What is the minimum completion cost of this project if there is a penalty of $1,000 for each day the project lasts longer than 27 days? Activity durations in days and crash costs in dollars are given in the table

Question

Activity Reg Length Crash Length Reg Cost Crash Cost Activity Reg Length Crash Length Reg Cost Crash Cost
A 7 6 400 1,200 L 7 5 800 1,500
C 1 1 450 450 N 6 5 500 1,250
D 9 6 550 2,350 R 4 4 600 600
E 9 7 500 1,650 S 10 8 450 1,350
J 2 1 600 1,800 Y 8 6 675 1,750

Answer 1

The initial project duration is 34 days. Path analysis and purchases made in order of least expensive to most expensive are given in the table.

Step Starting Path Lengths Activity Crashed # Days Crashed Cost per Day Total Cost
1 JALSY=34
JANDCY=33
JAERY=30 L 1 $350 $350
2 JALSY=33
JANDCY=33
JAERY=29 A 1 $800 $800
3 JALSY=31
JANDCY=31
JAERY=27 Y 2 $537.50 $1,075
4 JALSY=30
JANDCY=30
JAERY=27 L
D 1
1 $350
$600 $950
5 JALSY=29
JANDCY=29
JAERY=27

Subsequent purchases will exceed the $1,000 penalty, so the project manager is better served by paying two penalty days at $1,000 each. The total cost of the project including the penalties is $10,700.