Monte Carlo Simulation Concepts (return to DSS home)

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What is Monte Carlo Simulation?

The word simulation is used to describe the process of modeling a real life system to learn about its behavior. The model is a set of logical as well as mathematical relationships and can help determine how outputs vary as a function of random inputs. Without the aid of simulation, a spreadsheet model will only reveal a single outcome, generally the most likely or average scenario. Spreadsheet risk analysis uses both a spreadsheet model and simulation to automatically analyze the effect of varying inputs on outputs of the modeled system. One type of spreadsheet simulation is Monte Carlo Simulation (MCS). This is a technique for managing uncertainty in complex models or environments. It runs multiple “what if” scenario analyses using the selected input, or independent variables. MCS examines the relationship between variables by simulating numerous (in some cases, thousands) of possible situations using random numbers.

 MCS allows us to model risk in the input variables according to the probability distribution for each of the variables. It then generates an estimate of risk in the outcome so that the user of the data can evaluate the effect of decisions with respect to the input variables on the output variable. Simply put, it allows the user to assess the best and worst case scenarios for the environment or situation that has been modeled.

MCS expands upon the techniques used in sensitivity and scenario analysis. Sensitivity analysis allows a user to examine which input variable causes the greatest amount of change in the output variable, and scenario analysis allows a user to look at how the outcome changes when one or more of the independent variables change. In contrast, MCS allows a user to examine the probability of achieving a desired outcome of the dependent variable based on the range of up to several thousand potential values of the independent variables.

How is Monte Carlo Simulation Performed?

The first step in MCS is to determine which inputs should be modeled. For our model of firm demand we chose to examine Average Industry Price and Average Industry Advertising as inputs. We assumed that the industry size would not change so this was modeled as a constant distribution.

Outlined below are the key steps involved:

1. Develop a system flow diagram

2. Develop an Excel spreadsheet to model the system

3. Use Crystal Ball or @Risk to model uncertainty
- Determine essential variables that have uncertainty associated with them
- Study the uncertain variables and define possible values using a probability distribution. The type of distribution selected is based on the conditions surrounding the variable. Some typical distribution types are Normal, Triangular, Uniform and Lognormal.
- Perform Simulation. A simulation calculates multiple scenarios of a model by repeatedly sampling values from the probability distributions for the uncertain variables and using those values for the cell. During a single trial, Crystal Ball randomly selects a value from the defined possibilities (the range and shape of the distribution) for each uncertain variable and then recalculates the spreadsheet. 

4. Tabulate as well as chart outcome values. Try and describe the data using summary statistics.

5. Evaluate the risk.  

Why is Monte Carlo Simulation Appropriate for Managing Uncertainty?

MCS is appropriate where we have a limited understanding of what the values of the input variables will be due to uncertainty. While we can arbitrarily set values for the input variables and perform sensitivity analysis and scenario analysis, such a strategy involves inherent uncertainty because we have no basis for selecting the values used for the input variables. MCS allows us to overcome these limitations by generating thousands of “scenarios” and providing summary statistics on the mean, minimum, maximum, and standard deviation for the input and output variables across the thousands of possibilities.

Monte-Carlo Simulation is important because it allows managers to examine a very large range of inputs in an automated fashion. MCS also addresses the limitations of the sensitivity/scenario analysis, which are time consuming and provide a lot of data but do not indicate which outcomes are probable. With MCS, once the model has been created, the manager can also determine the risk associated with the model. If the risk associated is too great, the manager could make changes to the model such that the risk is minimized. By reducing risk and uncertainty, the manager can make effective decisions.