SM/0132 - OPERATIONS RESEARCH
Academic Year 2021/2022
Free text for the University
MASSIMO DI FRANCESCO (Tit.)
- Teaching style
- Lingua Insegnamento
|[60/65] MATHEMATICS||[65/60 - Ord. 2020] MATEMATICA APPLICATA||9||72|
1. Knowledge and understanding skills.
The course is designed for the students of the 1st year of the Master Degree in Mathematics.
This course aims to provide students with a deep knowledge in the theory and practice of (Integer) Linear Optimization, which has relevant applications in computer science, economics, engineering, as well as a number of other domains. The goals of the course are the following:
• To teach students how to model several problems by (Integer) Linear Optimization
• To present the state-of-the-art in the theory and practice for solving (Integer) Linear Optimization problems.
• To provide students with a rigorous analysis of algorithms for (Integer) Linear Optimization.
2. Ability to apply knowledge and understanding.
Students must apply the methods presented in the course to solve realistic problems, which are similar to those faced in the lectures. In the oral exam student must explain how some algorithms work.
3. Autonomy of judgment.
The modelling stage will be put in the position of critically thinking at the problem setting, evaluating which data are requested in their formulation. Students must also evaluate the most suitable algorithms to solve specific models.
4. Communicative Skills.
Communicative skills will be further evaluated in the oral exam.
5. Learning Skills.
The course provides students with sufficient preparation to understand more advanced mathematical texts and makes them able to expand their knowledge autonomously in the future.
1. Knowledge. The course would benefit from a good understanding of the basic concepts of Linear Algebra and Numerical Analysis, which can be learned both in the Bachelor Degree Program in Mathematics.
2. Skill. Students must be able to read and formalize algorithms’ pseudocodes.
3. No a-priori competences is requested.
No exam has to be passed before Ricerca Operativa.
3. No a-priori competences is requested.
No exam has to be passed before the exam of Ricerca Operativa.
• Mathematical Programming
• Linear Programming Models
• The simplex Method
• Duality theory
• Integer Programming
• Decomposition for Large Scale Optimization
The course consists of 72 hours of lectures in Italian. They cover theoretical concepts, as well as several exercises to review and reinforce the theoretical concepts. Finally, the professor provides regular support to students throughout the course by ad-hoc meetings and e-mails.
Verification of learning
Students must demonstrate their knowledge of the specific terminology, the ability to solve a realistic problem and the theoretical concepts presented in the lectures. Students are evaluated in two stages: a project on a problem and an oral exam. The project must be approved by the Professor and is typically made in cooperation with another student. The conclusion of the project is a necessary condition to give the oral exam. It is evaluated 16 points. Two questions are typically made in the oral exam. The answers are evaluated up to 15 points.
• The final mark ranges between 18/30 and 22/30 in the case of sufficient knowledge of the specific terminology, correct application of the methodological concepts and sufficient presentation of the concepts and results.
• The final mark ranges between 22/30 and 26/30 in the case of good knowledge of the terminology, good application of the methodological concepts and a good presentation of concepts and results.
• The final mark ranges between 27/30 and 30 cum laude in the case of an excellent mastery of specific terminology, a critical application of the methodological concepts and a clear display of concepts and results.
Students are advised to check their preparation during the lectures. They will test their skills by practicing with exercises and comparing their results to those presented by the Professor.
Matteo Fischetti. Lezioni di Ricerca Operativa. Kindle Publishing. 2018
Bersimas D., Tsitsiklis J.N. Introduction to Linear Optimization. Dynamic Ideas (1997).
The main teaching-supporting tool is the platform elearning platform (https://elearning.unica.it/), where additional information is available (e.g. a course diary reporting the topics of each lesson and further teaching files). Additional online support will be provided according to the evolution of the COVID-19 pandemic.