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CPAA group of workers is involved in a building project. The table shows the activities involved. Each worker can perform any of the given activities.
Activity Preceding activity
Duration (days) Number of workers
A - 3 5B A 8 2C A 7 3D B, C 8 4E C 10 2F C 3 3G D, E 3 4H F 6 1I G, H 2 3
CPAComplete the activity network for the project.
8D
10E
3F
3G
2I
8
7C
B
3A
6H
Activity Preceding activity
Duration (days)
Number of workers
A - 3 5
B A 8 2
C A 7 3
D B, C 8 4
E C 10 2
F C 3 3
G D, E 3 4
H F 6 1
I G, H 2 3
CPAFind the earliest start time and the latest finish time and insert their values in the appropriate boxes.
Duration
3
8 8 3
3 6
210
7C
D
E
F
GB
IA
H
Earliest start time Latest finish time
0
3
3
11
10
10
20
13
23 25
23
23
20
20
1710
12
3
CPAFind the critical path and state the minimum completion time
Duration
3
8 8 3
3 6
210
7C
D
E
F
GB
IA
H
Earliest start time Latest finish time
0
3
3
11
10
10
20
13
23 25
23
23
20
20
1710
12
3
Critical Path: A C E G I and the minimum completion time is: 25 days
CPA
3
8 8 3
3 6
210
7
C
D
E
F
GB
IA
H
0
3
3
11
10
10
20
13
23 25
23
23
20
20
1710
12
3
Activity FloatB 1
D 1
F 4
H 4
Activities A, C, E, G and I are “critical” – they must start on time and end on time for the minimum completion time to be 25 days.
Some activities do not have to start exactly on time and finish exactly on time without affecting the minimum finish time. They have a "float".
Now we can draw a Gantt Chart or Cascade Diagram. This gives us another way of displaying how the activities can be completed. In addition, the diagram can help us to figure out how many workers may be needed to complete the project within the minimum time of 25 days.
CPA
3
8 8 3
3 6
210
7
C
D
E
F
GB
IA
H
0
3
3
11
10
10
20
13
23 25
23
23
20
20
1710
12
3
A C E G I
B
F
D
H
We can draw a Gantt Chart or Cascade Diagram
First set down the Critical Path
Now set down each activityIncluding the float
CPA
3
8 8 3
3 6
210
7
C
D
E
F
GB
IA
H
0
3
3
11
10
10
20
13
23 25
23
23
20
20
1710
12
3
A C E G I
B
F
D
H
We can “shuffle” the activities to determine how many workers are needed to complete the project.
Activity Number of workers
A 5
B 2
C 3
D 4
E 2
F 3
G 4
H 1
I 3
D
H
CPA
3
8 8 3
3 6
210
7
C
D
E
F
GB
IA
H
0
3
3
11
10
10
20
13
23 25
23
23
20
20
1710
12
3
A C E G I
B
F
D
H
This is for D2, but some UoM students might find it interesting. Add in the number of workers for each activity.
Activity Number of workers
A 5
B 2
C 3
D 4
E 2
F 3
G 4
H 1
I 35
42
3 2
3
4
1
3
Can you see that in order to complete the project on time at least 2 and at most 9 workers are needed.
CPA
3
8 8 3
3 6
210
7
C
D
E
F
GB
IA
H
0
3
3
11
10
10
20
13
23 25
23
23
20
20
1710
12
3
B D 42
F H3 1
A C E G I5 3 2 4 3
D2: We could draw a “Resource Histogram” to show exactly how many workers are needed on each day
CPA
3
8 8 3
3 6
210
7
C
D
E
F
GB
IA
H
0
3
3
11
10
10
20
13
23 25
23
23
20
20
1710
12
3
D2: So this is what the resource histogram looks like. It’s a handy diagram to show haw many worker are needed throughout the duration of the project.
CPA
3
8 8 3
3 6
210
7
C
D
E
F
GB
IA
H
0
3
3
11
10
10
20
13
23 25
23
23
20
20
1710
12
3
For D2 only. Use “resource levelling” to explain why the project will overrun if there are only 7 workers available at any one time. Which activities need to be delayed so that the project will be delayed with the minimum extra time. What is the minimum completion time now.
A B
CD
E
F
G
H
IB
E E
F
E
Activity F is the problem at day 11. Delay the start of D by 2 days, but because there a 1 day of float, this means that G and I are only delayed by 1 day. The new minimum completion time is 26 days. Activity Number of
workers
A 5
B 2
C 3
D 4
E 2
F 3
G 4
H 1
I 3
