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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
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
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
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
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
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
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
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
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
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
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
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…
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.
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
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?
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
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)
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)
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)
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)
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).
Gantt diagrams and scheduling
Problem
Only four workers are available.
Is it possible to complete the project in the same amount of time?
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)
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)
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).
