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A simulation model is a mathematical model that calculates
the impact of uncertain inputs and decisions we make on outcomes
that we care about, such as profit and loss, investment returns,
environmental consequences, and the like. Such a model can be
created by writing code in a programming language, statements in a
simulation modeling language, or formulas in a Microsoft Excel
spreadsheet. Regardless of how it is expressed, a simulation model will include:
 | Model inputs that are uncertain
numbers -- we'll call
these uncertain variables |
| Intermediate calculations as required |
| Model outputs that depend on the inputs -- we'll
call these uncertain functions |
It's essential to realize that model outputs
that depend on uncertain inputs are uncertain themselves --
hence we talk about uncertain variables and uncertain
functions. When we perform a simulation with this model, we will
test many different numeric values for the uncertain variables, and
we'll obtain many different numeric values for the uncertain
functions. We'll use statistics to analyze and
summarize all the values for the uncertain functions (and, if we
wish, the uncertain variables).
An Excel spreadsheet can be a simple, yet powerful tool for
creating your model -- especially when paired with Monte
Carlo simulation software such as
Risk Solver. If your model is written in a
programming language, Monte Carlo simulation toolkits like the
one in Frontline's Solver Platform
SDK provide powerful aids.
An example model in Excel might look like this,
where cell B6 contains a formula =PsiTriangular(E9,G9,F9) to sample
values for the uncertain variable Unit Cost, and cell B10 contains a
formula =PsiMean(B9) to obtain the mean value of Net Profit across
all trials of the simulation.
A portion of an example model in the C#
programming language
might look like this, where the array Var[] receives sample values
for the two uncertain variables X and Y, and the uncertain function
values are computed and assigned to the Problem's FcnUncertain
object Value property:
We must also choose what random sample values to
use for the uncertain variables. During a simulation, a new
sample value will be drawn on each trial. In the simplest
case, we might generate random numbers between 0 and 1, and
use these as sample values. But in most cases, the range
of values, and chance that different values in the range will be
drawn on each trial, must be tailored to the uncertain variable.
To do this, we normally choose a probability distribution and
appropriate parameters for the uncertain
variable. This is a key step in
building a simulation model. To learn more about it, consult
Probability Distributions for
Simulation. We can choose:
Frontline's Risk Solver supports all of these
options for obtaining sample values for the uncertain variables in a
simulation model.
Probability
Distributions Simulation Analysis
Simulation Optimization
Risk Analysis Tutorial
Back to Simulation Introduction |
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