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Simulation
Simulation is a very powerful and widely used management science technique for the analy-
sis and study of complex systems. In previous chapters, we were concerned with the formu-
lation of models that could be solved analytically. In almost all of those models, our goal was
to determine optimal solutions. However, because of complexity, stochastic relations, and so
on, not all real-world problems can be represented adequately in the model forms of the pre-
vious chapters. Attempts to use analytical models for such systems usually require so many
simplifying assumptions that the solutions are likely to be inferior or inadequate for implemen-
tation. Often, in such instances, the only alternative form of modeling and analysis available to
the decision maker is simulation.
Simulation
may be deFned as a technique that imitates the operation of a real-world sys-
tem as it evolves over time. This is normally done by developing a simulation model. A
simu-
lation model
usually takes the form of a set of assumptions about the operation of the system,
expressed as mathematical or logical relations between the objects of interest in the system.
In contrast to the exact mathematical solutions available with most analytical models, the sim-
ulation process involves executing or running the model through time, usually on a computer,
to generate representative samples of the measures of performance. In this respect, simula-
tion may be seen as a sampling experiment on the real system, with the results being sample
points. ±or example, to obtain the best estimate of the mean of the measure of performance,
we average the sample results. Clearly, the more sample points we generate, the better our
estimate will be. However, other factors, such as the starting conditions of the simulation, the
length of the period being simulated, and the accuracy of the model itself, all have a bearing
on how good our Fnal estimate will be. We discuss such issues later in the chapter.
As with most other techniques, simulation has its advantages and disadvantages. The ma-
jor advantage of simulation is that simulation theory is relatively straightforward. In general, sim-
ulation methods are easier to apply than analytical methods. Whereas analytical models may
require us to make many simplifying assumptions, simulation models have few such restric-
tions, thereby allowing much greater ²exibility in representing the real system. Once a model
is built, it can be used repeatedly to analyze different policies, parameters, or designs. ±or ex-
ample, if a business Frm has a simulation model of its inventory system, various inventory poli-
cies can be tried on the model rather than taking the chance of experimenting on the real-
world system. However, it must be emphasized that simulation is not an optimizing technique.