Simulation in Decision
Making
© Copyright 2009 Herbert J.
Bernstein
Simulation plays an important role in decision making. In a simulation we use
a computer to calculate trial inputs and resulting outputs to explore alternatives
in the computer before facing them in reality.
- Models for Inputs:
- Deterministic input or outputs from earlier decisions
- Random inputs
- Must follow appropriate distributions
Need to know cumulative
distribution function (P(X≤x);
- Test by the Chi-squared goodness
of fit test
- Want uncorrelated numbers
- In Excel, the function RAND() gives a uniformly distributed random
number real between 0 and 1, not including 1.
- In Excel, the function RANDBETWEEN(LOW,HIGH) returns a uniformly
distributed random integer between LOW and HIGH, inclusive.
- In recent versions of Excel, NORMINV(RAND(), mean, standard_dev)
returns a normally distributed random number, but in older versions of Excel
you need to use the Box-Muller method
mean+standard_dev*SQRT(-2*LN(RAND()))*SIN(2*PI()*RAND())
(but you need to make both RAND() calls come from one cell). See
http://www.exceluser.com/explore/statsnormal.htm
- Processing inputs to outputs
- The real decision problem is modelled by equations that depend on
the inputs
- Usually done as a simulation table of intermediate values and outputs
with a trail in each row (or group of rows)
- Important to record a trial number (run number), each input value
and the equations used as well as the outputs
- Analysing output
- For each output, compute means, standard deviations, 5% and 95% values
- The mean gives a single import representative value of the output
- The standard deviation gives an idea of how much the values of the
out output varies
- The 5% and 95% values give bounds between which 90% of the output lies
- Graphical views (histograms, line graphs, trend lines)
- Many people understand graphical presentations of data better than lists
of numbers
- A histogram gives a
graphical approximation to the probability distribution involved, giving the populations
in discrete bins
- A line graph connects
data points with straight lines to give an idea of how the output depends on the input
- A trend line
tries to provide a straight line that relates the output to the input