The Course introduces to optimization models and methods for the solution of decision problems, with case-studies from environmental systems. It is structured according to the basic topics of problem modelling, its tractability, and its solution by means of algorithms that can be implemented on computers.
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.
The final examination consists of written and oral tests.
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. 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. Some concepts of decision theory, multiobjective optimization and game theory in the scalar and vector cases. 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.
MASSIMO PAOLUCCI (President)
ANGELA LUCIA PUSILLO (President)
ROBERTO SACILE (President)
CHIARA BERSANI
RICCARDO MINCIARDI
MICHELA ROBBA
ADRIANA SACCONE
