## 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.

## AIMS AND CONTENT

LEARNING OUTCOMES

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.

AIMS AND LEARNING OUTCOMES

The main objective is to provide students with the skills to define mathematical programming models to solve a series of decision problems by formulating them as optimization problems. Students will be able to solve continuous and mixed integer programming problems using appropriate methods and algorithms. Students will be able to solve problems using networks flow models and graphs. These models represent fundamental optimization tools for their possible applications in the management of natural risk and emergencies.

TEACHING METHODS

The course consists of classroom lectures.

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.

## TEACHERS AND EXAM BOARD

**Office hours:** Students can ask appointments directly contacting the professor by email or phone

Exam Board

ROBERTO SACILE (President)

CHIARA BERSANI

RICCARDO MINCIARDI

MICHELA ROBBA

ADRIANA SACCONE

MASSIMO PAOLUCCI (President Substitute)

MARCELLO SANGUINETI (President Substitute)

## LESSONS

TEACHING METHODS

The course consists of classroom lectures.

LESSONS START

Class schedule

All class schedules are posted on the EasyAcademy portal.

## EXAMS

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.

ASSESSMENT METHODS

The students will be asked to solve linear and integer programming problems using the learnt algorithms and applying concepts from theory. They have to be able to sove problems on graphs and networks. They have to demostrate to know the basic concepts of multi-criteria decision making.

Exam schedule

Date | Time | Location | Type | Notes |
---|---|---|---|---|

13/01/2022 | 08:30 | SAVONA | Orale | |

08/02/2022 | 08:30 | SAVONA | Orale | |

06/06/2022 | 09:00 | SAVONA | Orale | |

21/06/2022 | 08:30 | SAVONA | Orale | |

15/09/2022 | 08:30 | SAVONA | Orale |