The Department of Transportation has found that a proposed highway project is no
ID: 451246 • Letter: T
Question
The Department of Transportation has found that a proposed highway project is not going to be completed before the end of the summer. They have asked the contractor to prepare cost figures to shorten the project by up to 4 weeks.
The following table shows the Crashing Costs for each activity. For example, if you needed to shorten Activity 1-2 by 1 week this would cost $12. If you needed to shorten the same activity by 2 weeks it would cost $16. Note: If an activity lists a cost of $---, then this activity cannot be any shorter.
Activity
First Week
Second Week
Third Week
1-2
$12
$16
$ ---
2-5
6
8
10
5-7
7
8
11
7-11
7
11
---
11-13
4
8
10
1-3
12
14
19
3-8
5
---
---
8-11
12
13
14
3-9
14
16
16
9-12
8
8
10
12-13
7
11
---
1-4
10
14
18
4-6
12
14
18
6-10
11
12
---
10-12
14
15
---
Hint: Between 13 and 15
Note: For each week you are to include only the cost of shortening the activities in that particular week.
Activity
First Week
Second Week
Third Week
1-2
$12
$16
$ ---
2-5
6
8
10
5-7
7
8
11
7-11
7
11
---
11-13
4
8
10
1-3
12
14
19
3-8
5
---
---
8-11
12
13
14
3-9
14
16
16
9-12
8
8
10
12-13
7
11
---
1-4
10
14
18
4-6
12
14
18
6-10
11
12
---
10-12
14
15
---
Explanation / Answer
Activity times are mentioned in the question. Therefore the analysis is based on given cost data and the given list of activities.
Hint is given for activity 3-5 but this activity is not in the list. Similarly for 4th week Hint is between 13 and 15 but there is no activity 13--15.
As per given list of activities, the four paths are
1--2--5--7--11--13, 1--3--8--11--13, 1--3--9--12--13. and 1--4--6--10--12--13
For reducing the project completion duration, crashing of critical activities alone to be considered with the paths turning into critical paths.
Question is about reducing the project duration by 4(four) weeks as stated in the beginning but data is for 3weeks?
Activity First Week Second Week Third Week 1--2 12 16 -- 2--5 6 8 10 5--7 7 8 11 7--11 7 11 --- 11--13 4 8 10 1--3 12 14 19 3--8 5 --- --- 8--11 12 13 14 3--9 14 16 16 9--12 8 8 10 12--13 7 11 --- 1--4 10 14 18 4--6 12 14 18 6--10 11 12 --- 10--12 14 15 --- First week minimum cost is $ 4 for 11--13 Second week minimum cost is $8 for four activities Third week minimum cost is $10 for three activitiesRelated Questions
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