GATE 2019 CE (CE1) – Question 47
The construction project network is shown. Data below give normal duration / crash duration (days), normal cost / crash cost (INR):
P: 6 / 4, 15000 / 25000.
Q: 5 / 2, 6000 / 12000.
R: 5 / 3, 8000 / 9500.
S: 6 / 3, 7000 / 10000.
T: 3 / 2, 6000 / 9000.
U: 2 / 1, 4000 / 6000.
V: 4 / 2, 20000 / 28000.
Indirect cost is INR 5000/day. For a 16-day completion target, find the minimum total project cost (INR).
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Correct answer: 149500 to 149500
Explanation
Normal duration is $6+\max(5+2,5+3,6)+4=18$ days. Normal direct cost sums to INR 66000. Crash R from 5 to 3 days at INR 750/day and Q from 5 to 4 days at INR 2000/day. All three middle paths then take 6 days, and duration becomes 16. Added direct cost is $2(750)+2000=3500$. Total is $66000+3500+16(5000)=$ **INR 149500**. Shortening common activities P or V costs more per day.