Linear Algebra, Calculus I, Programming I

Specific Competences: 1. Ability to model optimization problems within the framework of operations research. 2. Ability to formulate, analyze, and solve linear optimization models using the graphical method, the simplex method, and specialized software. 3. Ability to formulate, analyze, and solve integer and combinatorial optimization models using the graphical method, the branch-and-bound method, and specialized software. 4. Ability to formulate, analyze, and solve network optimization models. Transversal Competences: 1. Analytical and synthesis skills 2. Ability in mathematical and statistical modeling 3. Problem-solving skills 4. Critical thinking 5. Oral and written communication

1. Introduction to mathematical optimization 1.1. The origins of operations research 1.2. Optimization models: basic terms and concepts 1.3. Modeling and axamples 2. Linear optimization 2.1. Linear optimization models 2.2. The simplex method: geometric interpretation 2.3. Duality, valid inequalities, and sensitivity analysis 3. Integer linear optimization 3.1. Integer linear optimization models 3.2. Logical conditions and reformulation techniques 3.3. Cutting planes 3.4. Branch-and-Bound algorithm 3.5. Branch-and-Cut algorithm 4. Optimization in networks 4.1. Network optimization models 4.2. Examples

Theory (3 ECTS). Theory classes with supporting material available in the course's web page. Practical classes (3 ECTS). Problem-solving classes. Practical classes with computers. Weekly individual tutoring sessions. The teaching methodology will have a theoretical and practical approach, based both on learning the fundamentals of operations research and on studying models and real-world cases.