L'objectif de ce cours est d'apprendre à appliquer une méthodologie d’analyse et de conception pour le développement des logiciels. En particulier, apprendre la modélisation objet avec le langage universel UML.

Connaissances préalables recommandées :  Algorithmique, Programmation Orientée Objet.

Optimization plays a central role in many decision-making fields, such as economics, resource management, and military planning. Among the most powerful tools developed to solve complex resource management and profit maximization problems, linear programming (LP) holds a prominent position. This method, which is part of the field of operations research, emerged in the mid-20th century. While its theoretical foundations were laid by pioneering mathematicians such as L.V. Kantorovich before 1947, it was primarily through the work of George B. Dantzig and his collaborators that resource optimization techniques were formalized and made applicable to a wide range of practical problems. The development of the Simplex method, although it is not a polynomial algorithm, remains one of the most effective approaches for solving practical problems involving limited resources, whether for profit maximization or cost minimization. This method has had a major impact, particularly in industrial and commercial applications, where it has enabled the solution of large-scale optimization problems. Other contributions, such as Khachiyan's 1979 polynomial-time method, paved the way for new, more efficient, and theoretically robust approaches. Today, linear programming is at the core of commercial software tools used by businesses and researchers, such as Cplex, Gurobi, and open-source solutions like Glpk. These tools leverage theoretical advances in optimization to offer practical solutions to increasingly complex problems, whether optimizing production in an industrial environment, allocating resources in supply chain management systems, or minimizing costs in financial management. At the heart of linear programming lies the fundamental idea of seeking an optimal solution—often in terms of profit maximization or cost minimization—in problems where the relationships between variables are linear and subject to linear constraints. This structure allows for a clear and precise mathematical representation of many real-world problems, while facilitating their resolution through powerful algorithms like the Simplex method. Decision variables, which determine the choices to be made in the optimization problem, play a key role in this process. They define the levels of production, investment, or consumption that help achieve the set objective. Once the linear relationships and constraints are clearly defined, the algorithm, such as Simplex, explores all possible solutions while respecting these constraints to find the optimal combination of variables. The linearity of the objective functions and constraints, an essential characteristic of linear programming, not only simplifies the formulation of problems but also their resolution. This simplification does not diminish the method's ability to solve complex problems. On the contrary, it enables the handling of a large number of variables and constraints while ensuring efficiency in the calculation of optimal solutions. Moreover, the linear framework of LP allows for its application across a wide range of fields, including production planning, supply chain management, finance, logistics, and many others. In summary, linear programming stands as an indispensable tool in the field of optimization, offering robust and reliable solutions to practical challenges across multiple sectors. Advances in both the theoretical and practical methods of linear optimization have led to a true revolution in decision-making and operational efficiency. Today, thanks to the power of modern algorithms and associated software tools, linear programming provides unprecedented capabilities for solving optimization problems in complex environments, whether economic, industrial, logistical, or financial. Researchers and practitioners continue to explore new extensions and variants, thus ensuring that linear programming remains a key tool in the field of optimization in the 21st century.

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Bibliography and Useful Links

Dans cours Les étudiants apprendront à installer, configurer et maintenir un SGBD.