

Since the validity of the solution obtained is bounded by the model s accuracy, a natural question that is of interest t Since the validity of the solution obtained is bounded by the model s accuracy, a natural question that is of interest to an analyst is How robust is the solution with respect to deviations in the assumptions inherent in the model and in the values of the parameters used to construct it. To illustrate this with our hypothetical production problem, examples of some questions that an analyst might wish to ask are, a Will the optimum production plan change if the profits associated with widgets were overestimated by 5 , and if so how. or b If some additional amount of Resource 2 could be purchased at a premium, would it be worth buying and if so, how much. or c If machine unreliability were to reduce the availability of Resource 3 by 8 , what effect would this have on the optimal policy. Such questions are especially of interest to managers and decisionmakers who live in an uncertain world, and one of the most important aspects of a good O. project is the ability to provide not just a recommended course of action, but also details on its range of applicability and its sensitivity to model parameters.Fassilia United States. Alabama
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The reason of course, is that this plan does not make the most effective use of the available resources and fails to tak The reason of course, is that this plan does not make the most effective use of the available resources and fails to take into account the interaction between profits and resource utilization. While the actual difference is small for this hypothetical example, the benefits of using a good O. technique can result in very significant improvements for large realworld problems. The second part of this step in the O. process is referred to as postoptimality analysis, or in layperson s terms, a whatif analysis. Recall that the model that forms the basis for the solution obtained is a a selective abstraction of the original system, and b constructed using data that in many cases is not 100 accurate.Fassilia United States. Alabama
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We conclude this section by examining the solution to the model constructed earlier for our hypothetical production prob We conclude this section by examining the solution to the model constructed earlier for our hypothetical production problem. Using linear programming to solve this model yields the optimal solution of G 540 and W 252, i. , the production plan that maximizes profits for the given data calls for the production of 540 gizmos and 252 widgets. The reader may easily verify that this results in a profit of 7668 and fully uses up all of the first two resources while leaving 18 units of the last resource unused. Note that this solution is certainly not obvious by just looking at the mathematical model  in fact, if one were greedy and tried to make as many gizmos as possible since they yield higher profits per unit than the widgets , this would yield G 708 and W 0 at which point all of the second resource is used up . However, the resulting profit of 7080 is about 8 less than the one obtained via the optimal plan.Fassilia United States. Alabama
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Some examples of popular O. Some examples of popular O. software systems include CPLEX, LINDO, OSL, MPL, SAS, and SIMAN, to name just a few. While it would clearly be impossible to describe herein the features of all available software, magazine such as OR MS Today and IE Solutions regularly publish separate surveys of various categories of software systems and packages. These publications also provide pointers to different types of software available; as an example, the December 1997 issue of OR MS Today pages 6175 provides a complete resource directory for software and consultants. Updates to such directories are provided periodically. The main point here is that the ability to solve complex models problems is far less of an issue today than it was a decade or two ago, and there are plenty of readily available resources to address this issue.Fassilia United States. Alabama
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Although there are still large scale problems whose solution requires the use of mainframe computers or powerful worksta Although there are still large scale problems whose solution requires the use of mainframe computers or powerful workstations, many big problems today are capable of being solved on desktop microcomputer systems. There are many computer packages and their number is growing by the day that have become popular because of their ease of use and that are typically available in various versions or sizes and interface seamlessly with other software systems; depending on their specific needs endusers can select an appropriate configuration. Many of the software vendors also offer training and consulting services to help users with getting the most out of the systems. Some specific techniques for which commercial software implementations are available today include optimization mathematical programming including linear, nonlinear, integer, dynamic and goal programming , network flows, simulation, statistical analysis, queuing, forecasting, neural networks, decision analysis, and PERT CPM. Also available today are commercial software systems that incorporate various O. techniques to address specific application areas including transportation and logistics, production planning, inventory control, scheduling, location analysis, forecasting, and supply chain management.Fassilia United States. Alabama
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