Cascade diagrams and resource histograms

1
Cascade diagrams and resource histograms
The table below shows the tasks involved in a
project, with their durations, immediate
predecessors and number of workers required.
How many workers are needed if all activities are
scheduled to start as early as possible?
2
Cascade diagrams and resource histograms
Initially, put all tasks at their earliest
possible time.
A
(2)
B
(1)
A, B and C can all start at time zero.
C
(2)
D
E
F
G
Days
2
4
6
8
10
12
14
16
3
Cascade diagrams and resource histograms
D must start after both A and B have finished
A
(2)
B
(1)
C
(2)
D
(2)
E
F
G
Days
2
4
6
8
10
12
14
16
4
Cascade diagrams and resource histograms
E and F must both start after C has finished
A
(2)
B
(1)
C
(2)
D
(2)
E
(2)
F
(2)
G
Days
2
4
6
8
10
12
14
16
5
Cascade diagrams and resource histograms
G must start after both D and E have finished
A
(2)
B
(1)
C
(2)
D
(2)
E
(2)
F
(2)
G
(2)
Days
2
4
6
8
10
12
14
16
6
Cascade diagrams and resource histograms
A
You can now use the cascade diagram to construct
a resource histogram showing the number of
workers needed on each day
(2)
B
(1)
C
(2)
D
(2)
E
(2)
F
(2)
G
(2)
Days
2
4
6
8
10
12
14
16
This shows that 6 workers are required
7
Cascade diagrams and resource histograms
Problem 1
Only four workers are available. Is it possible
to complete the project in the same amount of
time?
8
Cascade diagrams and resource histograms
A
We need to move some tasks so that only four
workers are needed at any given time.
(2)
B
C
(2)
Task B can be moved so that it starts after A has
finished. This means that D must also move.
D
E
(2)
F
(2)
G
(2)
Days
2
4
6
8
10
12
14
16
6
4
2
2
4
6
8
10
12
14
16
9
Cascade diagrams and resource histograms
A
The resource histogram is changed to show this
new arrangement.
(2)
B
C
(2)
D
E
(2)
F
(2)
G
(2)
Days
2
4
6
8
10
12
14
16
6
6 workers are still needed
4
2
2
4
6
8
10
12
14
16
10
Cascade diagrams and resource histograms
A
Task F can be moved forward to start after D
finishes.
(2)
B
(1)
C
(2)
D
(2)
E
(2)
F
(2)
G
(2)
Days
2
4
6
8
10
12
14
16
6
4
2
2
4
6
8
10
12
14
16
11
Cascade diagrams and resource histograms
A
The resource histogram changes again.
(2)
B
(1)
C
(2)
D
(2)
E
(2)
F
(2)
G
(2)
Days
2
4
6
8
10
12
14
16
6
Now only 4 workers are needed.
4
2
2
4
6
8
10
12
14
16
12
Cascade diagrams and resource histograms
Problem 2
Only three workers are now available. However,
both tasks D and F can be done by one person, but
taking double the amount of time. What is the
shortest possible time in which the project can
be completed?
13
Cascade diagrams and resource histograms
A
This is the new cascade diagram, with D and F
done by one person taking twice as long.
(2)
B
(1)
C
(2)
D
(1)
E
(2)
F
(1)
G
(2)
Days
2
4
6
8
10
12
14
16
18
14
Cascade diagrams and resource histograms
A
A new resource histogram is needed.
(2)
B
(1)
C
(2)
D
(1)
E
(2)
F
(1)
G
(2)
Days
2
4
6
8
10
12
14
16
18
15
Cascade diagrams and resource histograms
A
Since BDG is now the critical path, it is
probably best to try moving C. This means that E
and F must also move.
(2)
B
(1)
C
D
(1)
E
F
G
(2)
Days
2
4
6
8
10
12
14
16
18
16
Cascade diagrams and resource histograms
A
The resource histogram changes
B
C
D
E
F
G
Days
2
4
6
8
10
12
14
16
18
17
Cascade diagrams and resource histograms
A
Another change is needed. F is not required for
any other task, so it can be moved later.
(2)
B
(1)
C
(2)
D
(1)
E
(2)
F
(1)
G
(2)
Days
2
4
6
8
10
12
14
16
18
18
Cascade diagrams and resource histograms
A
The resource histogram changes again
(2)
B
and this time it shows that the project can be
completed using 3 people in 19 days.
(1)
C
(2)
D
(1)
E
(2)
F
(1)
G
(2)
Days
2
4
6
8
10
12
14
16
18