Teaching Methodologies
The lectures will cover concepts, techniques and methods, with a strong focus on practical applications. Computer support will be used to solve larger problems.
Some classes will be computer-based, encouraging the applied nature of the models and techniques presented, aimed at Management problems.
This way, some classes will have theoretical and theoretical-practical components, involving the exposition of concepts, methods and algorithms, including the resolution of small-scale applied cases. There will also be classes of a more applied nature, in which appropriate computer tools will be used for the computational resolution of larger applied cases.
Monitoring the learning process with periodic assessments should help the student to consolidate the syllabus elements, both the theoretical elements and the practical and applied subjects, which should strengthen the know-how acquisition and the students’ autonomy in the practical use of this knowledge. The aim is also for the students to gain skills that will enable them to discover ways of responding to new optimisation problems within the scope of the course.
Learning Results
This course introduces techniques to support the decision-making process, using linear and integer linear programming models, including network optimization and heuristics.
Techniques for solving the proposed mathematical models will be studied and their application within Management be encouraged.
Appropriate software will be used to solve the proposed optimisation models, including Python libraries.
The course also focuses on the study of algorithms for Artificial Intelligence, including heuristic and metaheuristic techniques for solving combinatorial optimization problems, with special attention to their practical application.
The aim is to make students aware of the mathematical modelling of the proposed problems. They will also be familiar with techniques for solving these problems, including its algorithmic resolution. The aim is thus to provide students with the theoretical and practical knowledge to apply quantitative techniques to support decision-making.
Program
1 Introduction to mathematical modelling
1.1 Mathematical formulation of problems
1.2 Application cases to Management
2 Linear Programming
2.1 Properties
2.2 Techniques and software for solving continuous linear models
2.3 Sensitivity analysis and economic interpretation of solutions
3 Network Optimization
3.1 Graphs/networks concepts and properties
3.2 Transportation and allocation
3.3 Shortest path problem
3.4 Maximum flow problem
4 Integer programming
4.1 Properties of linear formulations with integer variables
4.2 Modelling techniques using binary variables
4.3 Using computational tools to solve integer linear models
5 Heuristics and Metaheuristics in Artificial Intelligence
5.1 Introduction to Artificial Intelligence
5.2 Approximate techniques for solving combinatorial problems
5.3 Greedy heuristics
5.4 Local search heuristics
5.5 The A* algorithm
5.6 Metaheuristics with deterministic factors and with random factors
Internship(s)
NAO
Bibliography
– Gendreau, M., & Potvin J. Y. (Eds.) (2019). Handbook of Metaheuristics, International Series in Operations Research & ManagementScience, Springer. ISBN: 978-3-319-91085-7
– Hillier, F. S., & Lieberman, G. J. (2021). Introduction to Operations Research, Mc Graw-Hill. ISBN: 978-0-071-13989-2
– Mourão, M. C., Santiago Pinto, L., Simões, O., Valente, J., & Pato, M. V. (2019). Investigação Operacional: Exercícios e Aplicações,
Escolar Editora. ISBN: 978-9-725-92556-0