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.

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

Lezione videoregistrata

Presentazione orale - Prova di laboratorio di natura pratica sperimentale o informatico

P.D.2-2 - Marzo