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: Duration (weeks) Activity A (start) Precedes B, C Crash Cost/Week $400 $100 $200 $300 $400 F F (end) 2 Suppose that Rafay is only given 5 weeks (instead of 7) 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 (days) week(s) week(s) week(s) week(s) week(s) What is the total crashing cost? $ (Enter your response as a whole number.)

Answer 1

There are 2 paths for completing the project:

A-B-E-F => 1+1+2+2 = 6 weeks

A-C-F=> 1+4+2 = 7 weeks

Hence Critical Path is ACF and 7 weeks

The objective is to crash project from 7 to 5 weeks.

First we evaluate the Crticial path

Activity	Crash cost per week	Rank (l - h)
A	400	2
C	200	1
F	400	2

Hence we crash C by a week. Total Crash cost is $ 200 ...(1)

So we have two critical paths A-C-F and A-B-E-F of 6 weeks. We further need to crash 1 more week. Hence we evaluate again as follows:

Activity	Crash cost per week	Rank (l - h)
A	400	4
B	100	1
C	200	2
E	300	3
F	400	4

Hence, for ABEF we crash B by 1 week and for ACF we crash C by one week. So we have, Total Crash Cost 100+200 = 300$ ...(2)

Our New critical paths are ABEF and ACF and duration is 5 weeks.

So,

Activity	Reduced by weeks
A	0
B	1
C	2
E	0
F	0

Total Crash cost = (1) +(2) above => 200 + 300 = 500.