Operations Research consists 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: multiobjective optimization (pareto-optimality, solution approaches), outranking methods (ELECTRE II and III, ELECTRE for sorting and segmentation).

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.

Written test.