3.3.3 Decision Trees

Decision trees

🔗 Mathematical models used to help managers make decisions based on the net gain, costs and likelihood of outcomes.

It helps businesses decide whether the net gain of a decision is worthwhile via estimates and probabilities.

How a decision tree is constructed

1. Draw out the initial two options.
2. Add possible outcomes.
3. Add on associated costs, probabilities and financial results of each option.
4. Calculate the best option based on net gain.

Model

Method to calculate the net gain

$$High sales: 1,000,000 x 0.6 = :highlight[£600,000]$$ $$Low sales: 750,000 x 0.4 = :highlight[£300,000]$$ $$Total = :highlight[£900,000]$$ $$900,000 – 500,000 = :highlight[£400,000] (Net gain of launching loyalty card)$$

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$$High sales: 800,000 x 0.8 = :highlight[£640,000]$$ $$Low sales: 500,000 x 0.2 = :highlight[£100,000]$$ $$Total = :highlight[£740,000]$$ $$740,000 – 300,000 = :highlight[£440,000] (Net gain of cutting prices)$$

The net gain for cutting prices is higher therefore cutting prices is the best option.

Pros and cons of Decision trees

• The use of probabilities enables the "risk" of the options to be addressed
• Considers costs, benefits as well as best- and worst-case scenario
• Easy to understand & set out in a logical way
• Probabilities are just estimating – always prone to error
• Uses quantitative data only – ignores qualitative aspects of decisions