B, C

$ 380

B

2

E

$ 130

C

5

F

$ 240

E

2

F

$ 150

F (end)

4

long dash

$ 450

Suppose that Rafay is only given

8

weeks (instead of

11

)

to complete the project. By how many weeks should each activity be crashed in order to meet the deadline? Assume that you can crash an activity down to 0 weeks duration.

Activity

Each Activity Should be Reduced BY

(weeks)

A

nothing

week(s)

Enter your answer in the answer box and then click Check Answer.

Activity

Duration (weeks)

Precedes

Crash Cost/Week

A (start)

2

Explanation / Answer

Available Paths with Time (in weeks) -

ABEF = 10 weeks

ACF = 11 weeks

Critical Path is coming out to be ABEF with time = 10 weeks. Question says it as 11 weeks (if I not getting it wrong). There might be some error in values I guess.

Anyway, moving on with critical path as ABEF, we need to reduce 2 weeks here.

Now, the lowest crash cost is of Path B-E = $130 and then path E-F = $150.

Note: While crashing the activities to reduce the time taken, one should make sure that the critical path doesn't get changed while doing that. And also, always the least crash cost per week path should be reduced first (to the maximum allowable crashing) and then the next and so on. While doing this, you might get a new critical path. When two paths simultaneously become critical, activities on both paths must be reduced by the same amount.

Here in this question, such problem doesn't arise when we reduce time for B-E path by 2 weeks with a cost of $150*2 = $ 300.

Critical Path after crashing = ABEF with new time = 8 weeks and Crashing Cost = $ 300.

Rest activities won't have reduction in the time.

Activity Duration Precedes CrashCost per week A 2 B,C 380 B 2 E 130 C 5 F 240 E 2 F 150 F 4 - 450

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