The course presents a set of mathematical models and methods for solving decision problems with a particular reference to natural risk and emergency management. The purpose of this course is to provide the students with competences in using a set of models for problem solving. In particular, the course mainly considers optimization problems faced by mathematical programming techniques and problems on graph and networks.
The course allows acquire knowledge on a set of OR models and methods (mathematical programming models; integer programming methods; graphs and network models).
Capability of problem solving by a set of OR techniques (formulation of mathematical programming models and use of mathematical programming algorithms; algorithms for problem solving on graph and networks).
As regards mathematical programming, the main objective is to provide the students with skills for defining the right model to solve a set of decision problems formulating them as optimization problems. In particular, continuous an mixed integer programming algorithms are presented and applied to different cases. Such methods, together with methods for graph and network, represent fundamental optimization tools for their possible applications in natural risk and emergency management.
The course consists of classroom lectures.
Introduction to decisional problems and models.
Optimization problems and optimality conditions.
Basic concepts of non-linear mathematical programming.
The process of problem formulation by means of quantitative models.
Linear programming; graphic formulation and solution of linear programs; the simplex algorithm; duality theory; sensitivity analysis.
Integer programming and combinatorial optimization; the methods of cutting-planes and branch-and-bound.
Graph theory; the shortest paths problem; the minimum spanning tree problem. Network problems; min cost flow and max flow problems.
Vehicle routing problems.
Some concepts of multi-objective optimization
Basic concepts of the theory of complexity.
Introduction to Operations Research, 9/e
Frederick S Hillier, Stanford University
Gerald J Lieberman, Late of Stanford University
ISBN: 0073376299
McGraw-Hill Higher Education, 2010
Branzei-Dimitrov-Tijs "Models in cooperative game theory", Springer, 2008
Peters H., "Game Theory- A Multileveled Approach". Springer, 2008.
Ricevimento: Students can ask appointments directly contacting the professor by email or phone
MASSIMO PAOLUCCI (President)
ANGELA LUCIA PUSILLO (President)
ROBERTO SACILE (President)
CHIARA BERSANI
RICCARDO MINCIARDI
MICHELA ROBBA
ADRIANA SACCONE
