Typical real world optimization problems arise in the following areas:
A Survey of Real World Problems
Here we describe in general some areas in which applications of (linear and nonlinear) mixed integer optimization are found. This list is by far not complete.
The brief survey of real world problems given in this
section is typical for
Companies which are in a situation to utilize the advantages
of a complex
Cutting stock or trimloss problems occurs in the metal or
paper industry. Depending on the cutting machines, one-dimensional or
two-dimensional patterns are cut. It is important that the mathematical
optimization model and algorithms reflects precisely the cutting logic.
Typical for the chemical process industry, but in modified
form also for the
In planning it is often required to make a selection from a series of projects in an optimal manner. This is clearly another type of optimization problem.
The question of how a telecommunication network should
be structured and
Specific skills often mean that only certain people can
Problems of distribution and logistics are fruitful applications for optimization - choosing vehicles, routes, loads and so on. While the problems listed above can be solved with linear mixed-integer methods, problems occurring in process industry very often lead to nonlinear discrete problems. Problems in the refinery or petrcochemical industry include blending problems leading to so-called pooling problems. If, in addition, we have to consider that plants operate in discrete modes, or that connections between tanks and cracker or tanks and vacuum columns have to be chosen selectively, than mixed-integer nonlinear optimization problems need to be solved. Process network flow or process synthesis problems usually fall into this category too. Examples are heat exchanger network, distillation sequencing or mass exchange networks. It should not be inferred from this list of examples that optimization is confined to large sophisticated problems occurring in large organizations. Small problems are equally important, but it may be that the role of techniques to solve problems is less important. Some small problems lack the structure required for the use of optimization techniques and for others the use of techniques would be seen as using a sledge hammer to crack a nut. A balance is required where gains to be obtained by finding optimal answers to a problem outweigh the effort required to obtain these answers.
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