Base Knowledge
- Mathematic Analysis II
- Algebra
Teaching Methodologies
The course content is delivered through guided theoretical exposition, followed by practical problem-solving in class and collective discussion. Teaching methods emphasise active learning and collaborative work, particularly in the completion of tasks that integrate the critical and responsible use of Artificial Intelligence tools. The focus is on developing the mathematical competences proposed by Niss and highlighted by the
SEFI Mathematics SIG (thinking, reasoning, modelling and communicating mathematically), as well as on linking to real contexts of asset management. Teaching combines mathematical rigour with ethical and professional reflection, encouraging evidence-based decision-making.
Learning Results
By the end of this course unit, students should be able to:
- Think and reason mathematically, pose and solve mathematical problems, model real situations and represent them rigorously using mathematical symbols and formalisms.
- Communicate in, with and about mathematics, using different representations, digital resources and support tools.
- Formulate and solve problems in linear programming and network optimisation, applying appropriate methods (Simplex, transportation, assignment, shortest path, maximum flow).
- Use Artificial Intelligence tools critically and responsibly, recognising their limitations, validating results and reflecting on ethical and professional implications.
- Relate theoretical knowledge to practical applications, emphasising evidence-based decision-making in engineering and asset management contexts.
Program
- Introduction
- Linear Programming. Simplex method and its variants.
- Transport problems
- Matching problems
- Network problems
- Non-linear optimization and heuristic methods
- Fundamental notions of project management
- Organizational insights
- Methodologies
- Graphic representation
- Resource Planning and Control
Throughout all semester and whenever possible, students will be encouraged to use software that helps their understanding and problems resolution.
Curricular Unit Teachers
Deolinda Maria Lopes Dias Rasteiro
Internship(s)
Bibliography
– Martins, E.Q.V., Pascoal, M.M.B., Rasteiro, D.M.L.D., Santos, J.L.E.. (Junho 1999). The Optimal Path Problem, Investigação Operacional, Vol 19, no 1, pp. 43-60. (available at curricular unit Moodle webpage)
– Dias Rasteiro, D.M.L. , 9 – Shortest path problem and computer algorithms. (2020). Editor(s): Jesús Martín-Vaquero, Michael Carr, Araceli Queiruga-Dios, Daniela Richtáriková, In Mathematics in Science and Engineering, Calculus for Engineering Students, Academic Press. Pages 179-195, ISSN 00765392, ISBN 9780128172100, https://doi.org/10.1016/B978-0-12-817210-0.00016-3. (available at curricular unit
Moodle webpage)
– Syllabus elaborated by the lecturer. (available at curricular unit Moodle webpage)
– Hillier, F. , Lieberman, G. . (2004). “Introduction to Operations Research”, McGraw Hill. Localização na Biblioteca: 3-9-56 (ISEC) – 09160
– Dias Rasteiro, D.M.L., Chibeles-Martins, N., 10 – Random variables as arc parameters when solving shortest path problems. (2020). Editor(s): Jesús Martín-Vaquero, Michael Carr, Araceli Queiruga-Dios, Daniela Richtáriková, In Mathematics in Science and Engineering, Calculus for Engineering Students, Academic Press. Pages 197-219, ISSN 00765392, ISBN 9780128172100, https://doi.org/10.1016/B978-0-12-817210-0.00017-5.
– Mezzadri, D. The Paradox of Ethical AI-Assisted Research. J Acad Ethics (2025).
https://doi.org/10.1007/s10805-025-09671-7 (pdf available online)
– Lucas J. Wiese, Indira Patil, Daniel S. Schiff, Alejandra J. Magana, AI ethics education: A systematic literature review, Computers and Education: Artificial Intelligence, Volume 8, 2025, 100405, ISSN 2666-920X, https://doi.org/10.1016/j.caeai.2025.100405. (pdf available online)
Additional Bibliography:
– Valadares Tavares, L.. (1996). “Operational Research”. McGraw Hill
– Henggeler Antunes, C., Valadares Tavares, L.. (2000). Cases of Application of Operations Research. McGraw-Hill;
– Romão, M. C. , Pinto, L. S. , Simões, O. , Valente, J. and Vaz Pato, M. . (2011). Investigação Operacional – Exercícios e Aplicações, Verlag Dashofer.
