Decision Tree Analysis for Build vs. Upgrade Plant Decision
PMBOK v8 Definition
Decision tree analysis is a data representation technique used to evaluate decisions under uncertainty by modeling alternative paths, each with associated probabilities and monetary outcomes. The technique calculates the Expected Monetary Value (EMV) for each decision branch by multiplying scenario probabilities by their net payoffs (revenue minus investment costs), then selecting the decision with the highest EMV. This is a key tool within the Cost Management knowledge area, specifically used for quantitative risk analysis and cost contingency estimation.
Why It Matters for the Exam
Decision tree analysis appears frequently on the PMI exam in questions that test your ability to calculate EMV and select the optimal decision among alternatives. You will encounter it in situational questions where a project manager must choose between investment options (e.g., build new vs. upgrade existing) under uncertain demand conditions. The exam tests both the calculation mechanics and the interpretation of results, including risk considerations.
Key Points to Remember (for the exam)
- Decision Node vs. Chance Node: Decision nodes (squares) represent choices the project manager controls; chance nodes (circles) represent uncertain events with known probabilities.
- Net Path Value Formula: For each branch, calculate Net Path Value = Payoff – Investment Cost (e.g., $200M – $120M = $80M for strong demand with new plant).
- EMV Calculation: EMV = Σ (Probability × Net Path Value) for all chance node branches under a decision (e.g., Build New Plant EMV = 0.60 × $80M + 0.40 × (–$30M) = $36M).
- Decision Rule: Select the decision branch with the highest EMV (e.g., Upgrade Plant at $46M > Build New Plant at $36M).
- Investment Cost Inclusion: Always subtract investment costs from payoffs before calculating EMV—this is a common exam trap.
- Risk Consideration: The decision with highest EMV may also represent the lowest risk; in the PMBOK example, Upgrade avoids the worst-case loss of –$30M.
- Output: The decision tree produces a recommended decision (the branch with highest EMV) and the associated EMV value.
Typical PMI Exam Example
A project manager must decide between building a new plant (invest $120M) or upgrading an existing plant (invest $50M). Strong demand (60% probability) yields $200M revenue for new plant, $120M for upgrade. Weak demand (40% probability) yields $90M for new plant, $60M for upgrade. The upgrade decision has EMV of $46M, which is higher than the new plant EMV of $36M. The PM recommends upgrading the existing plant.
PMI Exam Traps
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Trap: Forgetting to subtract investment costs from payoffs before calculating EMV
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Reality: Net Path Value = Payoff – Investment Cost; the EMV calculation uses net values, not gross revenues
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Trap: Adding probabilities across different decision branches (e.g., 60% + 40% = 100% for both options)
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Reality: Each decision branch has its own set of chance nodes with probabilities that sum to 100% independently
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Trap: Selecting the decision with the highest potential payoff without considering probability
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Reality: EMV weights payoffs by their probability of occurrence; the highest EMV may come from a lower payoff with higher probability
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Trap: Ignoring the "worst-case" outcome when comparing decisions
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Reality: The PMBOK explicitly notes that the upgrade decision "also represents the lowest risk, avoiding the worst-case possible outcome of a loss of $30M"
Important PMI Connections
| Related Concept | Relationship Type | Exam Attention Point |
|---|---|---|
| Quantitative Risk Analysis | Tool & Technique | Decision trees are used in Perform Quantitative Risk Analysis to model uncertain outcomes |
| Cost Contingency Reserve | Output | EMV results inform the size of contingency reserves for cost estimates |
| Expected Monetary Value (EMV) | Core Calculation | EMV is the primary output metric; compare EMV across decision branches |
| Risk Probability and Impact | Input | Each chance node requires probability and impact (monetary value) inputs |
Quick Review Questions
- In a decision tree, what is the formula for calculating Net Path Value for a given branch?
- A project has two options: Option A (invest $100M) with 70% chance of $300M revenue and 30% chance of $50M revenue; Option B (invest $40M) with 70% chance of $150M and 30% chance of $80M. Which option has the higher EMV?
- What does a decision node represent in a decision tree, and what does a chance node represent?
- Why might a project manager choose a decision with lower potential maximum payoff but higher EMV?
- When calculating EMV, what is the consequence of using gross revenue instead of net path value?
PMBOK v8 Reference
Section 5.2 – "Data Representation Techniques: Decision Tree Analysis" (Figure 5-5 and accompanying notes)