How Monte Carlo schedule risk analysis works; how to perform Monte Carlo simulations of project schedules

1. Monte Carlo Schedule Analysis
The Concept, Benefits and Limitations
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2. What is Monte Carlo Analysis?
Monte Carlo simulation 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
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. Additional Resources
23
Project Think:
Why Good
Managers Make
Poor Project
Choices
Project Decisions:
The Art and Science
Introduction to
Project Risk
Management and
Decision Analysis
Project Risk
Analysis Made
Ridiculously Simple

24. Questions?