Study Notes
Decision Trees
- Level:
- AS, A-Level
- Board:
- AQA, Edexcel, OCR, IB
Last updated 22 Mar 2021
A decision tree is a mathematical model used to help managers make decisions.
- A decision tree uses estimates and probabilities to calculate likely outcomes.
- A decision tree helps to decide whether the net gain from a decision is worthwhile.
Let's look at an example of how a decision tree is constructed. We'll use the following data:
![](https://tutor2u-net.imgix.net/subjects/business/diagrams/decision-tree-example-datatable.png?auto=compress%2Cformat&fit=clip&q=80&w=800)
A decision tree starts with a decision to be made and the options that can be taken. Don't forget that there is always an option to decide to do nothing!
![](https://tutor2u-net.imgix.net/subjects/business/diagrams/decision-tree-example-tree.png?auto=compress%2Cformat&fit=clip&q=80&w=800)
The first task is to add possible outcomes to the tree (note: circles represent uncertain outcomes)
![](https://tutor2u-net.imgix.net/subjects/business/diagrams/decision-tree-stage1.png?auto=compress%2Cformat&fit=clip&q=80&w=800)
Next we add in the associated costs, outcome probabilities and financial results for each outcome.
These probabilities are particularly important to the outcome of a decision tree.
Probability is
- The percentage chance or possibility that an event will occur
- Ranges between 1 (100%) and 0
- If all the outcomes of an event are considered, the total probability must add up to 1
![](https://tutor2u-net.imgix.net/subjects/business/diagrams/decision-tree-stage2.png?auto=compress%2Cformat&fit=clip&q=80&w=800)
Finally we complete the maths in the model by calculating:
Expected value:
The financial value of an outcome calculated by multiplying the estimated financial effect by its probability
Net gain:
The value to be gained from taking a decision.
Net gain is calculated by adding together the expected value of each outcome and deducting the costs associated with the decision.
![](https://tutor2u-net.imgix.net/subjects/business/diagrams/decision-tree-stage3.png?auto=compress%2Cformat&fit=clip&q=80&w=800)
Let's look at the calculations. What do they suggest is the best option?
Option: Launch loyalty card:
High sales: (0.6 x £1,000,000) = £600,000
Low sales: (0.4 x £750,000) = £300,000
Total expected value = £900,000
Net gain: £900,000 - £500,000 = £400,000
Option: Cut prices:
High sales: (0.8 x £800,000) = £640,000
Low sales: (0.2 x £500,000) = £100,000
Total expected value = £740,000
Net gain: £740,000 - £300,000 = £440,000
Both options indicate a positive net gain, suggesting that either would be better than doing nothing.
However, cutting prices has a slightly higher net gain & looks the best option of the two considered.
BENEFITS OF USING DECISION TREES
- Choices are set out in a logical way
- Potential options & choices are considered at the same time
- Use of probabilities enables the “risk” of the options to be addressed
- Likely costs are considered as well as potential benefits
- Easy to understand & tangible results
DRAWBACKS OF USING DECISION TREES
- Probabilities are just estimates – always prone to error
- Uses quantitative data only – ignores qualitative aspects of decisions
- Assignment of probabilities and expected values prone to bias
- Decision-making technique doesn’t necessarily reduce the amount of risk
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