

Mathematical Models This is the final category of models, and the one that traditionally has been most commonly identifi Mathematical Models This is the final category of models, and the one that traditionally has been most commonly identified with O. In this type of model one captures the characteristics of a system or process through a set of mathematical relationships. Mathematical models can be deterministic or probabilistic. In the former type, all parameters used to describe the model are assumed to be known or estimated with a high degree of certainty . With probabilistic models, the exact values for some of the parameters may be unknown but it is assumed that they are capable of being characterized in some systematic fashion e. , through the use of a probability distribution .Fassilia United States. Alabama
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The reason these issues are emphasized here is that a modern simulation model can be very flashy and attractive, but its The reason these issues are emphasized here is that a modern simulation model can be very flashy and attractive, but its real value lies in its ability to yield insights into very complex problems. However, in order to obtain such insights a considerable level of technical skill is required. A final point to keep in mind with simulation is that it does not provide one with an indication of the optimal strategy. In some sense it is a trial and error process since one experiments with various strategies that seem to make sense and looks at the objective results that the simulation model provides in order to evaluate the merits of each strategy. If the number of decision variables is very large, then one must necessarily limit oneself to some subset of these to analyze, and it is possible that the final strategy selected may not be the optimal one. However, from a practitioner s perspective, the objective often is to find a good strategy and not necessarily the best one, and simulation models are very useful in providing a decisionmaker with good solutions.Fassilia United States. Alabama
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On the other hand, one has to be very careful with simulation models because it is also easy to misuse simulation. On the other hand, one has to be very careful with simulation models because it is also easy to misuse simulation. First, before using the model it must be properly validated. While validation is necessary with any model, it is especially important with simulation. Second, the analyst must be familiar with how to use a simulation model correctly, including things such as replication, run length, warmup etc; a detailed explanation of these concepts is beyond the scope of this chapter but the interested reader should refer to a good text on simulation. Third, the analyst must be familiar with various statistical techniques in order to analyze simulation output in a meaningful fashion. Fourth, constructing a complex simulation model on a computer can often be a challenging and relatively time consuming task, although simulation software has developed to the point where this is becoming easier by the day.Fassilia United States. Alabama
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Simulation models are analyzed by running the software over some length of time that represents a suitable period when t Simulation models are analyzed by running the software over some length of time that represents a suitable period when the original system is operating under steady state. The inputs to such models are the decision variables that are under the control of the decisionmaker. These are treated as parameters and the simulation is run for various combinations of values for these parameters. At the end of a run statistics are gathered on various measures of performance and these are then analyzed using standard techniques. The decisionmaker then selects the combination of values for the decision variables that yields the most desirable performance. Simulation models are extremely powerful and have one highly desirable feature they can be used to model very complex systems without the need to make too many simplifying assumptions and without the need to sacrifice detail.Fassilia United States. Alabama
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is typically identified with mathematical analysis, the use of an innovative model and problemsolving procedure such as is typically identified with mathematical analysis, the use of an innovative model and problemsolving procedure such as the one just described is an entirely legitimate way to conduct an O. Computer Simulation Models With the growth in computational power these models have become extremely popular over the last ten to fifteen years. A simulation model is one where the system is abstracted into a computer program. While the specific computer language used is not a defining characteristic, a number of languages and software systems have been developed solely for the purpose of building computer simulation models; a survey of the most popular systems may be found in OR MS Today October 1997, pp. Typically, such software has syntax as well as builtin constructs that allow for easy model development. Very often they also have provisions for graphics and animation that can help one visualize the system being simulated.Fassilia United States. Alabama
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