Question 3 (11 points) Question 3 options: The Department of Transportation has
ID: 3112920 • Letter: Q
Question
Question 3 (11 points)
Question 3 options:
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
---
Currently the Length of the Project is
weeks.
Determine the costs to shorten the project.
1st Week Cost =
Hint: Between 5 and 10
2nd Week Cost =
3rd Week Cost =
4th Week Cost =
Hint: Between 13 and 16
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
---
10 10 12 6 13Explanation / Answer
Clearly from the figure ,it can be seen that the length of the longest path in the entire chain will be the duration of the project.
Thus, we will find the length of all the chains.
path 1-2-5-7-11-13 = 25 weeks
path 1-3-8-11-13 = 27 weeks
path 1-3-9-12-13 =25 weeks
path 1-4-6-10-12-13 = 28 weeks
Clearly path 1-4-6-10-12-13 is the longest path and hence it will define the duration of the project and hence the project duration currently is 28 weeks.
Clearly the longest path will also be the critical path ie ,the longest path will also be that most important path which if fails will fail the project.
Thus path 1-4-6-10-12-13 is the critical path.
Now , If we follow the critical path the entire project will be completed. Thus to reduce the project duration we need only to focus on reducing the duration of the critical path.
Hence to reduce the duratino of the project by 1 week ,we need to reduce the duration of the ciritcal path by 1 week.
Now ,we should reduce the duration of critical path in such a way that it impacts the sponsor of the project to the least level.Hence we should observe the cost of reduction of each task and select the task which has the least cost of duration reduction.
Thus for path 1-4-6-10-12-13 ,
1) .to reduce the duration by 1 week
We observe that least expensive task in this chain is path 12-13 ( $7 ).
The path 12-13 should be reduced by 1 week to reducr the duration of entire project by 1 week .
2). to reduce the duration by 2 weeks
We observe that least expensive task in this chain is path 12-13 ( $11 ).
The path 12-13 should be reduced by 2 weeks to reduce the duration of entire project by 2 weeks .
3). to reduce the duration by 3 weeks
We observe that least expensive task in this chain is path 1-4 or 4-6 ( $18 ).
The any of 1-4 or 4-6 should be reduced by 3 weeks to reduce the duration of entire project by 3 weeks .
4). Any of 1-4 or 4-6 can be chosen to reduce the project cost by 4 weeks.
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