Decision Maths

1
Decision Maths

• Lesson 6 Resource Allocation

2
Notation

• Activities are represented by arcs.
• The nodes represent events.
• They can be specific points (dates) in a project.
• It is possible to refer to an activity by a
  unique pair of events i and j, ( i , j ).
• i represents the node (event) before the activity
  and j represents the node (event) after the
  activity.

3
Notation

• In the example below the activity A can be
  represented by the ordered pair ( 1 , 2 ).
• B ( 1 , 3 ) C ( 2 , 5 ) etc

4
Resource Allocation

• When Mr and Mrs Jaffrey go out together they get
  away more quickly than when Mr Jaffrey goes out
  on his own.

• Here are the activities involved.

5
Resource Allocation
6
Cascade (Gantt) Chart

• The example just shown illustrates how tasks can
  be made more efficient by careful planning.
• We have looked at illustrating problems using
  precedence networks.
• Another way to show the same information is by
  using a Cascade (Gantt) Chart.
• A Cascade Chart shows the information in the form
  of bars along a time scale.
• Hopefully you will see that they can be easier to
  interpret when allocating resources.

7
Cascade (Gantt) Chart

• We are now going to look at constructing a
  Cascade Chart.
• Through out the rest of this lesson we are going
  to be looking at the example below.
• A woman has an interview that she is running late
  for, and her two flat mates are going to help her
  get there on time.
• The table below shows the activities that need to
  be completed, their duration and the immediately
  preceding activities.

8
Cascade (Gantt) Chart

• The first thing to do is to construct a
  precedence network.
• Describe how to construct the network for the
  example.

9
Cascade (Gantt) Chart

• In the first chart the order of the activities is
  given by sorting on the i activity and then on
  the j.
• You must place the bars as far left as they will
  go.

2
1
Shower
10
Cascade (Gantt) Chart

• The rest of the activities will now be drawn,
  focusing first on all activities leaving node 1.
  Then Node 2 etc.
• They should be positioned as far left as possible.

2
1
Shower
0
5
15
20
25
30
35
40
45
10
Minutes
11
Cascade (Gantt) Chart

• Activity Dry hair cannot begin until Shower
  has finished.
• Dry hair is positioned as far left as it can go,
  so it starts at 3.
• A dotted line can be drawn to help show this
  relation between the two activities.

2
1
Shower
0
5
15
20
25
30
35
40
45
10
Minutes
12
Cascade (Gantt) Chart

• The bar for drying hair cannot be moved past the
  dotted line that joins iron and dress. If Drying
  Hair is delayed then it will affect Dress,
  Make-up
• The Critical activities are written in bold and
  the bars are shaded.

2
1
Shower
3
1
Iron Clothes
1
4
Fetch Car
Dry Hair
3
4
Dress, Make-up
4
5
Drive to interview
0
5
15
20
25
30
35
40
45
10
Minutes
13
Cascade (Gantt) Chart

• It is not as clear to see but activity Fetch
  car can be moved around until it reaches the
  activity Drive to interview
• If fetching the car takes longer then this will
  hold up driving to the Interview.

2
1
Shower
3
1
Iron Clothes
Fetch Car
3
2
Dry Hair
3
4
Dress, Make-up
4
5
Drive to interview
0
5
15
20
25
30
35
40
45
10
Minutes
14
Cascade (Gantt) Chart

• It is not as clear to see but activity Fetch
  car can be moved around until it reaches the
  activity Drive to interview
• If fetching the car takes longer then this will
  hold up driving to the Interview.

2
1
Shower
1
3
Iron Clothes
Fetch Car
3
2
Dry Hair
3
Dress, Make-up
Drive to interview
0
5
15
20
25
30
35
40
45
10
Minutes
15
Cascade (Gantt) Chart

• An alternative way of drawing a Cascade Chart is
  to group all of the critical activities in one
  bar. With the other activities as separate bars.
• The dotted lines can be drawn to show the float
  available.
• It is clear to see here that fetching the car has
  a lot of float until it reaches 22 minutes.

A
B
D
E
F
16
Cascade (Gantt) Chart

• Finally we could draw the chart from the point of
  view of each of the three people involved in the
  activities. Showing their responsibility
  throughout.
• We already know that there is a lot of float
  involved in fetching the car.
• We can also see that this activity could in fact
  be done by person 2.
• Person 3 is surplus to requirements. This is a
  valuable tool when allocating resources.

Person 3
Person 2
Person 1
17
Resource Histogram

• From the cascade it is a simple matter to draw a
  resource histogram to show the number of people
  required at any given time.

18
Resource Histogram

• As was shown on a previous slide the activity
  fetch the car can actually be done after person
  2 has ironed the clothes.
• In this case the resource histogram would look
  like this.

19
Resource Levelling

• Resource levelling is the process of making your
  project more efficient.
• There are three main objectives that can be
  looked at.
• Can you guess three areas that you might like to
  focus on?
• 1 Minimise total time
• This is typically the case with maintenance. If
  you have a piece of vital equipment that you
  don't want out of action for too long. An
  aeroplane or a heating system.
• Using extra resources to reduce completion time
  is known as crashing a network.

20
Resource Levelling

• 2 Minimise total cost
• When time is not a factor, you have the luxury of
  minimising cost. For example things that are
  required in the summer can be repaired through
  the winter.
• 3 Make max use of resources (people and
  equipment)
• If you need to work with a fixed team of workers,
  or if you want to avoid hiring two cement mixers
  when, with careful planning, one will do, then
  this kind of planning is appropriate.