d1,l8 critical path gantt diagrams
TRANSCRIPT
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Gantt diagrams – Example 1
The table below shows the tasks involved in a project, with their durations and immediate predecessors.
Task Duration Immediate predecessors
A 3 -
B 4 -
C 6 -
D 5 A
E 1 B
F 6 B
G 7 C, D, E
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Gantt diagrams – Example 1
The precedence network for this project, shown below, was found in Section 1.
A(3)
C(6)
B(4) E(1)
3
D(5)
F(6)
G(7)0
3
4
8
15 15
8
7
3
0
1
2
4
5
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Gantt diagrams - Example 1
2 4 6 8 10 12 14 16 Hours
The critical activities, A, D and G are placed at the top of the chart.
A D G
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Gantt diagrams - Example 1
The earliest that activity B can start is at time 0, and the latest that it can finish is at time 7.
2 4 6 8 10 12 14 16 Hours
A D G
B
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Gantt diagrams - Example 1
The earliest that activity C can start is at time 0, and the latest that it can finish is at time 8.
2 4 6 8 10 12 14 16 Hours
A D G
B
C
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Gantt diagrams - Example 1
The earliest that activity E can start is at time 4, and the latest that it can finish is at time 8.
E
2 4 6 8 10 12 14 16 Hours
A D G
B
C
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Gantt diagrams - Example 1
The earliest that activity F can start is at time 4, and the latest that it can finish is at time 15.
E
2 4 6 8 10 12 14 16 Hours
A D G
B
C
F
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Gantt diagrams – Example 1
A and B both require the use of the same piece of equipment. Can the
project still be completed in 15 hours?
Problem 1
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Gantt diagrams - Example 1
At present, A and B are both scheduled at the same time.
Since A is a critical activity, moving A would result in the project being delayed.
Moving B means that E and F must also move.
2 4 6 8 10 12 14 16 Hours
A D G
C
E
B
F
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Gantt diagrams - Example 1
The project can still be completed in 15 hours.
2 4 6 8 10 12 14 16 Hours
A D G
C
E
B
F
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Gantt diagrams – Example 1
A and C must both be done by a qualified person. There is only one qualified person available. Can the
project still be completed in 15 hours?
Problem 2
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Gantt diagrams - Example 1
At present, A and C are scheduled at the same time.
Again, as A is a critical activity, it is better to move C.
Neither E nor F depend on C, but G does depend on C.
2 4 6 8 10 12 14 16 Hours
A D G
C
E
B
F
C can be moved by two hours…
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Gantt diagrams - Example 1
2 4 6 8 10 12 14 16 Hours
A D G
C
E
B
F
At present, A and C are scheduled at the same time.
Again, as A is a critical activity, it is better to move C.
Neither E nor F depend on C, but G does depend on C.
C can be moved by two hours…
but if it moves a further hour to avoid overlap with A, then G must also move.
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Gantt diagrams - Example 1
The project can be completed in 16 hours.
2 4 6 8 10 12 14 16 Hours
A D G
C
E
B
F
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Gantt diagrams and scheduling
The table below shows the tasks involved in a project, with their durations, immediate predecessors and number of workers required.
Task Duration Immediate predecessors
Number of workers
A 2 - 2
B 3 - 1
C 5 - 2
D 6 A, B 2
E 8 C 2
F 2 C 2
G 4 D, E 2
How many workers are needed if all activities are scheduled to start as early as possible?
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Gantt diagrams and scheduling
The precedence network shown below was found in Section 1.
A(2)
B(3)
D(6)
2
3G(4)
C(5) E(8)
F(2)
0
2
3
5
13
17 17
13
5
7
7
0
65
4
1
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Gantt diagrams and scheduling
2 4 6 8 10 12 14 16 Days
Put the critical activities along the top.
C (2) E (2) G (2)
(The numbers in brackets show the number of workers required)
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Gantt diagrams and scheduling
2 4 6 8 10 12 14 16 Days
The earliest start time for activity A is at time 0, and the latest finish time is at time 7.
C (2) E (2) G (2)
A (2)
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Gantt diagrams and scheduling
2 4 6 8 10 12 14 16 Days
The earliest start time for activity B is at time 0, and the latest finish time is at time 7.
C (2) E (2) G (2)
A (2)
B (1)
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Gantt diagrams and scheduling
2 4 6 8 10 12 14 16 Days
The earliest start time for activity D is at time 3, and the latest finish time is at time 13.
C (2) E (2) G (2)
A (2)
B (1)
D (2)
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Gantt diagrams and scheduling
2 4 6 8 10 12 14 16 Days
The earliest start time for activity F is at time 5, and the latest finish time is at time 17.
C (2) E (2) G (2)
A (2)
B (1)
D (2)
F (2)
If this schedule is used, 6 workers are needed. (6 are needed on days 6 and 7).
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Gantt diagrams and scheduling
Problem
Only four workers are available.
Is it possible to complete the project in the same amount of time?
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Gantt diagrams and scheduling
We need to move some tasks so that only four workers are needed at any given time.
At present 5 workers are needed for the first two days. Task B can be moved so that it starts after A has finished. This means that D must also move.
2 4 6 8 10 12 14 16 Days
C (2) E (2) G (2)
A (2)
B (1)
D (2)
F (2)
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Gantt diagrams and scheduling
We need to move some tasks so that only four workers are needed at any given time.
At present 6 workers are needed for days 6 and 7. Task F can be moved so that it starts after D has finished.
2 4 6 8 10 12 14 16 Days
C (2) E (2) G (2)
A (2)
B (1)
D (2)
F (2)
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Gantt diagrams and scheduling
Now only four workers are needed at any given time.
2 4 6 8 10 12 14 16 Days
C (2) E (2) G (2)
A (2)
B (1)
D (2)
F (2)
Workers 1 and 2 could do activities C, E and G.
Worker 3 could do A, B, D and F
Worker 4 could do A, D and F (with 3 days off between A and D).