Monte Carlo Schedule Analysis

The Concept, Benefits and Limitations

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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.

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?