Problem 5-17 For the network shown: -O --809 a a-1. Determine the critical path.

Question

Problem 5-17 For the network shown: -O --809 a a-1. Determine the critical path. O O O O A-B-D-G A-B-E-G A-C-E-G A-C-F-G a-2. Determine the early completion time in weeks for the project. Early completion time weeks For the data shown, reduce the project completion time by three weeks. Assume a linear cost per week shortened. NORMAL NORMAL CRASH CRASH ACTIVITY TIME COST TIME COST S 7.2004 $13,300 12,300 18.700 5,100 6 7.500 4,400 3 6,500 3.300 6.400 6,600 3 7,375 7.7002 9,800 OWL b-1. Which activities in order of reduction would be shortened? O O O O G-E-A D-B-C D-D-D B-G-D b-2. Find the resulting cost to crash. Resulting cost SO

Explanation / Answer

a-1) In the given diagram, there are 3 paths available to complete the given task. The paths and the time taken for each are as below:

time taken for path A-B-D-G = 8+ 12+7+4= 31 weeks

time taken for path A-C-E-G = 8+7+7+4= 26 weeks

time taken for path A-C-F-G= 8+7+4+4=23 weeks

Critical path is the maximum time needed to complete a task. Here, the maximum time is taken for path A-B-D-G which is 31 weeks. Hence, the right answer is option 1, A-B-D-G.

a-2) The early completion time is time taken by the critical path A-B-D-G, i.e 31 weeks.

b-1) The critical path is A-B-D-G.

After observing the critical path activities, we can see that the activity with minimum cost to crash per week is activity D. It has maximum allowable reduction of 4 weeks. So activity D will be reduced by 3 weeks. Since, our requirement is for reduction by 3 weeks only.This does not change the critical path and the critical path remains the same.

Step Activity Cost Weeks reduced

1 D 525 1

2 D 525 2

3 D 525 3

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Total $ 1575 3

b-1) Hence, activities to be shortened in the correct sequence are D-D-D.

b-2) The resulting cost to crash is $1,575.

ACTIVITY NORMAL TIME (NT) NORMAL COST (NC) CRASH TIME (CT) CRASH COST (CC) TOTAL ALLOWABLE CRASH TIME=NT-CT COST/WEEK= ((CC-NC)/(NT-CT)) A 8 $7200 4 $13,300 4 $1525 B 12 12,300 4 18,700 8 800 C 7 5100 6 7,500 1 2,400 D 7 4,400 3 6,500 4 525 E 7 3,300 3 6,400 4 775 F 4 6,600 3 7,375 1 775 G 4 7,700 2 9800 2 1050

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