The following table contains a list of activities, with early- and late-start and finish times and crash costs for the network shown in the figure. All start and finish times and crash costs are on a per-week basis
Each activity can be reduced by one week at the most.
a. Determine the uncrashed activity lengths for activities A though K.
b. Determine the minimum completion cost for this project if each week carries a fixed cost of $1,000.
Activity ES EF LS LF Crash Cost/week
A 0 5 0 5 $1,100
B 5 9 13 17 $250
C 5 11 5 11 $1,200
D 0 6 1 7 $350
E 6 10 7 11 $900
F 9 14 17 22 $875
G 11 17 16 22 $1,500
H 11 18 11 18 $500
I 18 26 18 26 $300
J 17 21 22 26 $625
K 26 34 26 34 $750
Activity lengths for A—K can be found by subtracting the early start of each activity from the late start of each activity.
The activity lengths appear in this table:
a.
Activity Length LS LF Crash Cost/week
A 5 0 5 $1,100
B 4 13 17 $250
C 6 5 11 $1,200
D 6 1 7 $350
E 4 7 11 $900
F 5 17 22 $875
G 6 16 22 $1,500
H 7 11 18 $500
I 8 18 26 $300
J 4 22 26 $625
K 8 26 34 $750
b.
The critical path is ACHIK = 34 weeks. Other paths are DEHIK = 33; ACGJK = 29; DEGJK = 28; and ABFJK = 26. With a fixed cost of $1,000/week, the initial cost is 34 weeks @ $1,000 = $34,000.
The cheapest critical-path activity is I @ $300, so reducing I from 8 weeks to 7 weeks costs $300 but saves $1,000, resulting in a net savings of $700.
The next cheapest critical-path activity is H @ $500, so reducing H from 7 weeks to 6 weeks costs $500 but saves $1,000, for a net savings of $500.
The next cheapest critical-path activity is K @ $750, so reducing K from 8 weeks to 7 weeks costs $750 but saves $1,000, for a net savings of $250.
The other two activities on the critical path are more expensive to crash than the penalty cost, so the cheapest completion time is 34 weeks - 3 weeks (I, H, K) = 31 weeks for a cost of $31,000 plus the crash costs of $300 + $500 + $750 = $32,550.
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