1. Lesson Objective
Understand Cascade diagrams and be able to use them to draw resource histograms

2. Immediately preceding activities
Activity
Immediately preceding activities
duration A
Shower - 3 B
Dry hair 8 C
Fetch car 7 D
Iron clothes 12 E
Dress and make-up
B,D 10 F
Drive to interview
C,E 20
If you remember Jane could make her interview (in 50 mins time) by using her friends to do other tasks.
Does she need both friends in order to complete on time? 3 4 2
B(8)
A(3) 42 12
D(12) 1 3 5
E(10)
F(20)
C(7) 4 22

3. Immediately preceding activities
Activity
Immediately preceding activities
duration A
Shower - 3 B
Dry hair 8 C
Fetch car 7 D
Iron clothes 12 E
Dress and make-up
B,D 10 F
Drive to interview
C,E 20
An alternative way to represent this information is in a Cascade diagram. This is very useful when deciding the allocation of resources (people in this case) to solve the problem. A B C D E F 10 20 30 40

4. Immediately preceding activities
Activity
Immediately preceding activities
duration A
Shower - 3 B
Dry hair 8 C
Fetch car 7 D
Iron clothes 12 E
Dress and make-up
B,D 10 F
Drive to interview
C,E 20
An alternative way to represent this information is in a Cascade diagram. This is very useful when deciding the allocation of resources (people in this case) to solve the problem. A B C D E F 10 20 30 40

5. Immediately preceding activities
Activity
Immediately preceding activities
duration A
Shower - 3 B
Dry hair 8 C
Fetch car 7 D
Iron clothes 12 E
Dress and make-up
B,D 10 F
Drive to interview
C,E 20
An alternative way to represent this information is in a Cascade diagram. This is very useful when deciding the allocation of resources (people in this case) to solve the problem. A B C D E F 10 20 30 40

6. Immediately preceding activities
Activity
Immediately preceding activities
duration A
Shower - 3 B
Dry hair 8 C
Fetch car 7 D
Iron clothes 12 E
Dress and make-up
B,D 10 F
Drive to interview
C,E 20 A B C D E F 10 20 30 40 4 3 2 D C 1 A B E F 10 20 30 40

7. Christmas dinner – Cascade exercise (Ch4 D1)
A Prepare the Turkey Crown – 5 mins
B Cook the Turkey – 70 mins A
C Peel the potatoes – 7 mins
D Peel the carrots – 3 mins
E Boil the carrots – 12 mins D
F Prepare the Brussel sprouts – 2 mins
G Boil the Sprouts – 12 mins F
H Boil the potatoes – 20 mins C
I Roast the potatoes in the oven – 40 mins H
J Make the Yorkshire batter – 8 mins
K Cook the Yorkshire puddings – 25 mins J
L Boil the kettle – 4 mins
M Make the Gravy – 3 mins L
N Set the table – 10 mins
O Pour the “drinks” – 5 mins N
P Serve the dinner – 5 mins B E G I K M

8. 2 9 3 4 1 10 11 5 Activities Interfering Float C H I 8 D E 60 F G 61
B70 4 D3
E12 P5 1 10 11 5
G12 F2 J8
K25
Activities
Interfering Float
C H I 8
D E 60
F G 61
J K 42
L M 68
N O 65 6 M3 O5 L4
N10 7 8

9. D E F G J K N O C H I L M A B P 40 20 60 80
What if you didn’t need to stand with the “cooking” but could multi-task?

10. D E F G J K N O C H I L M A B P 40 20 60 80 E G K H I B A C D F J N O L M P 40 20 60 80

11. Cascade 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 E 1 F G 7
C, D, E
Draw a Cascade diagram for this sequence of activities.

12. Cascade diagrams - Example 1
Initially, put all tasks at their earliest possible time. A B
A, B and C can all start at time zero. C D E F G
Hours 2 4 6 8 10 12 14 16

13. Cascade diagrams - Example 1
D can start immediately after A finishes. A B C D E F G
Hours 2 4 6 8 10 12 14 16

14. Cascade diagrams - Example 1
E and F can start immediately after B finishes. A B C D E F G
Hours 2 4 6 8 10 12 14 16

15. Cascade diagrams - Example 1
G is dependent on C, D and E, so it can start after D finishes. A B C D E F G
Hours 2 4 6 8 10 12 14 16

16. Cascade diagrams - Example 1B C D E F G
Hours 2 4 6 8 10 12 14 16
Problem 1
A and B both require the use of the same piece of equipment. Can the project still be completed in 15 hours?

