Studying at the University of Verona
Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.
Study Plan
The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.
Please select your Study Plan based on your enrollment year.
1° Year
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2° Year activated in the A.Y. 2024/2025
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1 module among the following
2 courses among the following
2 courses among the following (a.a. 2023/24: Statistical methods for business intelligence not activated)
2 courses among the following
Legend | Type of training activity (TTA)
TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.
Discrete optimization and decision making (2023/2024)
Teaching code
4S009081
Academic staff
Coordinator
Credits
6
Also offered in courses:
- Mathematics for decisions of the course Master's degree in Mathematics
- Discrete Optimization of the course Master's degree in Artificial intelligence
Language
English
Scientific Disciplinary Sector (SSD)
MAT/09 - OPERATIONS RESEARCH
Period
Semester 2 dal Mar 4, 2024 al Jun 14, 2024.
Courses Single
Authorized
Learning objectives
The course aims to introduce the basics of mathematical programming, in order to develop modeling skills to formulate and solve complex real problems in both deterministic and probabilistic domains. The course will cover topics of integer and continuous linear programming, also providing good knowledge in the field of stochastic programming and robust optimization, as methods in the field of decision theory. The lectures will focus on the computational aspects of the different approaches, as well as on the respective modeling and application features in concrete areas. At the end of the course the student has to show to have acquired the following skills: i) ability to deal with modeling, optimization and decision-making problems, ii) ability to develop computational tools for the application of theoretical solutions in the field of optimization of, e.g., routing, industrial production and financial processes, iii) ability to use specific software solutions to solve mathematical formulations, e.g., Gurobi, Cplex
Prerequisites and basic notions
rudiments of analysis (numbers, sets, functions), algebra and calculus (equations and unknowns), analytic geometry (Cartesian coordinates, equations for the line or the plane), and linear algebra (vectors and matrices)
Program
- Basic notions on Problems, Models, Algorithms and Computational Complexity
- Linear Programming (reference: Vanderbei chapters 2,3,4,5, but no need to read the proof concerning Bland's rule)
- the tableau and the simplex algorithm
- duality theory
- complementary slackness
- economic interpretation
- Modeling
- the art of resorting to a Solver (Gurobi)
- Integer Linear Programming
- simple enumeration and implicit enumeration algorithms
- branch & bound
- branch & cut
- compact formulations
- approximation algorithms
- heuristics and meta-heuristics
- Graphs as models and problems on graphs
- shortest paths
- maximum flows
- maximum bipartite matching
- TSP
Bibliography
Didactic methods
The lessons will take place in a traditional classroom but can be followed also from remote and will be recorded.
Learning assessment procedures
The exam consists of two separate parts:
+ HOMEWORK and MINI-PROJECTS with marks produced as the projects are received, possibly after their discussion and/or presentation. These activities take place already during the course but the projects can be delivered even after the course has ended. The weighted average of all these marks will become the final mark for this part.
+ INDIVIDUAL ORAL, with mark produced at the time of the oral
the exam grade will be the arithmetic mean rounded up, where a 30L is counted as 32, and to obtain 30L as final mark you need at least a 30L and both grades must be at least 30.
Skills to be exhibited in the oral exam:
1. knowledge of the theorems discussed (at least their statements)
2. knowledge of some notable models.
3. ability to reason with examples and counterexamples.
4. being able to provide examples and classes of exact, approximate and metaheuristic algorithms.
5. mastery of the language of the LP and of the ILP.
6. ability to model a problem on an abstract level and also in practice.
7. knowledge of the topics treated during the course. At the end of the course a list of such topics will be agreed upon.
Evaluation criteria
Discussed and agreed with the aim that they can be both fair and reasonable, also considering the heterogeneity in the background and paths of the participants to be managed as a precious resource.
Exam language
English (official language of the course) is fine. Italiano va benissimo.