monte carlo schedule analysis the concept, benefits and limitations intaver institute inc. 303,...
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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
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 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
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
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%
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
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
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 durationCrucial tasks for project duration
Monte Carlo analysis identifies task cruciality, how often tasks are on the critical path.
Critical Risks
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
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
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
Questions?