1. Introduction to ModelingMonte Carlo Simulation Expensive Not always practical Time consuming Impossible for all situations Can be complex Cons Pros Experience More Pros Expensive Not always practical Time consuming Impossible for all situations Can be complex Cheap Flexible Fast Adaptable Simplifying Simulation Provides “Virtual Experience” Great teacher Many situations Deal with the unexpected Thorough understanding of processes Broader knowledge

2. Introduction to ModelingMonte 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

3. Introduction to ModelingMonte 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

4. Introduction to ModelingMonte Carlo Simulation Generating Random Variables Normal Distribution 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 CRYSTAL BALL: EXAMPLE: Normal Distribution of random variables having a mean value of 3.0 generated by the equation is X 2

5. Introduction to ModelingMonte Carlo Simulation Generating Other Distributions Triangle Distribution Lognormal Distribution Uniform Distribution Custom Distribution

6. Introduction to ModelingMonte 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

7. Introduction to ModelingMonte Carlo Simulation Distribution of Outcomes Distribution of outcomes depends on the distributions chosen for the assumption variables Outcome Frequency Chart - Normal DistributionOutcome Frequency Chart - Lognormal Distribution

8. Introduction to ModelingMonte Carlo Simulation Sensitivity Analysis and Risk One of Crystal Ball’s best features: it can easily and quickly perform sensitivity and risk analysis. 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.

9. Introduction to ModelingMonte Carlo Simulation Sensitivity Analysis and Risk Probability that the result will equal at least 1 is 53.60%

10. Introduction to ModelingBreak-Even Simulation

11. Introduction to ModelingDecision Tree Simulation