George Dantzig Quotes
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True optimization is the revolutionary contribution of modern research to decision processes.
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Industrial production, the flow of resources in the economy, the exertion of military effort in a war theater-all are complexes of numerous interrelated activities. Differences may exist in the goals to be achieved, the particular processes involved, and the magnitude of effort. Nevertheless, it is possible to abstract the underlying essential similarities in the management of these seemingly disparate systems.
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In retrospect... it is interesting to note that the original problem that started my research is still outstanding - namely the problem of planning or scheduling dynamically over time, particularly planning dynamically under uncertainty. If such a problem could be successfully solved it could eventually through better planning contribute to the well-being and stability of the world.
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Linear programming can be viewed as part of a great revolutionary development which has given mankind the ability to state general goals and to lay out a path of detailed decisions to take in order to "best" achieve its goals when faced with practical situations of great complexity.
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Linear programming is viewed as a revolutionary development giving man the ability to state general objectives and to find, by means of the simplex method, optimal policy decisions for a broad class of practical decision problems of great complexity. In the real world, planning tends to be ad hoc because of the many special-interest groups with their multiple objectives.
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If the system exhibits a structure which can be represented by a mathematical equivalent, called a mathematical model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of mathematical models is termed mathematical programming.
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The mathematician may be compared to a designer of garments, who is utterly oblivious of the creatures whom his garments may fit. To be sure, his art originated in the necessity for clothing such creatures, but this was long ago; to this day a shape will occasionally appear which will fit into the garment as if the garment had been made for it. Then there is no end of surprise and delight.
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All such problems can be formulated as mathematical programming problems. Naturally, we can propose many sophisticated algorithms and a theory but the final test of a theory is its capacity to solve the problems which originated it.