What is the minimum cost completion time for this project if the activities have normal and crash costs as indicated and there is a $1,000 fixed cost for each day on site plus a $500 penalty for each activity that is crashed? The crash costs
represent the cost of a fully expedited activity. For example, reducing activity Y from 13 days to 12 days costs an extra $100 on top of the $500 expediting cost for a total cost of $2,600. Reducing Y from 13 days to 10 days costs an extra $300 on top of the $500 expediting cost, for a total activity cost of $2,800.
Activity Predecessor Normal Time Normal Cost Crash Time Crash Cost
Z 2 $2,000 2 $2,000
Y 13 $2,000 10 $2,300
X 19 $2,000 15 $3,000
W Z 18 $2,000 15 $3,000
V X 10 $2,000 9 $3,000
U Y 13 $2,000 11 $3,000
T W 18 $2,000 14 $4,000
S V 4 $2,000 3 $3,000
R U 6 $2,000 5 $3,000
Q R, S 15 $2,000 13 $3,000
P T 13 $2,000 12 $3,000
N P, Q 4 $2,000 4 $2,000
The project before any expediting takes 55 days thanks to path ZWTPN. Path XVSQN has a 52-day duration and path YURQN has a 51-day duration. The initial cost of the project is $24,000 for the uncrashed activities plus $55,000 for the fixed cost for a total cost of $79,000.
Crashing should take place in this sequence:
1st: Reduce activity W by 3 days. This costs $1,000 plus the $500 expediting charge but trims three days off the fixed cost saving $3,000 for a net savings of $1,500.
The project is now 52 days thanks to path ZWTPN and XVSQN at a cost of $77,500. Any further action may reduce the project length but will increase the project's cost. Crashing activity T by one day and activity X by one day adds $1,750 to the cost column and saves only $1,000 for a net cost of $750.
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