Figure Example: Critical Path Method and Decision Tree Analysis

PMBOK v8 Definition

The Critical Path Method (CPM) is a schedule network analysis technique used to identify the minimum project duration and determine the amount of schedule flexibility on logical network paths within the schedule model. A Decision Tree is a diagramming technique used to evaluate the expected value of alternative courses of action under conditions of uncertainty, where each branch represents a decision or chance event.

Why It Matters for the Exam

PMI exam questions frequently test your ability to calculate critical path duration and identify float values, as these are fundamental to schedule management. Decision tree analysis appears in risk management questions where you must calculate Expected Monetary Value (EMV) to compare alternative project decisions. Both concepts are tested through calculation-based and scenario-interpretation questions.

Key Points to Remember (for the exam)

• Critical Path Definition: The longest path through the project schedule network diagram, determining the shortest possible project duration

• Float Calculation: Total float = Late Start - Early Start (or Late Finish - Early Finish); critical path activities have zero float

• Critical Path Characteristics: Activities on the critical path cannot be delayed without delaying the project; there can be multiple critical paths

• Decision Tree Components: Decision nodes (squares), chance nodes (circles), branches (alternatives), and outcomes (payoffs/probabilities)

• Expected Monetary Value (EMV): EMV = Probability × Impact; sum all EMV values for each branch to compare alternatives

• Schedule Compression Application: Crashing or fast-tracking always focuses on critical path activities first

Typical PMI Exam Example

You are managing a construction project with activities A (5 days), B (3 days), C (4 days), D (6 days), E (2 days). The network shows A→B→D (5+3+6=14 days) and A→C→E (5+4+2=11 days). The critical path is A→B→D with 14 days duration. Activity C has 3 days total float (14-11=3). A question asks: "If activity B is delayed by 2 days, what is the new project duration?" Answer: 16 days (critical path becomes 5+5+6=16).

PMI Exam Traps

• Trap: Confusing critical path with the path having the most activities

• Reality: Critical path is the LONGEST duration path, not the path with the most activities

• Trap: Thinking float only exists on non-critical activities

• Reality: Critical path activities have ZERO float, but non-critical paths can have positive float

• Trap: Calculating EMV without multiplying probability by impact for each branch

• Reality: EMV requires multiplying the probability percentage (as decimal) by the monetary impact, then summing all branches

• Trap: Assuming decision trees only apply to risk responses

• Reality: Decision trees are used for general decision-making under uncertainty, including make-or-buy analysis and vendor selection

Important PMI Connections

Quick Review Questions

1. A project has four paths with durations of 12, 15, 18, and 14 days. What is the total float of the 14-day path?

2. In a decision tree, a chance node has two branches: Branch A has 40% probability with $50,000 gain, Branch B has 60% probability with $20,000 loss. What is the EMV of this decision?

3. If a critical path activity is delayed by 3 days, what happens to the project duration?

4. What is the difference between total float and free float on the critical path?

5. A decision tree shows a decision node with two alternatives: Option 1 has EMV of $15,000, Option 2 has EMV of $12,000. Which option should the project manager select?

PMBOK v8 Reference

Section 5.3 - Develop Schedule (Critical Path Method) Section 5.5 - Plan Risk Management (Decision Tree Analysis) Figure 5-4: Example of Critical Path Method Figure 5-5: Example Decision Tree