decision-trees

An introduction to decision trees

• A decision tree is a quantitative method of tracing the outcomes of a decision so that the most profitable decision can be identified

  •  Research-based estimates and probabilities are used to calculate likely outcomes

  • The net gain from a decision can be identified and used to consider whether an investment is worthwhile 

Advantages of using decision trees

• Constructing a decision tree diagram may reveal options that haven’t previously been considered

• Managers are forced to consider the risks associated with their choice, ahead of implementation

• The quantitative approach requires deep research to be carried out

Limitations of using decision trees

• Constructing decision trees that can support effective decision-making requires skill to avoid bias and it takes time to gather reliable data

• Estimates rarely take full account of external factors and cannot include all possible eventualities

• Qualitative elements such as human resource impacts are not considered, which may affect the probability of success of a decision

• The time lag between the construction of a decision tree diagram and the implementation of the decision affects the reliability of expected values

Constructing and interpreting decision trees

• The key elements in a decision tree diagram are

  • Decision points

  • Outcomes

  • Probabilities

  • Expected monetary values

A simple decision tree diagram

Decision points

• Points where decisions need to be made are called decision points and are represented by squares

  • Square A represents the fact that a choice is required on opening a new store or expanding the website

Outcomes

• Points where there are different outcomes are represented by circles called nodes

  • Circles B and C represent points at which the different options have a range of outcomes – success or failure

Probability

• The probability or likelihood of each outcome is shown on the diagram

  • A certain outcome has a probability of 1

  • An impossible outcome has a probability of 0

    • Opening a new store has a 0.7 probability of success and a 0.3 probability of failure

    • Expanding the website has a 0.6 probability of success and a 0.4 probability of failure

Monetary values

• The monetary value of each decision is based on the expected profit or loss of the outcome

  • If opening a new store is successful, a £420,000 profit is expected

  • If opening a new store is unsuccessful, a £24,000 loss is expected

  • If expanding the website is successful, a £480,000 profit is expected

  • If expanding the website is unsuccessful, a £32,000 loss is expected

Calculating expected monetary values

• To compare the options, a business should take into account the expected values of each decision presented in the decision tree diagram

• The following formula is used to calculate the expected monetary value of a decision

(Expected value of success x Probability) + (Expected value of failure x Probability)

• Using the example above, the expected value of opening a new store is

• Using the example above the expected value of expanding the website is

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