Engineering Systems

Academic year
Subject Area
Applied Mathematics
Language of Instruction
Mode of Delivery
ECTS Credits
1st Cycle Studies

Recommended Prerequisites

Mathematical Analysis.

Teaching Methods

Lectures with the help of audiovisual media where concepts, principles and theories are presented in detail. Practical exercises that meet all the needs of students are solved, with guidelines provided.

The grading considers both the final exam (75%) and four individual practical assignments solved in class during the term (25%).

Learning Outcomes

Main objectives: to encourage the development of a systems perspective for intelligent planning and management of large-scale engineering systems; to provide students with scientific methodologies and quantitative tools of great value for decision-making and rational resource use in civil and environmental engineering, taking into consideration the various sustainability dimensions.


to acquire sensitivity for the need of rationality in resource use by engineering;

to use scientific methods for decision aiding;

to formulate formal models (mathematic models, network based, etc.) and apply algorithms for obtaining solutions in optimization problems in several fields (planning, design, construction and maintenance of engineering systems);

to apply critical reasoning in the interpretation of reality through formal models;

to develop sensitivity analysis;

to understand the conflicts that usually exist among multiple objectives and the need for searching compromise solutions.

Work Placement(s)




Resource optimization: goals, compatibility of aspects such as safety, economy, quality, sustainability. Resource optimization and sustainable development.

Types of models; mathematical models. Operations Research and applications. The importance of computer science in the analysis of complex engineering systems.

Linear Programming

Mathematical model in linear programming. Formulation; graphical and algebric methods; Simplex, particular cases, artificial variables, matrix and revised versions; duality; sensivity analysis; transportation problem, transshipment and assignment; integer and mixed programming -  the Branch-and-Bound method.

Formulation of models with multiple objectives.


Networks and algorithms: shortest path, minimal spanning tree, maximum flow, CPM/PERT.


Regional and urban planning, logistics and transportation, facility location, hydraulic systems, environmental and civil engineering project management.

Assessment Methods

Mini Tests: 25.0%
Exam: 75.0%


Coutinho-Rodrigues, João - Aplicações da Teoria de Sistemas – 6ª edição, Ediliber - Coimbra, 2009.

Guerreiro, J.; A. Magalhães; M. Ramalhete - Programação Linear, volumes 1 e 2, McGraw-Hill, 1995.

Hillier, F.; G. Lieberman - Introduction to Operations Research, McGraw-Hill, 2001.

Labi, S. - Introduction To Civil Engineering Systems, Wiley, 2012.

Ossenbruggen, P. - Systems Analysis for Civil Engineers: Technological and Economic Factors in Design, Wiley, NY, 1984.

Revelle, C.; E. Whitlatch; J. Wright. - Civil and Environmental Systems Engineering, 2nd ed., Prentice Hall, 2004.

Revelle, C.; A. McGarity - Design and Operation of Civil and Environmental Engineering Systems, Wiley, 1997.

Tavares, L.; R. Oliveira; I. Themido; F. Correia - Investigação Operacional, Ed. McGraw-Hill de Portugal Lda, 1996.

Templeman , A. - Civil Engineering Systems, Macmillan, 1982.