3.31 Development of Version 2.0 of a particular accounting software product is b
ID: 334552 • Letter: 3
Question
3.31 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 Activity Immediate Predecessor(s) Normal Time Crash Time Normal Cost Crash Cost (weeks) 4 (weeks) $2,000 2,200 500 2,300 $2,600 2,800 500 2,600 1,200 4,200 2,000 4 3,000 1,400 4 D, E a. b. c. What is the project completion date? What is the total cost required for completing this project on normal time? If you wish to reduce the time required to complete this project by 1 week, which activity should be crashed, and how much will this increase the total cost? d. What is the maximum time that can be crashed? How much would costs increase?Explanation / Answer
The precedence diagram as follows :
A
B
C
D
E
F
G
The possible parallel paths and their corresponding normal durations as follows :
A-D-G = 4 + 8 + 4 = 16
B-E-G = 2 + 6 + 4 = 12
C-F = 3 + 3 = 6
Since A-D-G has the longest duration, it forms the critical path . Duration of the critical path is same as project completion time.
Therefore , project completion time is 16 weeks
PROJECT COMPLETION TIME = 16 WEEKS
Total cost required for completing the project on normal time
= $2000 + $2300 + $1400
= $5700
TOTAL COST REQUIRED TO COMPLETE THE ON NORMAL TIME = $5700
If duration of the project has to be reduced by 1 week, it must be one of the activities on critical path ( i.e. A/D/G ) whose duration must be reduced.
Cost of crashing ( i.e. reducing duration ) by 1 week
= ( Crash cost – Normal cost ) / ( Normal duration – Crash duration )
Therefore ,
Weekly cost of crashing of A = ( $2600 - $2000) / ( 4 – 3 ) = $600
Weekly cost of crashing of D = ( $2600 - $2300) / ( 8 – 4 ) = $75
Weekly cost of crashing of G = ( $2000 - $1400) / ( 4 -2 ) = $300
Since weekly cost of crashing is least for activity D, same must be crashed .This would increase the total cost by $75
ACTIVITY A MUST BE CRASHED WHICH WOULD INCREASE THE TOTAL COST BY $75
Maximum time A-D-G can be crashed to from 16 weeks = 3 + 4 + 2 = 9 weeks
Maximum time B-E-G can be crashed to from 12 weeks = 1 + 3 + 2 = 6 weeks
Maximum time C-F can be crashed to from 7 weeks = 3 + 2 = 5 weeks
Therefore maximum time project can be crashed to = 9 weeks
Action plan for crashing the project to 9 weeks :
= Sum of ( Crash cost – Normal cost ) for A/D/G
= ( $2600 - $2000 ) + ( $2600 - $2300) + ( $2000 - $1400 )
= $600 + $300 + $600
= $1500
Crashing E from 6 days to 3 days at a cost of $300 (i.e $1200 - $900)
Total increase in cost = $1500 + $300 = $1800
MAXIMUM TIME PROJECT CAN BE CRASHED TO = 9 WEEKS
TOTAL INCREASE IN COST = $1800
A
B
C
D
E
F
G
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