Of the analytic methods that comprise operations research, simulation stands in sharp contrast to the mathematical programming algorithms and stochastic models presented earlier. With simulation, the analyst creates a model of a system that describes some process involving individual entities such as persons, products or messages. The components of the model try to reproduce, with varying degrees of accuracy, the actual operations of the real components of the process. Most likely the system will have time-varying inputs and time-varying outputs that are affected by random events. The components of the simulation are interconnected and can often be viewed as a network with complex input-output relationships. Moreover, the flow of entities through the system is controlled by logic rules that derive from the operating rules and policies associated with the process being modeled.

Because the model takes the form of a computer program, which operates as a facsimile of its real-world counterpart, it is much less restricted than analytical models such as those encountered in the queueing chapter. Within the limitations of the input and output interfaces, a skilled programmer can duplicate with a high level of accuracy, most systems that can be observed and rationalized. Because of this capacity for detail, simulation has become a very popular method of analysis. Particularly appealing is its ability to model random variables with arbitrary probability distributions and systems that have a variety of interacting random processes. Modern simulation languages are very powerful tools, allowing even a beginner to create representations of complex systems.

Several reasons that motivate the use of simulation are outlined below.

1. Simulation may be the only alternative to provide solutions to the problem under study. For example, it is not possible to obtain transient (time-dependent) solutions for complex queuing models in closed form or by solving a set of equations, but they are readily obtained with simulation methods.
   
2. Models to be simulated can represent a real-world process more realistically because fewer restrictive assumptions are required. Examples include the use of nondeterministic lead times in an inventory model, non-Poisson arrivals or service times in a queuing process, and nondeterministic parameters in a multiperiod production scheduling and inventory control problem. Each of these situations results in analytic models that are intractable.
3. Changes in configuration or structure can be easily implemented to answer "What happens if . . . ?" questions. For example, various decision rules can be tested for altering the number of servers in a network of queues.
4. In most cases, simulation is less costly than actual experimentation; in other cases, it may be the only reasonable initial approach, as when the system does not yet exist but theoretical relationships are well-known. For example, solar energy thermal collection systems for homes have been tested by simulation prior to being built to help solve site-specific problems or to explore new design issues.
5. Simulation can be used for pedagogical (teaching) purposes either to illustrate a model or to better comprehend a process, such as revenue management policies used by airlines to price tickets over time.
6. For many dynamic processes, simulation provides the only means for direct and detailed observation within specified time limits. The approach also allows time compression, whereby a simulation accomplishes in minutes what might require years of actual experimentation.

With these advantages and others one might ask "Why not approach all modeling through simulation?" First, simulation is time-consuming and costly compared to many analytic approaches. For example, a simulation to estimate optimal reorder levels and quantities for an inventory problem requires an extensive search for optimal values of controllable variables, whereas an analytic solution would not. Second, certain issues associated with design, validation, and estimation are complex at best and unresolved at worst. Because it attempts to reproduce significant amounts of detail, a simulation model may require a large programming effort, its accuracy may be difficult to verify, and the computational burden it imposes may be extensive compared to other approaches. Like queueing analysis, simulation is a tool that requires the enumeration of alternatives to determine an optimal design. Unlike queueing analysis, simulation does not yield expected values. Rather, a simulation run is like making an observation of a system in the real world and recording the relevant statistics. Since statistics are themselves random variables, the interpretation of the results must be done carefully, with procedures based on the appropriate theory. This requirement is often neglected in practice, giving rise to the possibility that the results will either be misinterpreted or misused.