UPI Study › Courses › Project Management › Free lessons › Lesson 5.6 Free with a free account
Monte Carlo Simulation for Risk Assessment and Planning
Project Management · Chapter 5: Project Management Tools and Analytical TechniquesSection 5.6 · lesson 35 of 7312 min · free with a free account
Free preview
Create a free account to keep watching
It takes a minute and costs nothing. Your free account unlocks all of Chapter 1 and 3 more lessons of Project Management.
Lesson complete
Earn the 3 college credits for Project Management
Enrolling adds a quiz after each lesson, the graded work and the official transcript. Recommended for credit by NCCRS.
Next lesson: S-Curves and Information Systems in Project Tracking →← PERT Analysis: Methodology and Completion EstimationNext lesson: S-Curves and Information Systems in Project Tracking →
In this lesson
Simulating many schedules to find realistic finish dates and contingency.
- Describe the steps of a Monte Carlo schedule simulation from input distributions to an outcome distribution
- Explain why merging paths and correlated activities push simulated finishes later and wider
- Read a cumulative probability curve, criticality index, and sensitivity ranking
- Calculate schedule contingency as the outcome at a chosen confidence level minus the plan date
Free study notes
Get this lesson's notes by email
The key points and 4 practice questions with answers, in your inbox. One email, free.
One email. Unsubscribe in one click.
Transcript
Everything said in the video, section by section (1,672 words). Read along, or search it.
Opening Question
A Twenty-Week Plan With a Thirteen Percent Chance
Ravi, a risk analyst at Tarn Valley Water, has simulated the schedule for replacing an old water main. The plan says 20 weeks. His report says that date has only about a 13 percent chance of being met. Dina, the finance director, asks the obvious question: what is she being asked to fund? How can a schedule have a probability at all? And how much extra time is enough?
How It Works
Thousands of Plausible Schedules
Monte Carlo simulation tests the schedule many times, each time with a different, randomly chosen but plausible set of durations. The name comes from games of chance. Step one: describe each uncertain duration with an input distribution, which values are possible, and which are likelier. Step two, one iteration: draw a duration for every activity, apply the schedule logic, and record the finish. Step three: repeat thousands of times. Step four: summarize the recorded finishes as a distribution of outcomes, not one date. Spreadsheet add-ins or scheduling-risk software do the work. No single iteration is a forecast. The information is in the thousands together.
Iterations
Two Zones and the Later Finish
The project has two zones, worked in parallel. In zone one, the crew lays pipe, then tests and flushes it. Zone two does the same. The main can't be switched back on until both zones are done, so the finish is whichever zone ends later. In the first iteration, zone one took about 20.4 weeks and zone two 18, so the finish was 20.4, set by zone one. In the ninth, the zones took 17.3 and 17.4 weeks, so zone two set the finish. Why thousands? A random method wobbles from run to run. Ravi's 80 percent reading varied by about 0.06 weeks, across runs of 5,000 iterations, but by 0.67 weeks, across runs of only 50.
Merge Points
Why Finishes Run Later Than Path Averages
Why go beyond the PERT path calculation? Because of merge points, where paths join and the next step must wait for all of them. At a merge, the later path governs, and which path is later changes from one outcome to the next. A single-path calculation adds the averages along zone one, 22.3 weeks, and treats zone two, at 20, as having slack. But the average simulated finish was 23.0 weeks. When two uncertain paths merge, the later of the two is, on average, later than either one's own average. The project feels whichever zone is worse.
Input Distributions
Triangular Ranges and Their Means
Back at his desk, Ravi sets the inputs. The simplest input, common in schedule work, is the triangular distribution: a minimum, a most likely value, and a maximum. Draws never fall outside the minimum and maximum, and values near the most likely come up more often. When the maximum is farther above the most likely than the minimum is below it, the range is right-skewed. Work can only go so fast, but it can go very slowly. Its mean is the plain average of the three. That's not PERT's weighting. It's the exact mean of a triangle. Zone one's pipe laying runs from 10 to 24 weeks, most likely 14, so its mean is 48 over 3: 16 weeks. Its testing averages 6.3, zone two's pipe laying 14.3, and zone two's testing 5.7. Every mean sits above its most likely value. The plan date uses most likely values: the later of 14 plus 6, and 13 plus 5. That's 20 weeks, and it's optimistic.
