Decision tree analysis

Key Points

• Visual model that maps decisions (squares) and uncertain events (circles) with branches for outcomes.
• Compares alternatives by calculating expected monetary value (EMV) and rolling back the tree from right to left.
• Useful for risk response selection, vendor choice, make-or-buy, and go/no-go decisions.
• Requires clear assumptions: probabilities that are complete and mutually exclusive, and monetized outcomes.
• Can include mitigation costs, residual risk, and value of information (e.g., paying for a test before deciding).
• Informs, but does not replace, judgment, risk appetite, and non-financial constraints.

Purpose of Analysis

Provide a structured, quantitative way to choose among alternatives under uncertainty by combining probabilities and impacts. It helps justify decisions, compare risk-adjusted costs or benefits, and communicate trade-offs transparently to stakeholders.

Method Steps

• Define the decision objective and whether you are minimizing cost or maximizing value.
• List feasible alternatives and decision criteria.
• Identify uncertain events and mutually exclusive states for each branch.
• Estimate probabilities using expert judgment, historical data, or models.
• Estimate monetary outcomes for each end path, including costs, benefits, penalties, and residual risk.
• Draw the tree with decision and chance nodes; annotate probabilities and payoffs.
• Compute EMV at each chance node by summing probability × payoff across branches.
• Roll back from right to left, selecting the branch with the best EMV at each decision node.
• Perform sensitivity analysis on key probabilities and impacts; consider utility or constraints if risk tolerance is a factor.
• Document assumptions, data sources, and rationale.

Inputs Needed

• Defined alternatives and decision criteria.
• Probability estimates for each state of uncertainty, including conditional probabilities when applicable.
• Impact estimates (costs, benefits, penalties, rework, savings).
• Costs and effects of risk responses or tests, and residual risk after responses.
• Time value of money assumptions (discount rate) for multi-period cash flows.
• Risk register entries, historical data, and expert judgment.
• Constraints, risk thresholds, and utility or preference considerations.

Outputs Produced

• Recommended alternative based on EMV and rollback results.
• EMV calculations for each path and a clear decision tree diagram.
• Sensitivity analysis results and break-even conditions.
• Documented assumptions, probabilities, and data sources.
• Optional: value of information metrics (EVPI/EVSI) to assess whether additional analysis or testing is worth the cost.

Interpretation Tips

• For cost-focused problems, choose the lowest expected cost; for value-focused problems, choose the highest EMV.
• Use consistent units by monetizing schedule or quality impacts where practical.
• Ensure probabilities are complete and appropriate (mutually exclusive and collectively exhaustive); handle conditional probabilities carefully.
• Consider risk appetite: EMV may not reflect stakeholder utility for one-time, high-impact risks.
• Run sensitivity tests to identify inputs that could flip the decision and to gauge robustness.
• Update the tree as new information arrives; revise probabilities rather than forcing outcomes.

Example

A team must select a vendor. Vendor A offers a fixed price of $300,000 with a 30% chance of a $50,000 delay penalty. Vendor B is time-and-materials with an expected base cost of $260,000 and a 40% chance of an $80,000 scope increase.

• Vendor A EMV (cost) = 300,000 + 0.30 × 50,000 = 315,000.
• Vendor B EMV (cost) = 260,000 + 0.40 × 80,000 = 292,000.
• Decision: Choose Vendor B because it has the lower expected cost.

Pitfalls

• Overprecision: assigning exact-looking numbers to weak estimates, creating false confidence.
• Incomplete or overlapping states that cause probabilities not to sum correctly.
• Ignoring correlations or double-counting risks across branches.
• Relying solely on EMV for single, high-impact decisions without considering utility or constraints.
• Omitting time value of money or lifecycle effects for multi-period outcomes.
• Overly complex trees that are hard to validate and explain to stakeholders.

PMP Example Question

A project manager is evaluating whether to implement a $40,000 mitigation that eliminates a 25% chance of a $200,000 failure. Using decision tree analysis, what should the PM recommend?

1. Implement mitigation because its expected cost (40,000) is lower than the expected failure cost (0.25 × 200,000 = 50,000).
2. Do not mitigate because it adds certain cost now.
3. Perform qualitative risk analysis first and postpone any decision.
4. Escalate the decision to the sponsor due to uncertainty.

Correct Answer: A — Implement mitigation because its expected cost is lower than the expected loss.

Explanation: Decision tree analysis compares EMVs; the mitigation has an EMV of 40,000, which is less than the 50,000 expected loss if the risk is accepted.