Conceptually, optimization is the process of optimizing, of making something optimal. It is the search for excellence, for the best-case scenario. It may occur in different ways, but here we are interested in what we call mathematical optimization.

Mathematical optimization consists of using mathematical equations and algorithms to solve problems in order to find the best possible solution among all viable. This means finding a solution that maximizes or minimizes something, according to its purposes.

And why do we use mathematics? Through mathematical models, resolution algorithms and computational techniques, problems that seemed impossible to be solved by thinking, manually calculating or using Excel spreadsheets become feasible and, at times, even elementary for us to find solutions.

Without the aid of mathematics, many times the simple fact of finding a solution is already quite difficult. We handle complex problems, with an enormous amount of variables, and defining values and making decisions for all of them can become extremely costly and difficult considering that a decision may impact others, not to mention that these decisions must also respect countless restrictions.

However, usually we don’t simply want to find a solution. The competitive context many companies are in makes it imperative that the decisions made are not only viable, but also very good. Why not great? Why not aiming at the solution that will bring the highest profit? Or the lowest cost? Best decisions can be adopted by using mathematical optimization.

How is this done? The existing problem must be mapped, and its variables, parameters, restrictions and goal defined. A mathematical model, or mathematical formulation, is then created: a set of equations that will represent this problem. Some simplifications may be necessary, and this is the expertise of who is developing the models come. Finally, the best approach for resolution is ed or created.

The mathematical optimization, therefore, can become a great tool for assistance. It is not about replacing those who make the decisions, but about allowing these people to have power over something that may further leverage what is being decided. It is giving the decision-makers greater input so that their time and their experiences can be used as efficiently as possible.

Cassiano Vinhas de Lima - Consultant at Cassotis Consulting

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