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Optimization means "the action of finding the best solution". Optimization modelling, also known as Mathematical Programming (MP) is a branch of mathematical modelling which is concerned with finding the best solution to a problem. The process of building a model and optimizing it is summarised in the diagram below:

Building a mathematical model of a problem involves abstracting its essence and representing it as a series of mathematical relationships. The best solution to the mathematical model can then be found using appropriate optimization software. If the model has been built well, this solution will translate back into the real world as a good solution to the real-world problem. If it does not, analysis of why it is no good leads to greater understanding of the real-world problem.

Optimization can help solve problems where there are:
  • many ways of doing something;
  • limited resources available.
Typical industrial examples include planning and scheduling, blending problems and supply-chain optimization. Application areas vary enormously, from agriculture to microchips, from the oil industry to banking, from aluminium smelting to telecommunications.

The way in which optimization is used also varies widely. Perhaps the most common use is as an aid to decision-making. Here an optimization model forms part of a larger system which people use to help them make decisions. The user is able to influence the solutions which the model produces and reviews them before making a final decision as to what to do. This mode of operation reflects the fact that a mathematical model is never an exact representation of the real world: optimization models can assist in finding good solutions but are not the complete solution.

Other uses of optimization may have either more or less human involvement in decision-making. At one extreme is its use in consultancy, where the model acts as a focus for gaining a better understanding of the system being modelled. At the other is its use in an on-line control system. Many such applications are concerned with blending, where some material (e.g. petrol) must be made to a quality specification from a number of components whose qualities can be measured. In such a case the relationships are sufficiently well-understood and there is sufficient feedback during operation for an optimization model to be run automatically. Even here, however, an engineer will review the operation of the system periodically.