OVERVIEW

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.

LEARNING OUTCOMES

The course allows acquire knowledge on a set of Operations Research (OR) models and methods (mathematical programming models; integer programming methods; graphs and network models) and problem solving capability 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).

AIMS AND LEARNING OUTCOMES

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 and 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.

Teaching methods

The course consists of classroom lectures.

The exam consists in a written and/or oral test

SYLLABUS/CONTENT

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.

Some concepts of multi-objective optimization

Basic concepts of the theory of complexity.

RECOMMENDED READING/BIBLIOGRAPHY

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.

Exam Board

MARCELLO SANGUINETI (President)

ROBERTO SACILE (President)

MASSIMO PAOLUCCI (President)

RICCARDO MINCIARDI

CHIARA BERSANI

ADRIANA SACCONE

MICHELA ROBBA

ROBERTO BRUSCHI (President Substitute)

Teaching methods

The course consists of classroom lectures.

The exam consists in a written and/or oral test

Exam description

Written exam text and oral exam (optional after passing the written text). The students who want to take the exam must register online and send an email to the professor.

Exam schedule