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Modeling and problem solving with stochastic programming
02UJSIU
A.A. 2020/21
Course Language
Inglese
Degree programme(s)
Doctorate Research in Ingegneria Informatica E Dei Sistemi - Torino
Course structure
| Teaching | Hours |
|---|---|
| Lezioni | 18 |
Lecturers
| Teacher | Status | SSD | h.Les | h.Ex | h.Lab | h.Tut | Years teaching |
|---|
Co-lectures
Context
| SSD | CFU | Activities | Area context | *** N/A *** |
|---|
Course description:
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 on the topic concerning the efficient resolution of the SP models will be also given.
Expected Learning Outcomes:
The student will be able to correctly identify sources of uncertainty in the problem setting and to correctly model them within the framework of the Stochastic Programming paradigm.
The student will be able to analyze the constructed models and assess the impact of the uncertainty.
The student will be aware of the limitations and the drawbacks of specific modelling decisions, of the computational burden of solving such models, and will have some intuitions in the direction of possible efficient solution methods.
Course description:
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 on the topic concerning the efficient resolution of the SP models will be also given.
Expected Learning Outcomes:
The student will be able to correctly identify sources of uncertainty in the problem setting and to correctly model them within the framework of the Stochastic Programming paradigm.
The student will be able to analyze the constructed models and assess the impact of the uncertainty.
The student will be aware of the limitations and the drawbacks of specific modelling decisions, of the computational burden of solving such models, and will have some intuitions in the direction of possible efficient solution methods.
No specific prerequirements 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 prerequirements 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 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 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
A distanza in modalità sincrona
On line synchronous mode
Sviluppo di project work in team
Team project work development
P.D.1-1 - Novembre
P.D.1-1 - November