CODE 97363 ACADEMIC YEAR 2025/2026 CREDITS 6 cfu anno 2 INGEGNERIA GESTIONALE 10716 (L-9) - GENOVA SCIENTIFIC DISCIPLINARY SECTOR MAT/09 LANGUAGE Italian TEACHING LOCATION GENOVA SEMESTER 1° Semester TEACHING MATERIALS AULAWEB OVERVIEW The teaching unit in Operations Research provides students with skills related to the construction of mathematical models and the use of algorithms to solve decision-making problems formulated as optimization problems. AIMS AND CONTENT LEARNING OUTCOMES The course provides the basic knowldge of optimization methods to solve decision-making problems. In particular, the course will provide knowledge to model from the mathematical viewpoint a decision problem, and solve it through linear programming, linear integer programming, nonlinear programming, and optimization over graphs. AIMS AND LEARNING OUTCOMES This teaching unit introduces fundamental concepts and methods in optimization for solving decision problems. In particular, students will acquire the ability to mathematically model decision-making situations and solve them using linear programming, integer linear programming, nonlinear programming, and graph-based optimization techniques. PREREQUISITES Basic knowledge of Mathematical Analysis, Geometry, and Computer Science TEACHING METHODS Traditional lessons. SYLLABUS/CONTENT * Basic concepts in computational complexity theory * Introduction to mathematical programming and decision problems * Linear programming with continuous variables: problem formulation, the simplex algorithm, post-optimality analysis, duality theory, and the dual simplex method * Integer linear programming: binary variables, problem formulation, total unimodularity, cutting planes method, and branch-and-bound algorithm * Graph optimization: fundamental definitions, the minimum spanning tree problem (Kruskal's and Prim's algorithms); the shortest path problem (Dijkstra, Bellman-Ford, and Floyd-Warshall algorithms) * Network flows: example formulations, the max-flow min-cut problem and the augmenting path algorithm; the minimum-cost flow problem, cycle-canceling algorithms, and the network simplex algorithm * Practical examples of modeling and solving linear and mixed-integer programming problems using IBM's CPLEX solver RECOMMENDED READING/BIBLIOGRAPHY Handouts provided by the lecturer. Books for possible further study: [1] Hillier, Lieberman – Introduction to operations research. McGraw-Hill, 2004. [2] D. Bertsimas, J.N. Tsitsiklis – Introduction to linear optimization. Athena Scientific, 1999. TEACHERS AND EXAM BOARD MASSIMO PAOLUCCI Ricevimento: Students can ask appointments directly contacting the professor by email or phone LESSONS LESSONS START https://corsi.unige.it/en/corsi/10716/studenti-orario Class schedule The timetable for this course is available here: Portale EasyAcademy EXAMS EXAM DESCRIPTION Written examination, potentially including: * Exercises requiring the application of algorithms to the problem classes presented in the course * Short theoretical questions * Formulation of simple combinatorial decision-making problems ASSESSMENT METHODS By the end of the teaching unit, students are expected to: * Demonstrate an understanding of the concepts covered in lectures and explain them using appropriate academic language * Be able to select and apply the most suitable algorithm for solving decision problems presented in the course * Formulate linear programming models to solve decision problems of a combinatorial nature FURTHER INFORMATION None.
