Determine optimum cost of optimum duration for the following data of a project .

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written 5.0 years ago by

Activity	Normal Duration $(N_T)$	Crash Duration $(C_T)$	Normal Cost $(N_C)$	Crash Cost $(C_C)$	Cost slope $\frac{C_c-N_c}{N_T-C_T}$
1-2	6	3	7000	14500	2500
1-3	8	5	4000	8500	1500
2-3	4	1	6000	9000	1000
2-4	5	3	8000	15000	3500
3-4	5	3	5000	11000	3000
4-5	7	4	8000	15000	2333.33
			38000

1st Iteration

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Critical path

$1)1,-2-3-4-5 = 6+4+5+7 = 22$

$2) 1-3-4-5 = 8+5+7 = 20 $

$3) 1-2-4-5 = 6+5+7 = 18$

Workout For Path $1-2-4-5$

$\therefore$ Project Duration = 22 Days

Total Project Cost =$38,000 + 22 \times 1000 = 60,000 Rs$

Critical Path	Critical Activity	Crash limit $(N_T-C_T)$	Cost slope
1-2-3-4-5	1-2	3	2500
	2-3	3	1000
	3-4	2	3000
	4-5	3	2333.33

2nd Iteration

Crash Activity by one only

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$1-2-3-4-5 = 6+3+5+7 = 21 \ days$

$1-3-4-5 = 8+5+7 = 20 \ day$

Project duration = 21 day

Cost = Previos Cost + Cost Slope - Indirect Cost

= $60000 + 1 \times 1000 - 1000 \times 1$

$Cost= 6000 \ Rs$

Critical Path	Critical Activity	Crash limit	Cost slope
1-2-3-4-5	1-2	3	2500
	2-3	2	1000
	3-4	2	3000
	4-5	3	2333.33

3rd Iteration

Crash activity 2-3 one day only

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$1-2-3-4-5 = 6+2+5+7 = 20$

$1-3-4-5 = 8+5+7=20$

Project Duration = 20 Day

$Cost = 60,000 + (1 \times 1000) - (1 \times 1000) = 60,000 \ Rs$

Critical Path	Critical Activity	Crash limit	Cost slope
1-2-3-4-5	1-2	3	2500
	2-3	2	1000
	3-4	2	3000
	4-5	3	2333.33
1-3-4-5	1-3	3	1500
	3-4	2	3000
	4-5	3	2333.33

4th Iteration

Crash Activity 1--3 and 2-3 by one only

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$1-2-4-5 = 6+5+7 = 18$

$1-3-4-5 = 7+5+7 = 19$

$1-2-3-4-5 = 6 + 1+5+7 = 19$

Project duration = 19 day

$Cost = 60,000 + (1 \times 1500 + 1 \times 1000) - (1 \times 1000) = 61,500 \ Rs$

Since the total cost of this Iteration Four is more than the previous Iteration.STOP The procedure and treat the solution of previous Iteration '3' Cost the best solution for optimization.The final Crash project duration is 20 Days and Optimum cost is 60,000 Rs,.

ADD COMMENT EDIT

Activity	1-2	1-3	2-3	2-4	3-4	4-5
National Duration(days)	6	8	4	5	5	7
Crash Duration (days)	3	5	1	3	3	4
Normal Cost (Rs).	7000	4000	6000	8000	5000	8000
Crash Cost ( Rs)	14500	8500	9000	15000	11000	15000