Eliciting Ranges
Anchoring, Optimism Bias, and Documented Basis
The ranges come from people who know the work, like Hugo, the construction manager, and two tendencies distort them. Anchoring: an estimate stays close to the first number mentioned. Optimism bias: expecting better than experience justifies, so maximums come out too low. The established pattern is that stated ranges are too narrow. Real outcomes fall outside them more often than they should. So Ravi asks for the maximum and minimum first, and the most likely last, and asks several experts separately. Above all, he documents each range's basis: who gave it, when, and on what evidence. Zone one's wide range is recorded with its reason: poor records of buried obstacles.
Correlation
Delays That Move Together
So far, each draw is independent. But real activities often move together. That's correlation, two quantities that rise and fall together. If one short-staffed crew does both the pipe laying and the testing in zone one, both run long together. One late supplier can delay two activities at once. Ignoring that makes results look more certain than they are. Independent delays partly cancel out. Correlated delays pile up, and extreme finishes become more common. Ravi re-ran the model, with a strong link between each zone's two activities. The spread from the tenth to the ninetieth percentile widened, from 7.1 weeks to 8.4. Where a link's strength is unknown, try several plausible strengths, and see how much the answer moves.
Reading the Output
Histogram and Cumulative Probability Curve
After 5,000 iterations, Ravi has two views. A histogram counts how many finishes fell in each interval. Here they ranged from about 16 to 32 weeks, and the most common week was between 21 and 22. The cumulative probability curve answers Dina's question directly. For each finish time, it shows the share of iterations that finished by then. It only ever rises. A confidence level is a stated chance of finishing by a date. The 80 percent confidence finish is the time that 80 percent of iterations met or beat. The plan date of 20 weeks was met only about 13 percent of the time. The 50 percent point is 22.8 weeks, and the 80 percent point is 25.3. Two cautions. A confidence level describes the model, and holds for the project only as far as the inputs do. And it isn't a cost S-curve, which plots spending against calendar time.
Criticality and Sensitivity
How Often Versus How Much
Two more readings. The criticality index of an activity is the share of iterations, in which it sits on the critical path. The plan labels zone one critical, and zone two as having two weeks of slack. But zone one was later in about 71 percent of iterations, and zone two in about 29. A team watching only zone one would be unprepared for roughly 29 times in 100. A sensitivity ranking orders the inputs by how much each one moves the finish. Ravi uses each activity's correlation with the finish, from minus 1 to plus 1. Zone one's pipe laying is a clear first, at about 0.84. Zone one's testing and zone two's pipe laying come next, and they're close. Zone one's testing is critical far more often, but its range is narrow, so it barely outranks. Criticality asks how often. Sensitivity asks how much. Cutting the pipe laying's maximum, from 24 weeks to 20, lowered the 80 percent finish from 25.3 to 23.7. A correlation shows association, not cause.
Quick Check
Which Estimate to Investigate First
Quick check, from a different simulation. Activity K is critical in 95 percent of iterations, but its range is only 1 week wide. Activity M is critical in 40 percent, with a 12-week range. Which estimate is worth investigating first? Pause, and decide. M. Its wide range moves the finish far more, even though it sets the finish less often. Narrowing K's one-week range can't change much. Choosing K confuses how often with how much.
Sizing Contingency
Confidence Level Minus Plan Date
Now Dina's question. A contingency is time or money held beyond the plan, to absorb the risks its single numbers don't cover. Contingency equals the outcome at the chosen confidence level, minus the plan value. At 50 percent confidence, that's 22.8 minus 20: 2.8 weeks. At 80 percent, 5.3 weeks. At 90 percent, 6.8. In whole weeks, 5.3 rounds up to 6, a committed finish at week 26, met in about 85 percent of iterations. Rounding down to 5 would give about 77. Which level to choose is contested. With a high level, a plan date met only 13 percent of the time stops posing as a commitment. A lower level keeps the project from looking slower and costlier than it needs to, and avoids work expanding into the time given. The simulation can't settle how much risk a sponsor carries.
