Published on May 7, 2014
Monte Carlo Schedule Analysis The Concept, Benefits and Limitations Intaver Institute Inc. 303, 6707, Elbow Drive S.W, Calgary, AB, Canada Tel: +1(403)692-2252 Fax: +1(403)459-4533 www.intaver.com
What is Monte Carlo Analysis? Monte Carlo simulations is a mathematical method used in risk analysis. Monte Carlo simulations are used to approximate the distribution of potential results based on probabilistic inputs.
Monte Carlo Simulations Input Parameters Output Parameters Calculation Engine Critical Path Scheduling Engine ( ) Task duration cost, finish time, etc. cost, finish time, etc. Project duration Monte Carlo simulations use distributions as inputs, which are also the results
Monte Carlo Schedule Analysis 4 5 6321 7 7 82 3 654 1 4 5 632 7 8 9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 Task 1 Task 2 Task 3 Monte Carlo simulations take multiple distributions and create histograms to depict the results of the analysis
Two Approaches to Estimating Probabilities • The relative frequency approach, where probability equals the number of occurrences of specific outcome (or event) divided by the total number of possible outcomes. • The subjective approach represents an expert’s degree of belief that a particular outcome will occur.
Two of Approaches for Defining Uncertainties • Distribution-based approach • Event-based approach • Monte Carlo can be used to simulate the results of discrete risk events with probability and impact on multiple activities
What Distribution Should Be Used? Normal Triangual Uniform Also useful for Monte Carlo simulations: • Lognornal • Beta
Ignoring Base-Rate Frequencies • Historically, the probability that a particular component will be defective is 1%. • The component is tested before installation. • The test showed that the component is defective. • The test usually successfully identifies defective components 80% of the time. • What is the probability that a component is defective? The correct answer is close to 4%, however, most people would think that answer is a little bit lower than 80%.
Role of Emotions Emotions can affect our judgment
Eliciting Judgment About Probabilities of Single Events • Pose a direct question: “What is the probability that the project will be canceled due to budgetary problems?” • Ask the experts two opposing questions: (1) “What is the probability that the project will be canceled?” and (2) “What is the probability the project will be completed?” The sum of these two assessments should be 100%. • Break compound events into simple events and review them separately.
Probability Wheel 25% No delay of activity 35% 3 day delay of activity 40% 5 day delay of activity Use of visual aids like a probability wheel can aid in the increasing validity of estimates
Task Duration 4 8 12 16 20 100% 80% 60% 40% 20% Frequency Probability 2 3 4 5 6 (days) Question: What is the chance that duration is less than 3 days? Eliciting Judgment: Probability Method
Eliciting Judgment: Method of Relative Heights Task Duration 2 4 6 8 10 2 3 4 5 6 50% 40% 30% 20% 10% Frequency Probability (days) Question: How many times the duration will be between 2 and 3 days? Plotting possible estimates on a histogram can help improve estimatesc
How Many Trials Are Required? Huge number of trials (> 1000) usually does not increase accuracy of analysis • Incorporate rare events • Use convergence monitoring
What Is The Chance That a Project Will Be on Time And Within Budget?
Analysis of Monte Carlo Results • Sensitivity and Correlations • Critical Indices • Crucial tasks • Critical Risks • Probabilistic Calendars • Deadlines • Conditional Branching • Probabilistic Branching • Chance of Task Existence
Crucial Tasks Crucial tasks for project duration Crucial tasks for project duration Monte Carlo analysis identifies task cruciality, how often tasks are on the critical path.
Conditional Branching 6 days If duration <= 6 days If duration > 6 days
Monte Carlo and Critical Chain Monitoring Project Buffer
Tracking Chance of Project Meeting a Deadline Project Duration Chanceofprojectmeetingadealine 0% 20% 40% 60% 80% 100% (weeks) 0 2 4 6 8 10 12 14 Chance to meet a deadline is reducing as a results of events Mitigation efforts can increase a chance to meet a deadline
When Monte Carlo Is Useful • You have reliable historical data • You have tools to track actual data for each phase of the project • You have a group of experts who understand the project, have experience in similar projects, and are trained to avoid cognitive and motivational biases
Future Reading Lev Virine and Michael Trumper Project Decisions: The Art and Science Management Concepts, Vienna, VA, 2007 Project Think: Why Good Managers Make Poor Project Choices Gower, 2013
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