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Find out optimum cost & optimum duration for the project.

Mumbai University > Civil Engineering > SEM 8 > Construction Management

Marks: 10M

Find out optimum cost & optimum duration for the project. Indirect cost of project is Rs. 3500/- day.

Activity Normal Duration (days) Normal Cost (Rs.) Crash Duration (days) Crash Cost (Rs.)
1-2 7 7500 4 15000
1-3 9 4500 5 9000
2-3 5 6000 2 9000
2-4 6 8500 3 14000
3-4 6 8000 3 12000
4-5 8 9000 4 15000
1 Answer
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Activity Normal Duration (days) Normal Cost (Rs.) Crash Duration (days) Crash Cost (Rs.) Cost Slope
1-2 7 7500 4 15000 2500
1-3 9 4500 5 9000 1125
2-3 5 6000 2 9000 1000
2-4 6 8500 3 14000 1833.33
3-4 6 8000 3 12000 1333.33
4-5 8 9000 4 15000 1500
43500 74000

$\text{Cost Slope} = \frac{\text{Crash Cost - Normal Cost}}{\text{Normal Time - Crash Time}}$

Stage 1 :- Normal Time:-

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Critical path = 1-2-3-4-5

Project duration = 26 days

Stage 2 :- All Crash

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Critical path = 1-2-6-4-5

Project Duration = 13 days

Stage 3 :- Stage 1 + Crash C by 3 days & Crash E by 1 day.

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Critical path = 1-2-3-4-5 or 1-3-4-5

Project duration = 22 days

Stage 4 : - Stage 3 + Crash D by 3 days & Crash E by 2 days.

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Critical path = 1-2-3-4-5

1-3-4-5

Project duration = 20 days

Stage Description Duration Direct Indirect Addition Total
I All Normal 26 43500 26×3500=91000 - 134500
II All Crash 13 74000 13×3500=45500 - 19500
III Stage I+ Crash C by 3 days and Crash E by 1 day 22 43500 22×3500 3×1000+ 1333.33 124833.33
IV Stage 3 +Crash D by 3 day & Crash E by 2 day 20 43500 20×3500 3000+1333.33×1833.33+2× 1333.33 125999.98

Optimum cost = Rs. 124833.33

Optimum duration = 22 days.

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