The management of a factory is going to erect a maintenance building. Given the
ID: 432955 • Letter: T
Question
The management of a factory is going to erect a maintenance building. Given the following table of activities
and times, determine the critical path and duration.
What are the main concepts related to this problem?
Activity
Description
Predecessor
Duration (week)
A
Evacuate
---
2
B
Erect building
A
6
C
Install generator
A
4
D
Install tank
A
2
E
Install maintenance equipment
B
4
F
Connect generator to building
B,c,d
3
G
Paint on a finish
B
6
H
Check out facility
E,f
2
Activity
Description
Predecessor
Duration (week)
A
Evacuate
---
2
B
Erect building
A
6
C
Install generator
A
4
D
Install tank
A
2
E
Install maintenance equipment
B
4
F
Connect generator to building
B,c,d
3
G
Paint on a finish
B
6
H
Check out facility
E,f
2
Explanation / Answer
The precedence diagram of activities as follows :
A
B
C
D
G
E
F
H
The parallel paths and their corresponding durations as follows :
A-B-G = 2 + 6 + 6 = 14
A-B-E-H = 2 + 6 + 4 + 2 = 14
A-B-F-H = 2 + 6 + 3 + 2 = 13
A-C-F-H = 2 + 4 + 3 + 2 = 11
A-D-F-H = 2 + 2 + 3 + 2 = 9
Out of above , A-B-G as well as A-B-E-H have the longest duration and both of them are therefore the critical paths .
This problem is a typical example of Project management through Critical Path method. As per this method, the critical activities in a project are first identified. Critical activities are those which lie on critical path. Critical path is the set of activities which decide overall duration of the project and any delay in duration of any activity lying on critical path will delay overall duration of the project. Resources are therefore allocated in such a way so that such activities lying on critical path are not delayed at all.
The quantum of allowance by which any activity may get delayed is described as SLACK. Therefore activities lying on critical path would have ZERO slack.
The other paths ( which are not critical paths ) are called non critical paths. Activities on such paths have certain amount of slack . Any activity on this path may get delayed upto the value of corresponding slack and yet the overall project duration does not get affect. Once the delay exceeds the slack value only then the project duration gets affected.
It is therefore very important to clearly identify the critical and non critical activities with corresponding slack so that necessary planning and resources can be allocated to ensure smooth execution of the project.
A
B
C
D
G
E
F
H
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