Decision Trees

This section explains decision trees covering, the construct and interpretation of simple decision tree diagrams, the calculations and interpretations of figures generated by these techniques and the limitations of using decision trees. 

A decision tree is a popular quantitative decision-making tool used by businesses to make informed choices between different alternatives, especially when outcomes are uncertain. It involves mapping out the different decision paths, possible outcomes, and associated probabilities, along with their financial or other impacts. Decision trees help decision-makers visualise the various possible outcomes and choose the option with the best expected value.

In this section, we will explore how to construct and interpret simple decision tree diagrams, how to perform calculations and make interpretations based on these figures, and the limitations of using decision trees.

Construct and Interpret Simple Decision Tree Diagrams

A decision tree diagram is composed of nodes and branches:

1. Decision nodes (squares): Represent choices or decisions that the business must make.
2. Chance nodes (circles): Represent possible outcomes of each decision, with probabilities assigned to each possible outcome.
3. Branches: Connect the nodes and show the different alternatives and their respective outcomes or probabilities.
4. End nodes: Represent the final outcomes or payoffs of each decision path.

Step-by-Step Construction of a Simple Decision Tree

Let’s take an example of a business deciding whether to launch a new product.

Step 1: Identify the decision

The business needs to decide whether to launch or not launch the new product.

Step 2: Identify the possible outcomes

If the product is launched, there are two possible outcomes:

• The product is successful (with a 60% probability).
• The product is unsuccessful (with a 40% probability).

Step 3: Assign values to the outcomes

If the product is successful, the business expects a profit of £50,000.

If the product is unsuccessful, the business expects a loss of £20,000.

Step 4: Construct the decision tree

Here’s what the decision tree for this example would look like:

                        [Launch?]

                     /                    \

              [Success]        [Failure]

               60% £50,000   40% -£20,000

Calculations and Interpretations of Figures Generated by These Techniques

Once the decision tree is constructed, the next step is to calculate the expected monetary value (EMV) for each decision path. The EMV is calculated by multiplying the probability of each outcome by the payoff associated with it, then adding the results for each path.

Step 1: Calculate the EMV for each branch

For Success:

$$\text{EMV(Success)} = 60\% \times £50,000 = £30,000$$ 

For Failure:

$$\text{EMV(Failure)} = 40\% \times -£20,000 = -£8,000$$

Step 2: Calculate the EMV for the decision node The expected monetary value for the decision node is the sum of the EMVs of each branch:

$$\text{EMV(Launch)} = £30,000 + (-£8,000) = £22,000$$ 

Thus, the expected monetary value of launching the product is £22,000.

Interpretation of Results

• The expected monetary value (EMV) of £22,000 represents the average profit (or loss) the business can expect, taking into account both the potential profits and losses, and their respective probabilities.
• If the business has an alternative decision, such as not launching the product (which might have a known, fixed outcome such as zero profit), the business can compare the EMVs to decide which option offers the best return.

Limitations of Using Decision Trees

While decision trees are a useful tool for decision-making, they do have several limitations:

Simplification of Complex Decisions

• Decision trees simplify complex decisions by focusing on a limited number of choices and outcomes. In reality, many business decisions involve more complex factors, such as multiple decisions happening simultaneously or interconnected outcomes that cannot easily be represented in a tree structure.
• Example: A company might face a situation with multiple products, markets, and a range of factors (e.g. economic conditions, competitor reactions), which could make it difficult to represent all relevant decisions and their probabilities in a decision tree.

Reliance on Accurate Probabilities

• Decision trees rely heavily on probability estimates, which can often be subjective. Inaccurate or overly optimistic estimates of probabilities can lead to misleading results.
• Example: Estimating a 60% probability of success for a new product launch might be based on past experience, but if the market conditions change, the probability could be completely different.

Ignoring Qualitative Factors

• Decision trees focus primarily on quantifiable outcomes, such as monetary value, and tend to ignore qualitative factors such as brand reputation, customer satisfaction, or long-term strategic goals.
• Example: A decision tree may suggest launching a new product based on expected profit, but it might overlook the importance of brand image or customer loyalty, which could be impacted by a failed product launch.

Time-Consuming to Construct

• Constructing a decision tree can become time-consuming, especially when dealing with complex decisions with multiple variables, outcomes, and interdependencies.
• Example: For large, multi-national companies, constructing decision trees for every project or investment decision could require significant resources and effort, making the process less practical.

Linear Path Assumptions

• Decision trees assume that the decision-making process follows a linear path. This is not always the case, as decisions might evolve over time and might require revisiting or altering the decision tree as new information becomes available.
• Example: A company may find new information about customer preferences after a product launch, requiring a reassessment of the decision, which is not easily reflected in an initial decision tree.

Limited to Quantifiable Outcomes

• Decision trees are best suited to situations where the outcomes are measurable and quantifiable (e.g., financial outcomes). However, they are less effective when the outcomes are difficult to quantify, such as intangible benefits or risks.
• Example: In situations where customer loyalty or market reputation is a key factor, decision trees might fail to account for these intangible elements, making them less useful in certain strategic decisions.

Summary

Decision trees are a valuable tool for businesses to make decisions in uncertain environments, particularly when there are clear choices, probabilities, and quantifiable outcomes. They provide a structured approach to evaluating decisions, allowing businesses to visualise their options and calculate the expected monetary value of each alternative. However, decision trees have limitations, including reliance on accurate probability estimates, the simplification of complex decisions, and the exclusion of qualitative factors. Therefore, while decision trees can be a powerful tool, they should be used in conjunction with other decision-making techniques and a broader understanding of the decision context.