Quantitative methods seek in building up rational models for the representation of complex problems and in devising the related solution algorithms. Objective of the course is to deepen the student skills on several major topics of operations research with emphasis on computational complexity, combinatorial optimization and multi-criteria analysis.

At the end of the course the student must be able to determine the computational complexity of given algorithms, to design exact and heuristic algorithms for real world combinatorial optimization problem, to know methods of multi-criteria analysis and use them in relation to specific decision problem situations.

Bases of operations research with emphasis on linear programming.

Computational complexity. Elements of graph theory. Combinatorial optimization: exact methods, heuristic approaches, approximation algorithms. Multi-criteria analysis: introduction to multiobjective optimization (pareto-optimality, solution approaches) and to multicriteria outranking methods, ELECTRE methods for sorting decision problems.

The exercise classes are related to the topics presented in the course. In the laboratories commercial software tools are used to deal with more complex problems.

Slides will be provided directly by the teacher. Reference textbooks that contain part of the topics presented in the course are among others • M.R. Garey, D.S. Johnson (1979), Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman and Co. • C.H. Papadimitriou, K. Steiglitz (1982), Combinatorial Optimization. Algorithms and Complexity, Prentice Hall. • V. Vazirani (2001), Approximation Algorithms, Springer. • P. Vincke (1992), Multicriteria decision-Aid, Wiley, Chichester. • L.A. Wolsey (1999), Integer Programming and Combinatorial Optimization, Wiley.

Modalità di esame: Prova scritta (in aula);

Exam: Written test;

... Written exam.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.