Simulation is the process of studying the behavior of a real system by using a model that replicates the behavior of the system under different scenarios. A simulation model is constructed by identifying the mathematical expressions and logical relationships that describe how the system operates.

Simulation -vs- Optimization In an optimization model, the decision variable values are outputs. The model provides the values that maximizes/minimizes the stated objective function. In a simulation model, the decision variable values are inputs. The model then evaluates what the objective function might be for that particular set of values.

Advantages of Computer Simulation It offers the ability to gain insights into the model solution which may be impossible to attain through other techniques. It provides a convenient experimental laboratory to perform "what if" and risk analysis.

Disadvantages of Computer Simulation A large amount of time may be required to develop the simulation model. There is no guarantee that the solution obtained will actually be optimal. Simulation is, in effect, a trial and error method of comparing different policy inputs. It does not determine if some input which was not considered could have provided a better solution for the model.

Building a Simulation Model ¬ Identify the decision variables, random variables and objective in the problem. ­ Model the logic of the problem: Flowchart Formulas to describe relationships Probability distributions for random variables Program code ® Validate the model ¯ Experimental Design ° Perform simulation runs and analyze output results

Random Variables Random variable values are utilized in the model through a technique known as Monte Carlo simulation. Each random variable is mapped to a set of numbers N so that each time one number in N is generated, the corresponding value of the random variable is given as an input to the model. The mapping is done in such a way that the long run percentage of time that a particular number is simulated in the model occurs according to the probability of that value for the random variable.

Excel’s Random Number Generator (RNG) =rand() Randomly simulates a value between 0 and 1 in the cell where the function is entered Press [F9] to recalculate the function manually Formula automatically recalculates anytime a number or formula is entered in another cell

=Randbetween(a,b) function Simulates an integer value between a and b Assumes that every number between a and b is equally likely to occur in the system Maps numbers generated between 0 and 1 using rand() function to the interval (a,b)

“Trials”, “Runs” and “Iterations” Every time a set of input values are simulated, output results should be collected. The outputs associated with a trial represent one snapshot of what could occur in the real system and under what conditions Many trials (e.g. runs, iterations) should be performed so that a distribution describing the key outputs can be created and the mean outcomes and risk can be viewed