03UJSRT

A.A. 2022/23

Course Language

Inglese

Course degree

Doctorate Research in Matematica Pura E Applicata - Torino

Course structure

Teaching | Hours |
---|---|

Lezioni | 18 |

Teachers

Teacher | Status | SSD | h.Les | h.Ex | h.Lab | h.Tut | Years teaching |
---|---|---|---|---|---|---|---|

Fadda Edoardo | Ricercatore L240/10 | MAT/09 | 18 | 0 | 0 | 0 | 2 |

Teaching assistant

Context

SSD | CFU | Activities | Area context |
---|---|---|---|

*** N/A *** |

The course aims at introducing the issues to be considered when facing and constructing
mathematical models for optimization problems (i.e., planning decisions to be implemented in order
to optimize an objective function, subject to constraints) in the presence of uncertainty about the
knowledge of the input parameters. After analyzing several possible intuitive approaches and their
limitations, the modeling framework known as Stochastic Programming (SP) will be examined in
depth, outlining its characteristics, advantages, and possible variants. The course will also analyze
indicators to assess the impact of stochasticity on the decision-making process and the problems
related to the creation of a representative Scenario-Tree. Some insights concerning the efficient
resolution of the SP models through specific algorithms will be also given.
To achieve a certificate of attendance with profit of the course, the student will be asked to deliver an
assignment with an adequate level of quality. The project could be either a critical review of the
existing literature on a specific topic related to the course (to be decided with the teacher) or the
application of the Stochastic Programming framework to an optimization problem relevant for the
Ph.D. student’s field of research. Depending of the content, the assignment could be done in group
of max. 3 students. Finally, an attendance of at least the 2/3 of the course is required (12 hours).
The teacher will provide tailored slides and other material to support the lessons.
Some suggested books are:
• J. R. Birge and F. Louveaux, 1997. Introduction to Stochastic Programming. Springer Series
in Operations Research. Springer-Verlag New York • A. J. King and S. W. Wallace, 2012. Modeling with Stochastic Programming. Springer Series
in Operations Research and Financial Engineering. Springer Science+Business Media New York

The course aims at introducing the issues to be considered when facing and constructing
mathematical models for optimization problems (i.e., planning decisions to be implemented in order
to optimize an objective function, subject to constraints) in the presence of uncertainty about the
knowledge of the input parameters. After analyzing several possible intuitive approaches and their
limitations, the modeling framework known as Stochastic Programming (SP) will be examined in
depth, outlining its characteristics, advantages, and possible variants. The course will also analyze
indicators to assess the impact of stochasticity on the decision-making process and the problems
related to the creation of a representative Scenario-Tree. Some insights concerning the efficient
resolution of the SP models through specific algorithms will be also given.
To achieve a certificate of attendance with profit of the course, the student will be asked to deliver an
assignment with an adequate level of quality. The project could be either a critical review of the
existing literature on a specific topic related to the course (to be decided with the teacher) or the
application of the Stochastic Programming framework to an optimization problem relevant for the
Ph.D. student’s field of research. Depending of the content, the assignment could be done in group
of max. 3 students. Finally, an attendance of at least the 2/3 of the course is required (12 hours).
The teacher will provide tailored slides and other material to support the lessons.
Some suggested books are:
• J. R. Birge and F. Louveaux, 1997. Introduction to Stochastic Programming. Springer Series
in Operations Research. Springer-Verlag New York • A. J. King and S. W. Wallace, 2012. Modeling with Stochastic Programming. Springer Series
in Operations Research and Financial Engineering. Springer Science+Business Media New York

No specific pre-requirements are needed. However, it is assumed that the student has a basic level
of confidence with mathematical modeling, statistics, computer, and data science.

No specific pre-requirements are needed. However, it is assumed that the student has a basic level
of confidence with mathematical modeling, statistics, computer, and data science.

The course is composed of theoretical lessons with examples, with a final description of a real-case
application of Stochastic Programming. Possible brief presentations could be done by the Ph.D.
students concerning the applicability of Stochastic Programming to their research field (see
assessment).
The course will be composed by the following macro-themes:
-Optimization problems and Mathematical Programming (basics)
-Data uncertainty: consequences and possible intuitive approaches
-Two-stage Stochastic Programming and Deterministic Equivalent Problem
-Stochastic Programming indicators
-Possible tailored solution approaches
-Multi-stage Stochastic Programming
-Scenario-Tree generation
-Case study

The course is composed of theoretical lessons with examples, with a final description of a real-case
application of Stochastic Programming. Possible brief presentations could be done by the Ph.D.
students concerning the applicability of Stochastic Programming to their research field (see
assessment).
The course will be composed by the following macro-themes:
-Optimization problems and Mathematical Programming (basics)
-Data uncertainty: consequences and possible intuitive approaches
-Two-stage Stochastic Programming and Deterministic Equivalent Problem
-Stochastic Programming indicators
-Possible tailored solution approaches
-Multi-stage Stochastic Programming
-Scenario-Tree generation
-Case study

In presenza

On site

Presentazione report scritto

Written report presentation

P.D.1-1 - Novembre

P.D.1-1 - November

• mercoledì 9 marzo dalle 14:30 alle 17:30 aula 3P;
• venerdì 11 marzo dalle 14:30 alle 17:30 aula 7;
• mercoledì 16 marzo dalle 14:30 alle 17:30 aula 3P;
• venerdì 18 marzo dalle 14:30 alle 17:30 aula 7;
• mercoledì 23 marzo dalle 14:30 alle 17:30 aula 3P;
• venerdì 25 marzo dalle 14:30 alle 17:30 aula 7.

• mercoledì 9 marzo dalle 14:30 alle 17:30 aula 3P;
• venerdì 11 marzo dalle 14:30 alle 17:30 aula 7;
• mercoledì 16 marzo dalle 14:30 alle 17:30 aula 3P;
• venerdì 18 marzo dalle 14:30 alle 17:30 aula 7;
• mercoledì 23 marzo dalle 14:30 alle 17:30 aula 3P;
• venerdì 25 marzo dalle 14:30 alle 17:30 aula 7.

© Politecnico di Torino

Corso Duca degli Abruzzi, 24 - 10129 Torino, ITALY

Corso Duca degli Abruzzi, 24 - 10129 Torino, ITALY