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Find out the optimum cost and optimum duration for this project. The indirect cost of the project is Rs.3000/week
written 5.1 years ago by gravatar for teamques10 teamques10 ★ 64k •   modified 4.0 years ago
Activity Immediate predecessor Normal duration(weeks) Normal Cost(Rs) Crash duration (weeks) Crash cost(Rs)
A - 3 3000 1 4500
B A 2 5000 1 8000
C B 4 2000 2 4000
D B 3 7000 1 10,000
E B 2 12,500 2 12,500
F C 3 10,000 1 13,500
G D,E 5 6500 3 9000
H F 4 4300 2 8000
construction management
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written 5.0 years ago by gravatar for teamques10 teamques10 ★ 64k •   modified 5.0 years ago

Solution:

Activity Immediate predecessor Normal duration(weeks) Normal Cost(Rs) Crash duration (weeks) Crash cost(Rs) Cost slope
$ ( \frac{C_c - N_c}{N_T - C_T} )$
A - 3 3000 1 4500 750
B A 2 5000 1 8000 3000
C B 4 2000 2 4000 1000
D B 3 7000 1 10,000 1500
E B 2 12,500 2 12,500 0
F C 3 10,000 1 13,500 1500
G D,E 5 6500 3 9000 1250
H F 4 4300
------
50,300		 2 8000 1850

1st Iteration:

Starting activity - A

Ending: H, G

enter image description here

A B
Project duration: 16 weeks Normal cost = 50,300
Critical path: 1 - 2 - 3 - 4 - 7 8
= 3 + 2 + 4 + 3 + 4 = 16 weeks		 Indirect cost = 3000 X 16
T.C = 98,300
Critical path Critical activity Crash limit Cost slope
1 - 2 - 3 - 4 - 7 - 8 1 - 2(A) 2 750*
2 - 3 (B) 1 3000
3 - 4 (C) 2 1000
4 - 7 (F) 2 1500
7 - 8 (H) 2 1850

Crash activity A by one week


2nd Iteration:

enter image description here

A - B - C - F - H = 2 +2 + 4 + 3 + 4 = 15 week

cost = previous cost + cost slope - Indirect cost

= 98300 + 750 X 1 - 3000 X 1

= Rs.96,050

Critical path Critical activity Crash limit Cost slope
1 - 2 - 3 - 4 - 7 - 8 A 1 750*
B 1 3000
C 2 1000
F 2 1500
H 2 1850


3rd Iteration:

enter image description here

A - B - C - F - H = 1 + 2 + 4 + 3 + 4 = 14 week

cost = previous cost + cost slope + Indirect cost

= 96050 + 750 X 1 - 3000 X 1

= Rs.93,800

Critical path Critical activity Crash limit Cost slope
1 - 2 - 3 - 4 - 7 - 8 A 0 750
B 1 3000
C 2 1000*
F 2 1500
H 2 1850

Crash activity 'C' by two week


4th Iteration:

enter image description here

A - B - C - F - H = 1 + 2 + 2 + 3 + 4 = 12 week

cost = previous cost + cost slope - Indirect cost

= 93800 + 1000 X 2 - 3000 X 2

= Rs. 89,800

Critical path Critical activity Crash limit Cost slope
1 - 2 - 3 - 4 - 7 - 8 A 0 750*
B 1 3000
C 0 1000
F 2 1500*
H 2 1850

Crash activity F by one week


5th Iteration:

enter image description here

A - B - D - d1 -c1 = 1 + 2 + 3 + 0 + 5 = 11 week

A - B - C - F - H = 1 + 2 + 2 + 2 + 4 = 11 week

cost = 89800 + 1500 X 1 - 3000 X 1 = Rs. 88300

Critical path Critical activity Crash limit Cost slope
1 - 2 - 3 - 4 - 7 - 8 A 0 750
B 1 3000
C 0 1000
F 1 1500
H 2 1850
1 - 2 - 3 - 5 - 6 - 8 A 0 750
B 1 3000
D 2 1500
G 2 1250

Crash activity F and G simultaneously

6th Iteration:

enter image description here

Cost: Rs. 88,050

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