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In simulation analysis, we create a
mathematical model or a
system or process, usually on a computer, and we explore the
behavior of the model by running a simulation. A
simulation consists of many -- often thousands of -- trials.
Each trial is an experiment where we supply numerical values for
input variables, evaluate the model to compute numerical values for
outcomes of interest, and collect these values for later analysis.
A simulation yields many possible values
for the outcomes we care about -- from Net Profit to environmental
impact. The role of simulation analysis is to summarize
and analyze the results, in a way that will yield maximum insight
and help with decision-making.
It is very useful to create charts to help us visualize the results
-- such as frequency histogram
charts and cumulative frequency
charts.
Statistics often play a key
role in summarizing the range of values for each outcome of interest
in a simulation analysis. When the outcome is important to us,
statistics come to life! A good simulation software package,
such as Frontline's Risk Solver,
provides a variety of statistics:
 | Measures of central tendency such as the
mean, median and mode |
| Measures of variation such as the variance
or standard deviation, skewness, and kurtosis |
| Risk measures such as mean absolute
deviation, semivariance or lower partial moment, and semideviation |
| Quantile measures such as percentiles,
cumulative targets, Value at Risk, and Conditional Value at Risk |
| Confidence intervals that tell us how
close our computed sample mean or standard deviation is to the true
value |
It's important to look at quantile measures,
such as percentiles and Value at Risk, in addition to measures of
central tendency and variation. Quantile measures help you
answer questions such as "How much money might we lose, with 5% or
10% probability?” or “What are the chances that we’ll make at least
$100,000?” based on your simulation model.
A simulation uses a
sample of the possible values of your uncertain variables;
hence any statistic resulting from the simulation involves some
degree of sampling error. Confidence intervals
help you assess this error, and estimate the range or interval in
which you can be confident that the true statistic lies, at a
confidence level that you specify.
A powerful tool for assessing
model results is sensitivity analysis, which can help us
identify the uncertain inputs with the biggest impact on our key
outcomes. For example, a
tornado chart can
give us a quick visual summary of the uncertainties with the
greatest positive and negative impact on Net Profit. Using
software, we can also run multiple simulations, with an input
we choose taking a different value on each simulation, and assess
the results. Analyzing the model can give us more information,
but also insight about our real-world problem.
Another powerful method for simulation analysis is
running a parameterized simulation. In this method, we
run a series of simulations, where we vary the value of one or more
variable(s) that we can control -- such as our offering
price, our inventory restocking level, or our allocation of
investment funds to different asset classes. Each simulation
run tests a wide range of values for the uncertain variables in our
model, collects results for our outcomes of interest, and produces
summary statistics, charts and graphs. We can then compare
the different simulations to each other, to better understand how
varying the decision variable(s) affects our outcomes, in the
presence of uncertainty.
Next: Simulation Optimization
Simulation Models
Risk Analysis Tutorial
Back to Simulation Introduction |
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