Intro to Project Management: Project Risk Management Quantitative Analysis Sensitivity Analysis Tornado Diagram Expected Monetary Value EMV Decision Trees Monte Carlo Simulation

What This Is

Quantitative Analysis is a set of techniques used to evaluate and manage project risks, costs, and outcomes. It helps project managers make informed decisions by analyzing various scenarios and outcomes. For example, consider building a new highway. A project manager uses Quantitative Analysis to determine the best route, considering factors like cost, traffic flow, and environmental impact.

Key Terms & Formulas

• Sensitivity Analysis: A technique to analyze how changes in input variables affect project outcomes.
• Tornado Diagram: A graphical representation of sensitivity analysis, showing the most critical input variables.
• Expected Monetary Value (EMV): The expected value of a decision, calculated by multiplying the probability of each outcome by its monetary value.
• Decision Trees: A visual representation of possible decisions and their outcomes, used to evaluate and compare different options.
• Monte Carlo Simulation: A statistical technique to model and analyze complex systems by generating multiple random scenarios.
• Expected Value (EV): The average value of a decision, calculated by multiplying the probability of each outcome by its monetary value.
• Probability Distribution: A mathematical representation of the likelihood of different outcomes.
• Confidence Interval: A range of values within which a parameter is likely to lie.
• Standard Deviation (σ): A measure of the spread of a probability distribution.
• Coefficient of Variation (CV): The ratio of the standard deviation to the mean.
• Return on Investment (ROI): The ratio of benefits to costs.
• Net Present Value (NPV): The present value of future cash flows, discounted by the time value of money.
• Internal Rate of Return (IRR): The rate at which the NPV equals zero.

Step-by-Step / Process Flow

1. Identify the Problem: Determine the project issue or decision that requires Quantitative Analysis.
2. Gather Data: Collect relevant data and information about the project, including input variables and their probability distributions.
3. Develop a Model: Create a mathematical model of the project, using techniques like decision trees or Monte Carlo simulation.
4. Run the Model: Generate multiple scenarios and outcomes using the model, considering different input variables and their probability distributions.
5. Analyze the Results: Evaluate the outcomes and identify the most critical input variables and their impact on the project.
6. Make a Decision: Use the results of the Quantitative Analysis to make an informed decision, considering the expected outcomes and risks.

Common Mistakes

• Mistake: Failing to consider all relevant input variables and their probability distributions.
• Correction: Ensure that all relevant data is collected and incorporated into the model.
• Mistake: Not accounting for the time value of money when calculating NPV or IRR.
• Correction: Discount future cash flows by the time value of money to accurately reflect their present value.
• Mistake: Misinterpreting the results of a Monte Carlo simulation.
• Correction: Understand the limitations and assumptions of the simulation and interpret the results accordingly.

Exam Tips

• Tip: Be aware of the distinction between sensitivity analysis and decision trees. Sensitivity analysis is used to analyze how changes in input variables affect project outcomes, while decision trees are used to evaluate and compare different options.
• Tip: Understand the concept of expected value and how it is calculated. The expected value is the average value of a decision, calculated by multiplying the probability of each outcome by its monetary value.
• Tip: Be familiar with the different types of probability distributions, including normal, uniform, and triangular distributions.

Quick Practice Questions

1. If the CPI is 0.8, is the project under or over budget? Answer: Under budget. Explanation: A CPI of 0.8 indicates that the project is completing work at a rate that is 20% faster than planned, resulting in a cost savings.
2. What is the expected value of a decision with a 50% chance of a $10,000 gain and a 50% chance of a $5,000 loss? Answer: $2,500. Explanation: The expected value is calculated by multiplying the probability of each outcome by its monetary value and summing the results: (0.5 x $10,000) + (0.5 x -$5,000) = $2,500.
3. What is the net present value of a project with a $10,000 initial investment and a $15,000 return in one year, assuming a 10% discount rate? Answer: $1,500. Explanation: The net present value is calculated by discounting the future cash flow by the time value of money: -$10,000 + ($15,000 / (1 + 0.10)) = $1,500.

Last-Minute Cram Sheet

• Sensitivity analysis is used to analyze how changes in input variables affect project outcomes.
• Tornado diagrams show the most critical input variables.
• Expected monetary value (EMV) is the expected value of a decision, calculated by multiplying the probability of each outcome by its monetary value.
• Decision trees are used to evaluate and compare different options.
• Monte Carlo simulation is a statistical technique to model and analyze complex systems.
• Expected value (EV) is the average value of a decision, calculated by multiplying the probability of each outcome by its monetary value.
• Probability distribution is a mathematical representation of the likelihood of different outcomes.
• Confidence interval is a range of values within which a parameter is likely to lie.
• Standard deviation (σ) is a measure of the spread of a probability distribution.
• Coefficient of variation (CV) is the ratio of the standard deviation to the mean.
• Return on investment (ROI) is the ratio of benefits to costs.
• Net present value (NPV) is the present value of future cash flows, discounted by the time value of money.
• Internal rate of return (IRR) is the rate at which the NPV equals zero.
• ⚠️ Decomposition breaks down work, not activities – it creates the WBS, not the activity list.
• ⚠️ Contingency is a reserve for unexpected events, not a management reserve.
• ⚠️ Quality assurance is a process to ensure quality, not quality control, which is a process to ensure conformance to requirements.