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Home / Oferta Formativa / Coimbra Institute of Engineering / Master / Master in Enginnering and Management of Physical Assets

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

Grading Methods

Periodic Assessment

Continuous assessment consists of two in-class tasks and two written tests. Each in-class task lasts 2 hours, allows the use of AI (with critical validation), and is worth 3 points: one focused on network optimisation and the other on linear programming. The in-class tasks can be carried out individually or in pairs. The written tests are individual, without consultation, each also lasting 2 hours, one on networks and the other on linear programming, and are worth 7 points each. The final grade is the sum of these components, for a total of 20 points.
Each written test requires a minimum score of 3.5 points to pass the continuous assessment. In-class tasks must include a record of the AI tool used, the prompt, and the consultation date, and will be assessed on their critical and ethical analysis.
If, in continuous assessment, the student does not achieve the minimum score (3.5 points) in one of the components, they may, if they wish, repeat in the final examination only the missing part, with the same distribution of marks as in this component of assessment.
A student who does not pass the continuous assessment or does not participate in it may sit the final examination during the periods defined in the ISEC academic calendar. The exam also consists of two parts, each worth 10 points, with a minimum of 4.75 points required in each part. This choice excludes the marks obtained in the in-class tasks.
Proposed dates for the written tests during the semester:
1st Test: 8th week's classes
2nd Test: last week's classes
(both carried out during scheduled class hours).
Assessment rubrics (per activity/test):
In-class tasks (3 points):
Technical accuracy/validation - 1.0 points
Critical analysis of AI + ethics - 1.0 points
Clarity and presentation - 1.0 points
Written tests (7 points):
Modelling / correct formulation - 2 points
Algorithm or step-by-step resolution - 3.5 points
Interpretation/sensitivity/minimum reflection - 1.5 points

    Internship(s)

    NAO

    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.