© 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

- Must follow appropriate distributions

- Procesing 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
- Graphical views (histograms, line graphs, trend lines)