17. Cascade diagrams - Example 1
At present, A and B are both scheduled at the same time. A B
Since A is a critical activity, moving A would result in the project being delayed. C D
Moving B means that E and F must also move. E F G
Hours 2 4 6 8 10 12 14 16
A and B both require the use of the same piece of equipment. Can the project still be completed in 15 hours?

18. Cascade diagrams - Example 1
The project can still be completed in 15 hours. A B C D E F G
Hours 2 4 6 8 10 12 14 16
A and B both require the use of the same piece of equipment. Can the project still be completed in 15 hours?

19. Cascade diagrams - Example 1B C D E F G
Hours 2 4 6 8 10 12 14 16
Problem 2
In addition 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?

20. Cascade diagrams - Example 1
At present, A and C are scheduled at the same time. A B
Again, as A is a critical activity, it is probably better to move C. C
C can fly over the first dotted line, since neither E nor F depend on C, but G does depend on C. D E F G
Hours 2 4 6 8 10 12 14 16
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?

21. Cascade diagrams - Example 1
At present, A and C are scheduled at the same time. A B
Again, as A is a critical activity, it is probably better to move C. C
C can fly over the first dotted line, since neither E nor F depend on C, but G does depend on C. D E F G
Hours 2 4 6 8 10 12 14 16
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?

22. Cascade diagrams - Example 1
The project can be completed in 16 hours. A B C D E F G
Hours 2 4 6 8 10 12 14 16
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?

23. 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.
Task
Duration
Immediate predecessors
Number of workers A 2 - B 3 1 C 5 D 6
A, B E 8 F G 4
D, E
How many workers are needed if all activities are scheduled to start as early as possible?

24. Cascade diagrams and resource histograms
Initially, put all tasks at their earliest possible time.
(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

25. Cascade diagrams and resource histograms
D must start after both A and B have finished
(2) B
(1) C
(2) D
(2) E F G
Days 2 4 6 8 10 12 14 16

26. Cascade diagrams and resource histograms
E and F must both start after C has finished
(2) B
(1) C
(2) D
(2) E
(2) F
(2) G
Days 2 4 6 8 10 12 14 16

27. Cascade diagrams and resource histograms
G must start after both D and E have finished
(2) B
(1) C
(2) D
(2) E
(2) F
(2) G
(2)
Days 2 4 6 8 10 12 14 16

28. Cascade diagrams and resource histograms
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 4 2 6 8 10 12 14 16
This shows that 6 workers are required

29. 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?

30. Cascade diagrams and resource histograms
We need to move some tasks so that only four workers are needed at any given time.
(1)
(2)
(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

31. Cascade diagrams and resource histograms
The resource histogram is changed to show this new arrangement.
(2)
(1)
(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

32. Cascade diagrams and resource histograms
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

33. Cascade diagrams and resource histograms
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

34. 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?

35. Cascade diagrams and resource histograms
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

36. Cascade diagrams and resource histograms
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 4 2 6 8 10 12 14 16 18

37. Cascade diagrams and resource histograms
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
(1)
(2) D
(1) E F G
(2)
Days 2 4 6 8 10 12 14 16 18 4 2 6 8 10 12 14 16 18

38. Cascade diagrams and resource histograms
The resource histogram changes
(1)
(2) B C D E F G
Days 2 4 6 8 10 12 14 16 18 4 2 6 8 10 12 14 16 18

39. Cascade diagrams and resource histograms
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 4 2 6 8 10 12 14 16 18

40. Cascade diagrams and resource histograms
The resource histogram changes again …
(2) B
(1)
… and this time it shows that the project can be completed using 3 people in 19 days. C
(2) D
(1) E
(2) F
(1) G
(2)
Days 2 4 6 8 10 12 14 16 18 4 2 6 8 10 12 14 16 18

41. Resource levelling is usually based on:
Minimising the total time - sometimes adding in extra resources can speed things up (this is called Network Crashing)
Minimising the total cost - sometimes there’s plenty of time so using fewer resources over a longer period makes sense (eg Renovating a hotel in the closed season)
Making a maximum use of resources (people or equipment) – if you work with a fixed team of people you need to keep them occupied at a steady rate.
Do Exercise 4B page 115