Welcome to Decision Trees!
Hi there! Have you ever had to make a tough choice where you weren't quite sure what the outcome would be? Maybe you were deciding whether to study for an extra hour or get some sleep, weighing up the chance of a better grade against the risk of being too tired to think.
Businesses face these "what-if" scenarios every day. Should they launch a new product? Should they enter a new market? To help them make these choices logically, they use a tool called a Decision Tree. This chapter will show you how to build them, crunch the numbers, and decide if they are actually helpful. Don't worry if the math looks a bit scary at first—we will break it down step-by-step!
1. What is a Decision Tree?
A Decision Tree is a mathematical model used to help managers make decisions by representing different choices and their possible outcomes in a diagram that looks like the branches of a tree. It is a quantitative decision-making tool, meaning it relies on numbers and data rather than just "gut feeling."
The Purpose of Decision Trees
The main goal is to help a business choose the path that is likely to provide the best economic outcome. It forces managers to account for risk and uncertainty by assigning probabilities to different events.
The Key Symbols
To read a decision tree, you only need to know two main shapes:
1. Decision Node (Square): This represents a point where a manager has to make a choice between different courses of action. The lines coming out of a square are the options available (e.g., "Build a large factory" or "Build a small factory").
2. Probability/Chance Node (Circle): This represents a point where the outcome is uncertain. The lines coming out of a circle are the possible results of a choice (e.g., "High demand" or "Low demand").
Section Summary: Decision trees are visual, numerical maps that help businesses compare different options by looking at costs, potential profits, and the likelihood of success.
2. Understanding the Numbers: Probabilities and Outcomes
Before we can calculate which path is best, we need to understand the two types of numbers found on the "branches" of the tree.
Probabilities
A probability is the likelihood of a specific outcome occurring. In your exam, these will be given as decimals (e.g., 0.6) or percentages (e.g., 60%).
The Golden Rule: The probabilities on the branches coming out of a single circle (chance node) must always add up to 1.0 (for decimals) or 100% (for percentages). If there is a 60% chance of success, there must be a 40% chance of failure.
Economic Outcomes (Payoffs)
At the very end of the branches, you will see a value. This is the Expected Return or the profit/loss the business expects to make if that specific path is taken.
Did you know? Probabilities are usually based on past data or expert opinions. If a business has launched ten similar products and six were successful, they might set the probability of success at 0.6.
3. Calculating the Tree: Step-by-Step
To find the best option, we calculate the Expected Value (EV) and then the Net Gain. We always work from right to left on the diagram.
Step 1: Calculate the Expected Value (EV)
The Expected Value is the average return the business would get from a choice, taking all probabilities into account. The formula is:
\( \text{Expected Value} = (\text{Probability 1} \times \text{Outcome 1}) + (\text{Probability 2} \times \text{Outcome 2}) \)
Step 2: Calculate the Net Gain
Just because an option has a high EV doesn't mean it's the best. You have to subtract the cost of making that choice (the initial investment).
\( \text{Net Gain} = \text{Expected Value} - \text{Initial Cost of Option} \)
A Real-World Example
Imagine "Burger World" is deciding whether to launch a Vegan Burger. It costs £100,000 to launch.
- There is a 0.7 (70%) chance it is a hit, making £300,000.
- There is a 0.3 (30%) chance it fails, making only £20,000.
1. Find the EV:
\( (0.7 \times 300,000) + (0.3 \times 20,000) = 210,000 + 6,000 = £216,000 \)
2. Find the Net Gain:
\( 216,000 - 100,000 = £116,000 \)
The Net Gain of £116,000 is the final number the manager uses to compare this burger launch to other options!
Common Mistake to Avoid: Many students forget to subtract the initial cost at the end! Always check if a choice has a cost attached to it before you finalize your answer.
4. Assessing Usefulness: Should Businesses Use Them?
Once you have the numbers, you need to evaluate how useful they actually are. In Business H431, evaluation is the key to high marks!
The Benefits (Importance)
- Forces Logical Thinking: Managers can't just guess; they have to actually consider the risks and costs of every option.
- Visual Clarity: It lays out a complex problem in a simple, easy-to-read diagram.
- Considers Risk: By using probabilities, it acknowledges that the future is not certain.
- Good for Comparison: It provides a single "Net Gain" figure for each option, making it easy to see which one is mathematically superior.
The Limitations (The "But..." Factors)
- Garbage In, Garbage Out: If the probabilities or the outcome figures are just "guesses," the final answer will be wrong. This is the biggest risk!
- Quantitative Only: Decision trees ignore qualitative factors. For example, a decision might have the highest Net Gain but might destroy the brand's reputation or upset the employees.
- Dynamic Environment: The external environment (like the economy or new laws) changes fast. A tree drawn today might be useless by the time the project starts.
- Bias: Managers might choose "optimistic" numbers to make their favorite project look better on the tree.
Section Summary: Decision trees are useful for logical, data-driven choices, but they are only as good as the data put into them. They should be used alongside other factors, not in isolation.
5. Quick Review & Tips for Success
Quick Review Box
- Squares = Decisions; Circles = Probabilities.
- Probabilities must sum to 1.0 or 100%.
- EV = Probability multiplied by the Outcome.
- Net Gain = EV minus the Initial Cost.
- Work from right to left.
How to answer "Should the business take this course of action?"
Don't worry if this seems tricky at first! Follow this checklist for your answer:
1. State the result: "Based on the decision tree, Option A has a higher Net Gain of £X compared to Option B."
2. Consider the Risk: "However, Option A also has a higher chance of a negative outcome (failure)."
3. Add Qualitative Factors: "The business must also consider how this choice affects their long-term objectives or their stakeholders, like their staff or the local community."
4. Question the Data: "How reliable are these probabilities? If they are just estimates, the manager should be cautious."
Memory Aid: Use the mnemonic "C.R.A.P." to evaluate any decision-making tool:
C - Accuracy of Costs/Data?
R - Reliability of Results?
A - Alternative options ignored?
P - People/Qualitative factors?