Monte Carlo Schedule Risk Analysis: The Concept, Benefits, and Limitations. How Monte Carlo schedule risk analysis works; how to perform Monte Carlo simulations of project schedules. For more information how to perform schedule risk analysis using RiskyProject software please visit Intaver Institute web site: http://www.intaver.com. About Intaver Institute. Intaver Institute Inc. develops project risk management and project risk analysis software. Intaver's flagship product is RiskyProject: project risk management software. RiskyProject integrates with Microsoft Project, Oracle Primavera, other project management software or can run standalone. RiskyProject comes in three configurations: RiskyProject Lite, RiskyProject Professional, and RiskyProject Enterprise.

1. Monte Carlo Schedule Analysis
The Concept, Benefits and Limitations
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2. 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.

3. 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

4. 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

5. 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.

6. 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

7. What Distribution Should Be Used?
Normal Triangual Uniform
Also useful for Monte Carlo simulations:
• Lognornal
• Beta

8. 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%.

9. Role of Emotions
Emotions can affect our judgment

10. 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.

11. 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

12. 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

13. 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

14. How Many Trials Are Required?
Huge number of trials (> 1000) usually does not increase
accuracy of analysis
• Incorporate rare events
• Use convergence monitoring

15. What Is The Chance That a Project Will Be on Time And Within
Budget?

16. 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

17. 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.

18. Critical Risks

19. Conditional Branching
6 days
If duration <= 6 days
If duration > 6 days

20. Monte Carlo and Critical Chain
Monitoring Project Buffer

21. 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

22. 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

23. 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

24. Questions?