The network of a small construction project awarded to a contractor is shown in the following figure. The normal duration, crash duration, normal cost, and crash cost of all the activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per day. Activity Normal Duration (days) Crash Duration (days) Normal Cost (NR) 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 If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by the contractor would be

GATE Civil Engineering (CE) 2019 Shift 1 Solved Paper

Question : 39 of 65

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The network of a small construction project awarded to a contractor is shown in the following figure. The normal duration, crash duration, normal cost, and crash cost of all the activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per day.

Activity	Normal Duration (days)	Crash Duration (days)	Normal Cost (NR)	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

If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by the contractor would be

Your Answer:

Validate

Solution:

Path PRTV is critical path and corresponding normal duration is 18 days.

Activity	$\t_\n$	$\t_\c$	$\C_\n$	$\C_\c$	$\C_{n}=\;{\C_{\c}-\C_{\n}}/{\t_{\n}-t_{k}}$
P	6	4	15000	25000	5000
Q	5	2	6000	12000	2000
R	5	3	8000	9500	750
S	6	3	7000	100000	1000
T	3	2	6000	9000	3000
U	2	1	4000	6000	2000
V	1	2	2800	2800	4000

For 18 days:
Direct cost

=66000

Indirect cost

=18 × 5000=90000

Total project cost

=156000

1st stage crashing :
Crash activity

{R}

by 1 day.
New project duration

=17

days.
T.P.C

=156000+1 × 750-1 × 5000=151750

2nd stage crashing :
Crash activity

Q

R

simultaneously by 1 day. New project duration

=16

days.
T.P.C

=151750+1 ×(750+2000)-5000=149500

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