Question

Development of Version 2.0 of a particular accounting software product is being considered by Jose Noguera's technology firm in Baton Rouge. The activities necessary for the completion of this project are listed in the following table Total Cost Normal Time Crash Time Normal Activi weeks 4 weeks Cost Crashing Immediate Predecessor(s $2,100 $2,750 $2,100 $2,700 $600 $2,500 $2,780 $800 $1,250 $3,400 $4,600 $1,400 $1,800 $600 2

1) Based on the given information regarding the activities for the project, the project length= ___ weeks.

2) The total cost required for completing this project on normal time= $____

3) For reducing the duration of the project by one week, the activity that should be crashed first is activity ___.

4) The cost of the project based on the first activity selected for crashing will increase by $___.

5) The maximum weeks by which the project can be reduced by crashing= ___ weeks.

6) Total cost of crashing the project to minimum (or maximum weeks possible)= $____

Answer 1

Let us first draw the network diagram to identify critical path and project duration -

Possible network paths and their duration are -

ADG --> 4+8+4 = 16 weeks
BEG --> 2+6+4 = 12 weeks
CF --> 3+3 = 6 weeks

1. Hence, the project length is maximum duration = 16 weeks

2. Total cost required to complete the project = sum of costs for A, B, C, D, E, F, G

= 2100 + 2100 + 600 + 2500 + 800 + 3400 + 1400 = $12900

3. To reduce the duration by 1 week, either of A, D or G should be crashed.

Among A, D and G, D has the lowest increment in the crashing cost/week

Hence D should be crashed first

4. If Activity A is crashed, the project cost will increase by 2750-2100 = $650

5. A can be crashed by 1 week, D can be crashed by 4 weeks, G can be crashed by 2 weeks => Duration of path ADG = 16 -1-4-2 = 9 weeks

B can be crashed by 1 week, E by 3 weeks, G by 2 weeks, bringing down the duration of path BEG to 6 weeks. However ADG has the highest duration. Hence, BEG should be reduced by 3 weeks. Hence only E (with lowest crashing cost/week) should be crashed.

None of activities on path CF needs to be crashed.

Hence, the maximum weeks by which the project duration can be reduced = 16-9 = 7 weeks

6. Total cost after crashing the project to minimum = Crashed cost of A + Crashed cost of D + Crashed cost of G + Crashed cost of E + Normal cost of B + Normal cost of C + Normal cost of F = 2750 + 2780 + 1800 + 1250 + 2700 + 600 + 4600 = $16480

Hence, cost of crashing = 16480 - 12900 = $3580