Unit 6: Business Management Toolkit — BMT 6 Decision Trees
What is a Decision Tree?
Decision Trees are analytical diagrams that map possible outcomes for business decisions. Each branch represents a choice or event, and the endpoints show resulting outcomes, costs, or benefits. This tool helps managers to visually compare alternatives and choose the most beneficial course of action.
Key Uses: Strategic planning, investment decisions, risk analysis, process improvements, project selection.
Structure of a Decision Tree
| Component | Description |
|---|---|
| Decision Node | Point where choices branch out (usually represented by a square) |
| Chance Node | Point where outcomes depend on probability (represented by a circle) |
| Branches | Possible courses of action or events |
| Outcome/Leaf | Final result, either benefit or cost, at the end of each path |
| Expected Value | Weighted average outcome, key for decision-making |
How to Create a Decision Tree
- Define the decision to be made and list all possible alternatives
- Map possible outcomes for each alternative, along with probabilities and payoffs
- Calculate expected values for each option
- Choose the option with the highest expected return or suitability
Expected Value Formula:
Expected\ Value = \sum_{i=1}^{n} (Probability_{i} \times Payoff_{i})
Where \(Probability_{i}\) is the chance of outcome \(i\), and \(Payoff_{i}\) is the profit/cost of that outcome.
Expected\ Value = \sum_{i=1}^{n} (Probability_{i} \times Payoff_{i})
Where \(Probability_{i}\) is the chance of outcome \(i\), and \(Payoff_{i}\) is the profit/cost of that outcome.
Worked Example
Scenario: Invest \$10,000 in Product A or Product B.
Product A: Success (60% chance; payoff \$18,000), Failure (40% chance; payoff \$5,000).
Product B: Success (50% chance; payoff \$19,000), Failure (50% chance; payoff \$9,000).
Product A: Success (60% chance; payoff \$18,000), Failure (40% chance; payoff \$5,000).
Product B: Success (50% chance; payoff \$19,000), Failure (50% chance; payoff \$9,000).
Product A Expected Value:
EV = 0.6 \times 18{,}000 + 0.4 \times 5{,}000 = \$12{,}800
Product B Expected Value:
EV = 0.5 \times 19{,}000 + 0.5 \times 9{,}000 = \$14{,}000
Decision: Choose Product B.
EV = 0.6 \times 18{,}000 + 0.4 \times 5{,}000 = \$12{,}800
Product B Expected Value:
EV = 0.5 \times 19{,}000 + 0.5 \times 9{,}000 = \$14{,}000
Decision: Choose Product B.
Benefits & Limitations
| Benefits | Limitations |
|---|---|
|
- Clarifies complex choices - Quantifies risk and reward - Justifies decisions and reduces bias |
- Assumes probabilities are known - Can become complicated with many branches - Subject to oversimplification if real-life variables are missed |
Conclusion
Decision trees are essential tools for business managers seeking structured, evidence-based decisions—especially when multiple outcomes and risks must be weighed.