Mathematics for decisions (2019/2020)

Course code
4S008838
Name of lecturer
Romeo Rizzi
Coordinator
Romeo Rizzi
Number of ECTS credits allocated
6
Academic sector
MAT/09 - OPERATIONS RESEARCH
Language of instruction
English
Period
II semestre dal Mar 2, 2020 al Jun 12, 2020.

Lesson timetable

Go to lesson schedule

Learning outcomes

Mathematics for decisions is a seminar course comprising: + interventions by external professors (seminars, mini-courses); + interventions by professionals (statements of problems from the applications, description of needs and/or projects); + interventions by the referent of the course, collaborators of him, or colleagues by the department (both classes and proposal of problems and projects from the applications). + presentations delivered by the students on arguments of their interests and as agreed upon (seminars). The aim of this offert is to provide the studens with opportunities to meet and/or get involved into working or research projects, activating and developing their own interests, motivations and talents. Among the targets of this offert: + provide the students with opportunities to get in touch with working and/or research environments, developing motivations, interests, attitudes; + allow connections with professionalities and disciplines, not necessarily within mathematics but that can motivate the work of a matematician or help appreciating its possible applicability; + stimulate and develope the competence in designing mathematical models for the managing of production facilities, networks, and services; + provide the students with occasions to experiment their computational and informatics skills and to become more aware of their impact and role. With this the aim is to lead our students to: + have the competence and attitude to cover technical and professional roles with an high-level modellistic-math profile; + have the necessary starting background and the attitude to document themselves by accessing math texts, research articles, project deliverables, technical documentation.

Syllabus

- Problems, Instances, Models
- Constraint Programming
- Abstract modeling programming languages - AMPL/GMPL:
- Recall the basics of Linear Programming (if needed)
- Some fact from Polyhedral Combinatorics
- Polytopes, polyhedra and equivalent representations
- Basic lemmas and characterizations
- Integrality of polyhedra
- Solution approaches to NP-hard problems:
- Enumeration
- Implicit enumeration and Branch-and-Bound
- Branch-and-Cut
- Approximation algorithms
- Complete and incomplete formulations (e.g., Traveling Salesman Problem, Perfect Matching)
- Gomory's cuts and cutting planes
- Separation oracles and callbacks
- Compact formulations
- Decomposition techniques:
- Column generation
- Dantzig-Wolfe decomposition
- Isomorphism free generation

Projects will be proposed during the course, some already at the very beginning, some others from invited companies.
Depending on their interests, students are invited to choose (or even propose and tune together) projects from three categories: industrial, academic, didactics.

Reference books
Author Title Publisher Year ISBN Note
Robert J. Vanderbei Linear Programming: Foundations and Extensions (Edizione 4) Springer 2001 978-1-4614-7630-6
Robert Fourer, David M. Gay, and Brian W. Kernighan THE AMPL BOOK. AMPL: A Modeling Language for Mathematical Programming   0-534-38809-4

Assessment methods and criteria

The students are required to develop a project. This might either come from industry, from other research centers or universities, from colleagues or on research lines of interest by the department, or even from ourselves included the students themselves).
We also encourage projects that contribute to the rather technical material (TuringArena based) we strive resorting onto in offering active and interactive learning experiences to our students.
We will propose several projects on each one of these main lines, the students are also encouraged to propose and stear themself according to their interests and competences.

Most projects comprise a development phase where the student must exhibit his/her technical and informatics skills in implementing the models and the algorithms developed or adopted to solve a given problem.

Depending on the project, other phases will be required as part of the exam or might naturally follow:
study of a topic or subject, study of a technique to employ in order to solve a problem or to be illustrated, experiments, deployment, documentation, design of a didactic problem, exposition, writing of paper, stages, thesis, internship.