Quick Check
Contingency for Eighty Percent Confidence
Quick check, on another project. Its plan date is 30 weeks, and the curve's 80 percent confidence finish is 34 weeks. How much contingency does 80 percent confidence need? Pause, and decide. 4 weeks: 34 minus 30. Contingency is the gap between the confidence point and the plan. It isn't 80 percent of anything, and it isn't the whole finish time.
Limitations
Inputs, False Precision, and Risk Events
Simulation is only as good as its inputs and model. Ranges made too narrow by anchoring or optimism make the plan date look safer than it is. A schedule that misses an activity, or links one wrongly, is faithfully simulated wrong, with thousands of iterations lending it authority. Beware false precision. A finish quoted as 25.34 weeks implies a certainty three-point estimates can't support. Report whole weeks, or a narrow range. And duration ranges don't represent risk events, discrete things that may or may not happen, like a regulator halting work for a month. Those are identified separately, and can be added with their own chance and effect.
Back to the Meeting
Six Weeks for a Week 26 Finish
Back to the meeting. Ravi lays out three options from the same curve, and recommends 80 percent. Switching the main back on is tied to a planned supply interruption, so lateness costs more than unused contingency. But the pool is shared across projects, which makes 90 percent hard to justify. Hugo objects that zone one's range is too wide, because a recent job nearby went smoothly. Ravi answers that one good experience can anchor a range too narrow, and shows the documented basis and the sensitivity ranking. Hugo accepts, and asks for trial excavations. Ravi requests 6 weeks, for a committed finish at week 26, about 85 percent. He records the level, the reason, and the rounding, so the decision can be reviewed.
Key Takeaways
Iterations, Merges, and Confidence Levels
To recap. Simulation runs thousands of plausible versions of the schedule, and summarizes the finishes. At merges, the later path governs, so finishes run later than path averages. Criticality asks how often an activity drives the finish, and sensitivity asks how much. Contingency is the outcome at the chosen confidence, minus the plan, and the choice of level belongs to the sponsor.
About Project Management at UPI Study
Project Management (Business 230) is a self-paced online course of 73 video lessons in 12 chapters, from starting and defining a project to planning, budgets, scheduling tools, proposals, contracts, execution, monitoring, closure, teams and certification. It carries a NCCRS credit recommendation for 3 semester credits.
Every lesson transcript is free on pages like this one, and the videos are free with a free UPI Study account. Enrolling adds a practice quiz after each lesson, the graded work and final exam that earn the credit, lifetime access, and an official transcript on completion. UPI Study has helped over 130,000 students with college credits. ACE and NCCRS have over 2,100 cooperating colleges that will consider accepting credits; the final decision is with the universities.
Enroll now → Course details Download the syllabus All Business courses Every course with PRO →
Why take it here
Why students take Project Management with UPI Study
Where the credit goes
Universities that work with NCCRS
Project Management carries a NCCRS credit recommendation. These universities work with NCCRS; some are UPI Study's signed partners. ACE and NCCRS have over 2,100 cooperating colleges that will consider accepting credits; the final decision is with the universities.
Thomas Edison State UniversitySigned partner
University of the PeopleSigned partner
Charter Oak State CollegeSigned partner
Strayer UniversitySigned partner
Columbia Southern UniversitySigned partner
Indiana TechSigned partner
Penn StateWorks with NCCRS
Southern New Hampshire UniversityWorks with NCCRS
SUNYWorks with NCCRS
+many more cooperating universitiesFind my college →Find my college → Not listed? Ask Athena in the corner of this page, or book a 15-minute call.
FAQ
Questions students ask us
About Monte Carlo Simulation for Risk Assessment and Planning
What is Monte Carlo simulation in project scheduling?
Why does a merge point make a project finish later than its path averages suggest?
What is the difference between a criticality index and a sensitivity ranking?
How do you size schedule contingency from a Monte Carlo simulation?
About the Project Management course
How many college credits is Project Management?
How much does Project Management cost and what is included?
Which universities accept UPI Study credits?
How long does Project Management take?
How are the exams done?
How do my credits reach my college?
Ready for the full course? Earn 3 credits in Project Management.
73 video lessons, a quiz after each one, and the graded work that earns the credit. Recommended for credit by NCCRS.
3 credits · NCCRSEnroll →