**Description:** An optimization model is a mathematical approach that seeks to maximize or minimize an objective function by systematically selecting input values within a permitted set. This type of model is based on formulating problems that can be represented through mathematical equations, where variables, constraints, and an objective function are defined. Optimization is used in various disciplines, including economics, engineering, logistics, and operations research, to make informed decisions that improve the efficiency and effectiveness of processes. The main characteristics of an optimization model include a clear identification of objectives, consideration of constraints that limit available options, and the search for optimal solutions that meet established conditions. The relevance of these models lies in their ability to provide quantitative solutions to complex problems, facilitating decision-making in environments where resources are limited and variables are interdependent.
**History:** The concept of optimization has its roots in calculus and mathematical programming theory, which developed in the mid-20th century. One of the most significant milestones was the formulation of the simplex method by George Dantzig in 1947, which allowed for the efficient solving of linear programming problems. Since then, optimization has evolved, incorporating techniques such as nonlinear programming, integer programming, and evolutionary algorithms, broadening its application across various fields.
**Uses:** Optimization models are used in a variety of fields, including logistics for managing transportation routes, in finance for portfolio allocation, in engineering for designing efficient systems, and in production for resource planning. They are also fundamental in operations research, where they help solve complex decision-making problems.
**Examples:** A practical example of an optimization model is the traveling salesman problem, where the shortest route a salesman must take to visit a set of cities is sought. Another example is supply chain optimization, where transportation and storage costs are minimized while meeting customer demands.
