

Clearly, constraints dictate the values that can be feasibly assigned to the decision variables, i. Clearly, constraints dictate the values that can be feasibly assigned to the decision variables, i. , the specific decisions on the system or process that can be taken. The third and final component of a mathematical model is the objective function. This is a mathematical statement of some measure of performance such as cost, profit, time, revenue, utilization, etc. and is expressed as a function of the decision variables for the model. It is usually desired either to maximize or to minimize the value of the objective function, depending on what it represents.Fassilia United States. Alabama
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An analysis of the model will seek specific values for these variables that are desirable from one or more perspectives. An analysis of the model will seek specific values for these variables that are desirable from one or more perspectives. Very often especially in large models it is also common to define additional convenience variables for the purpose of simplifying the model or for making it clearer. Strictly speaking, such variables are not under the control of the decisionmaker, but they are also referred to as decision variables. Constraints are used to set limits on the range of values that each decision variable can take on, and each constraint is typically a translation of some specific restriction e. , the availability of some resource or requirement e. , the need to meet contracted demand .Fassilia United States. Alabama
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As an illustration, the Critical Path Method CPM and the Program Evaluation and Review Technique PERT are two very simil As an illustration, the Critical Path Method CPM and the Program Evaluation and Review Technique PERT are two very similar O. techniques used in the area of project planning. However, CPM is based on a deterministic mathematical model that assumes that the duration of each project activity is a known constant, while PERT is based on a probabilistic model that assumes that each activity duration is random but follows some specific probability distribution typically, the Beta distribution . Very broadly speaking, deterministic models tend to be somewhat easier to analyze than probabilistic ones; however, this is not universally true. Most mathematical models tend to be characterized by three main elements decision variables, constraints and objective function s . Decision variables are used to model specific actions that are under the control of the decisionmaker.Fassilia United States. Alabama
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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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