Question

A project following six activities

Activity	Normal time(days)	Normal cost(₹)	time(days)	cost(₹)	Cost slope
1 - 2	4	1600	3	1800	200
1 - 3	9	2700	7	3500	400
2 - 3	3	1500	3	1500	0
3 - 4	6	2400	5	2800	400
3 - 5	7	4200	5	5000	400
4 -5	3	1800	2	2400	600

• A. 22300 and 14 days
• B. 22300 and 18 days
• C. ₹22150 and 15 days
• D. ₹22200 and 16 days

Answer 1

The correct option is C ₹22150 and 15 days


Critical path = 1 - 2 -3 - 4 - 5
Critical path duration = 9 + 6 + 3 = 18 days
Total cost = (1600 + 2700 + 1500 + 2400 + 4200 + 1800) + (18 x 450)
= ₹22300
We can crash activity along the critical path for reducing the project duration. Crashing activity 1 - 3 by two days.


Now there are two critcal paths.
1 - 2 - 3 -4 - 5 = 4 + 3 + 6 + 3 = 16 days
1- 3 - 4 - 5 = 7 + 6 + 3 = 16 days
Total cost after crashing = 1600 + 3500 +1500 + 2400 + 4200 + 1800 + (16 x 450)
= ₹22200
Crashing activity 3 - 4 by one more day.





Critical path = 1 - 2 - 3 - 4 - 5 = 4 + 3+ 5 +3 = 15 days
= 1 - 3 - 4 -5 = 7 + 5 + 3 = 15 days
Project cost = 1600 + 3500 + 1500 + 2800 + 4200 + 1800 + (15 x 450)
= ₹22150
For during critical path, activity 4-5 can be crashed by one day.


$\because$ Critical path duration = 1 - 2 - 3 - 4 - 5 = 4 +3 + 5 + 2 = 14 days
$\Rightarrow$ 1 - 3 - 5 Duration 14 days
$\Rightarrow$1 - 2 - 3 - 4 - 5 Duration 14 days
$\Rightarrow$1 -2 - 3 - 5 Duration 14 days
$\Rightarrow$ 1- 3 - 4 - 5 Duration 14 days
Total project cost = 1600 + 3500 + 1500 + 2800 + 4200 + 2400 + (14 + 450)
= ₹22300
Crashed critical path duration = 14 days
Crash project cost = ₹22300
Ans: Project cost is minimum for 15 days. So optimum cost is ₹22150 and optimum project duration is 15 days