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Operations Research Models and Methods
Computation Section
Random Variables
 - Functions

Most spreadsheet models compute one or more output values that depend on one or more input variables. The notation defines n inputs, m outputs and m functions relating the input variables to the output values.

The values for the inputs are placed in cells on the worksheet and the values for the outputs appear in other cells. The spreadsheet model converts the inputs to the outputs using formulas on the worksheet or perhaps algorithms implemented in VBA. We consider here situations in which at least one of the inputs is not known with certainty. Although it may be that the analyst has no idea what values an input might take, it is often useful to assume that its value follows a known probability distribution. Then we can say that the input is a random variable and use probability theory to make statements about the outputs. That is the purpose of the Function and associated Moments features of the Random Variables add-in.

When some collection of inputs are defined as random variables with specified distributions, we want to be able to compute moments of the output values, specifically the mean and variance. Two methods are provided, enumeration and Monte Carlo simulation. When the random variables are discrete, enumeration generates all possible values of the random variables and uses probability theory to compute exact values of the moments. When the random variables are continuous, the enumeration method provides only approximate results.

Monte Carlo simulation samples the probability space by randomly drawing values for each input variable. Using the samples, the method estimates the moments using simple statistics.

Later, we allow some of the variables to be set by an optimization method such as linear programming. With this capability we can begin to discuss some issues related to Stochastic Programming.

There are several pages describing the Functions command. Click a link at the left to review them.

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Operations Research Models and Methods
by Paul A. Jensen
Copyright 2004 - All rights reserved