Decision Trees
A simple and visual way
of presenting
alternative options
when making a
decision, based on logic
and probability
Learning Objectives
• Define and identify the reasons for
constructing decision trees
• Interpret simple decision trees based
on a selection of scenarios
• Compare the benefits and drawbacks
of using decision trees to make
decisions
`````````````````````````
Pampered Pets is receiving a lot of complaints
from customers, unhappy about the quality
of pet food being sold. Pampered Pets’ sales
are falling rapidly.
The owner, Ben Canine, has been looking into
a change of supplier for his pet food and has
discovered that he has two choices:
•
•
Use a local supplier well-known for
manufacturing high-quality foods
Import cheaper, but consistent quality
pet foods from a supplier in France
If Ben doesn’t take any action, he estimates Pampered Pets will lose £5,000
of sales revenue this year…
So, how can he decide what to do?
Ben could construct
a
Here’s the first
option the business
DECISION TREE
could choose…
Buy local
A diagram setting out all the options available when
making a decision…
plus
an
estimate
of
their
This is a decision
likelihoodnode…
(chance) of occurring…
It indicates the
decision to be
made… more on
this later…
Let’s have a look HOW…
Success
Buy local
0.5
Failure
0.5
This is a chance
node…
It indicates that
there is a number
of possible
outcomes
And here,
expressed as
decimals, are the
chances of
success and
failure of the
options… in this
case it’s 50/50
£15,000
£ 6,000
These are the
predicted
financial
outcomes in
each case.
Success
Buy local
0.5
Failure
0.5
£15,000
£ 6,000
Import
Here’s the second
option the business
could choose…
Success
Buy local
0.5
Failure
0.5
Success
Import
0.7
Failure
0.3
Again, expressed as decimals,
are the chances of success
and failure of the options… in
this case it’s 70/30
£15,000
£ 6,000
£20,000
-£ 5,000
And, again, these are the
predicted financial outcomes
in each case.
Success
Here’s the
final option –
to do
nothing!
Buy local
0.5
Failure
0.5
Success
Import
0.7
Failure
0.3
Do nothing
£15,000
£ 6,000
£20,000
-£ 5,000
Success
Buy local
0.5
Failure
0.5
Success
Import
0.7
Failure
0.3
Do nothing
£15,000
£ 6,000
£20,000
-£ 5,000
And its predicted
financial outcome...
-£ 5,000
We can now calculate the
EXPECTED VALUE of the first
option:
0.5 x £15,000 =
0.5 x £ 6,000 =
Expected value
=
Success
Buy local
0.5
£15,000
EV =
£10,500
£7,500
£3,000
_______
£10,500
Failure
0.5
Success
Import
0.7
Failure
0.3
Do nothing
£ 6,000
£20,000
-£ 5,000
-£ 5,000
And we can also calculate the
EXPECTED VALUE of the second
option:
Success
Buy local
0.5
£15,000
EV =
£10,500
0.7 x £20,000 = £ 14,000
0.3 x -£ 5,000 = -£ 1,500
_______
Expected value =
£12,500
Failure
0.5
Success
Import
0.7
£ 6,000
£20,000
EV =
£12,500
Failure
0.3
Do nothing
-£ 5,000
-£ 5,000
Importing pet
food from
France generates
the higher
Expected Value
Success
Buy local
0.5
£15,000
EV =
£10,500
Failure
0.5
Success
Import
0.7
£ 6,000
£20,000
EV =
£12,500
Failure
0.3
The Expected Value of
doing nothing…
1.0 x -£ 5,000 = -£ 5,000
Do nothing
-£ 5,000
-£ 5,000
Decision Tree
Decision Node
Chance Node
Expected value
Let’s return to Pampered Pets.
As we saw, the option to import generates a
higher Expected Value than using a local
supplier or doing nothing.
But what if there’s a cost involved in
implementing a decision? (there usually is…)
• Buying from the local supplier will cost
£1,000
• Importing pet food from France will cost
£4,000
Does that change things?
Success
Buy local
0.5
£15,000
EV =
£10,500
NG =
£9,500
Failure
£1,000
0.5
Success
Import
0.7
£ 6,000
£20,000
EV =
£12,500
If we know costs, we can
calculate the NET GAIN of the
first option:
EV
Cost
Net Gain
£10,500
£ 1,000
_______
£ 9,500
£4,000
Failure
0.3
Do nothing
-£ 5,000
-£ 5,000
Success
Buy local
0.5
£15,000
EV =
£10,500
Failure
£1,000
NG =
£9,500
0.5
Success
NG =
£8,500
Import
0.7
£ 6,000
£20,000
EV =
£12,500
£4,000
0.3
And we can calculate the NET
GAIN of the second option:
EV
Cost
Net Gain
£12,500
£ 4,000
_______
£ 8,500
Failure
Do nothing
-£ 5,000
-£ 5,000
Success
Buy local
0.5
£15,000
EV =
£10,500
NG =
£9,500
Failure
£1,000
NG =
£9,500
0.5
Success
NG =
£8,500
Because the Net Gain is
higher for Buy Local, its
value is placed in the
decision node. And this is
the option to be chosen.
Import
0.7
£ 6,000
£20,000
EV =
£12,500
£4,000
Failure
0.3
Do nothing
-£ 5,000
-£ 5,000
Success
Buy local
0.5
£15,000
EV =
£10,500
Failure
£1,000
0.5
Success
NG =
£9,500
Import
0.7
£ 6,000
£20,000
EV =
£12,500
£4,000
Failure
0.3
Do nothing
-£ 5,000
Finally, single lines are
crossed through the
-£
less valuable options
5,000
So, by using a Decision Tree, Ben Canine has
worked out, in a logical way, that his best
course of action would be to use a local
supplier.
It’s a scientific approach to
decision-making…
The decision tree’s purpose has been
to help Ben to identify:
• When a decision has to be made
• The choices available
• The cost associated with each option
• The possible outcomes related to each
option
• The likelihood (probability of each option
occurring)
• The estimated financial result of each
option
Net Gain
Probability
Scientific Decision
Making
Expected value
A challenge… construct and interpret…
The Cleaning Fairy Ltd has an objective of growth.
The business owner, Kira Durrani, wonders whether she should
promote the business by:
• Sponsoring a local youth football team at a cost of £2,500
Or
• Hiring an expert to design a new webpage and set up a social
media presence at a cost of £3,500
Over to you…
The Cleaning Fairy Ltd has an objective of growth.
Draw up a decision tree based on the data in the table below:
High Growth
Option
Low Growth
Cost
Probability
Outcome
Probability
Outcome
Sponsor
football team
£2,500
0.3
£8,000
0.7
£6,000
Website and
social media
£3,500
0.6
£8,000
0.4
£4,000
Option
Cost
High Growth
Low Growth
Probability
Outcome
Probability
Outcome
Sponsor football
team
£2,500
0.3
£8,000
0.7
£6,000
Website and
social media
£3,500
0.6
£8,000
0.4
£4,000
Draw the decision tree
Calculate the Estimated Value and Net Value of each option…. Which option should The Cleaning Fairy choose?
Easy to understand
Too simplistic?
Costs and benefits
considered
Possibility of bias
Level of risk considered
Doesn’t reduce risk
Options considered at the
same time
Ignores qualitative factors
Logical
Probabilities are estimated
Benefits
Drawbacks
Learning Objectives
• Define and identify the reasons for
constructing decision trees
• Construct and interpret simple
decision trees based on a selection of
scenarios
• Compare the benefits and drawbacks
of using decision trees to make
decisions