Introduction to Modeling
Monte Carlo Simulation
Simulation
Experience
Provides
“Virtual
Experience”
Pros
Cons
• Great teacher
•Expensive
• Many situations
• Deal with the unexpected
•Thorough understanding of
processes
• Broader knowledge
•Not always practical
•Time consuming
•Impossible for all situations
•Can be complex
•Expensive
• Cheap
•Not always practical
•Time consuming
•Impossible for all situations
•Can be complex
• Flexible
• Fast
• Adaptable
• Simplifying
Introduction to Modeling
Monte Carlo Simulation
Key Points of Simulation Models
• Allow for interactivity and experimentation by the modeler
• Generates a range of possibilities from criteria given rather than optimizing the
goal
• Applicable to short run, temporary and specific behavior
Analytic (statistical) models predict average, or steady state, long run behavior
• Deals well with uncertainty
• Can deal with ‘complicating factors’ that make analytical modeling difficult or
impossible to estimate: uncertainty, risk, multiple locations, volatile sales
• Inexpensive, relatively simple process using software like Excel and
Crystal Ball
Introduction to Modeling
Monte Carlo Simulation
Monte Carlo Simulation - named for the roulette wheels of Monte Carlo
As in roulette, variable values are known with uncertainty
Unlike roulette, specific probability distributions define the range of outcomes
Crystal Ball - an application specializing in Monte Carlo simulation
Introduction to Modeling
Monte Carlo Simulation
Generating Random Variables
CRYSTAL BALL:
Normal Distribution
A1
• Generates random variables across
a distribution specified by the user
• Lets users select distributions from
a gallery or generate their own
• Generates a report containing all of
the model’s assumptions
2 .1 0
2 .5 5
3 .0 0
3 .4 5
3 .9 0
Assumption: A1
EXAMPLE:
Normal Distribution of random
variables having a mean value of
3.0 generated by the equation is X2
Normal distribution with parameters:
Mean
Standard Dev.
3.00
0.30
Selected range is from -Infinity to +Infinity
Mean value in simulation was 3.00
Introduction to Modeling
Monte Carlo Simulation
Generating Other Distributions
Uniform Distribution
Triangle Distribution
A1
0 .9 0
0 .9 5
1 .0 0
A1
1 .0 5
1 .1 0
0 .0 0
1 .5 0
Custom Distribution
3 .0 0
4 .5 0
6 .0 0
Lognormal Distribution
A1
A1
.2 3 1
.1 7 3
.1 1 5
.0 5 8
.0 0 0
2 .0 0
2 .5 0
3 .0 0
3 .5 0
4 .0 0
0 .7 4
0 .8 9
1 .0 4
1 .1 9
1 .3 4
Introduction to Modeling
Monte Carlo Simulation
The User
• Defines distribution assumptions
• Selects the number of trials
• Sets the forecast variables
Crystal Ball
• Repeats the simulation for the predetermined number of trials
• Calculates forecast values for each trial
• Reports the results
Monte Carlo Simulation Via Crystal Ball
1) Specify the model’s equation(s)
2) Define the variable distributions
3) Define the forecasts
4) Select number of trials
5) Run the Monte Carlo Simulation
6) Interpret the results
7) Make decisions
Introduction to Modeling
Monte Carlo Simulation
Distribution of Outcomes
Distribution of outcomes depends on the distributions chosen for
the assumption variables
Outcome Frequency Chart - Normal Distribution
Outcome Frequency Chart - Lognormal Distribution
Forecast: B1
Forecast: B1
10,000 Trials
85 Outliers 1,000 Trials
Frequency Chart
Frequency Chart
28 Outliers
.010
99
.021
21
.007
74.25
.016
15.75
.005
49.5
.011
10.5
.002
24.75
.005
5.25
.000
0
.000
0
5.00
7.50
10.00
12.50
15.00
0.00
1.25
2.50
3.75
5.00
Introduction to Modeling
Monte Carlo Simulation
Sensitivity Analysis and Risk
One of Crystal Ball’s best features: it can easily and quickly perform
sensitivity and risk analysis.
Forecast: B1
1,000 Trials
Frequency Chart
5 Outliers
.013
13
.010
9.75
.007
6.5
.003
3.25
.000
0
0.40
0.70
1.00
1.30
1.60
Goal: Determine the likelihood that, given the normal distribution used, the result
will equal at least 1.
Result: Drag the arrow to where the frequency chart equals 1 and the
probability will be calculated by Crystal Ball.
Introduction to Modeling
Monte Carlo Simulation
Sensitivity Analysis and Risk
Forecast: B1
1,000 Trials
Frequency Chart
5 Outliers
.013
13
.010
9.75
.007
6.5
.003
3.25
.000
0
0.40
0.70
1.00
1.30
1.60
Certainty is 53.60% from -Infinity to 1.00
Probability that the result will equal at least 1 is 53.60%
Introduction to Modeling
Price 12
Fixed Cost 15000
Variable Unit Cost 8
Break-Even Output Level 3750
Break-Even Simulation
65,000
60,000
55,000
50,000
45,000
40,000
35,000
Litas
30,000
25,000
20,000
15,000
10,000
5,000
0
-5,000 0
250 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 4000 4250 4500 4750 5000
-10,000
-15,000
-20,000
Output
Total Revenue
Total Cost
Profit
Introduction to Modeling
Decision Tree Simulation
0.40
Airport built at A
13
31.00
Buy A
-18
-2.00
13
0.60
Airport built at B
-12
6.00
-12
0.40
Airport built at A
-8
4.00
Buy B
-12
3.40
-8
0.60
Airport built at B
11
23.00
2
11
3.40
0.40
Airport built at A
5
35.00
Buy A & B
-30
1.40
5
0.60
Airport built at B
-1
29.00
-1
Buy Nothing
0
0
0.00