Monte Carlo Schedule Risk Analysis
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Monte Carlo Schedule Analysis
The Concept, Benefits and Limitations
Intaver Institute Inc.303, 6707, Elbow Drive S.W, Calgary, AB, CanadaTel: +1(403)692-2252Fax: +1(403)459-4533www.intaver.com
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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.
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Monte Carlo Simulations
Input Parameters Output Parameters
Calculation
Engine
Critical PathScheduling
Engine
(
)
Task durationcost, finish time,etc.
cost, finish time,etc.
Project duration
Monte Carlo simulations use distributions as inputs, which are also the results
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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 2Task 3
Monte Carlo simulations take multiple distributions and create histograms to depict the results of the analysis
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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.
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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
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What Distribution Should Be Used?
Normal Triangual Uniform
Also useful for Monte Carlo simulations:
• Lognornal
• Beta
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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%.
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Role of Emotions
Emotions can affect our judgment
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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.
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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
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Task Duration
4
8
12
16
20 100%
80%
60%
40%
20%
Fre
quen
c y
Pro
babi
lity
2 3 4 5 6
(days)
Question: What is the chance that durationis less than 3 days?
Eliciting Judgment: Probability Method
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Eliciting Judgment: Method of Relative Heights
Task Duration
2
4
6
8
10
2 3 4 5 6
50%
40%
30%
20%
10%
Fre
q uen
cy
Pro
b abi
li ty
(days)
Question: How many times the durationwill be between 2 and 3 days?
Plotting possible estimates on a histogram can help improve estimatesc
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How Many Trials Are Required?
Huge number of trials (> 1000) usually does not increase accuracy of analysis• Incorporate rare events • Use convergence monitoring
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What Is The Chance That a Project Will Be on Time And Within Budget?
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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
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Crucial Tasks
Crucial tasks for project durationCrucial tasks for project duration
Monte Carlo analysis identifies task cruciality, how often tasks are on the critical path.
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Critical Risks
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Conditional Branching
6 days
If duration <= 6 days
If duration > 6 days
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Monte Carlo and Critical Chain
Monitoring Project Buffer
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Tracking Chance of Project Meeting a Deadline
Project Duration
Cha
nce
o f p
r oje
c t m
e et in
g a
deal
ine
0%
20%
40%
60%
80%
100%
(weeks)0 2 4 6 8 10 12 14
Chance to meet a deadlineis reducing as a results of events
Mitigation efforts can increasea chance to meet a deadline
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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
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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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Questions?