Operational Research

Code:

L.EC017

Acronym:

IO

Keywords
Classification	Keyword
OFICIAL	Complementary Sciences/Technologies

Instance: 2025/2026 - 2S

Active?	Yes
Web Page:	https://moodle.up.pt/course/view.php?id=3904
Responsible unit:	Department of Civil and Georesources Engineering
Course/CS Responsible:	Bachelor in Civil Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L.EC	169	Syllabus	2	-	6	45,5	162

Teaching language

Portuguese

Objectives

This course aims to acquaint students with skills (methods) on problem solving (processes and decision making).
This course also aims to develop students’ skills to identify and to have a structured approach to solve problems, to construct models of problems of decision, to use quantitative methods to obtain solutions, as a support to reasoned decisions, as well as to know how to use information from models to introduce changes in the processes.

Learning outcomes and competences

Knowledge: To be acquainted with the methodology of problem solving and dominate research techniques used as a support of decision making processes.

Skills: To apply the analytical tools of operational research to the approach, structure and rational resolution of decision problems.

Understanding: To understand decision making and mathematical reasoning processes and geometrical visualization of methods of resolution problems of linear programming, sensitivity and post-optimal analysis, problems of transportation, allocation problems, network optimization problems, problem of , game theory and decisions problem theory.

Competencies: To handle different methodologies of decision support, by clearly identifying which are the most appropriate methodologies in decision in different types of situation. To develop skills on decision making.

Working method

Presencial

Program

1 Introduction to Operational Research:
1.1 Nature and Operational Research Methodology. Modelling: objectives, characteristics and techniques
1.2 Cases of Study: methodological approach, structuring of the problem, and conclusions
1.3. Importance of Operational Investigation in the decision-making process.
2 OR method
2.1 Problem formulation,
2.2 Construction of the model
2.3 Validation of the model
2.4 Testing of solution
2.5 Implementation of the solution.
3 Mathematical Techniques 
3.1 Linear Programming. Formulation of a linear programming problem
3.2 Simplex Method
3.3 Duality
3.4 The Transportation problem and the Assignment problem
3.5 Network Analysis and Project Planning (PERT/ CPM)
3.6 Entire programming and/or multipurpose
3.7 Queueing Theory: decision under uncertainty, problem formulation, modelling of waiting systems, stationary regime and congestion, performance measures


Evidence of the syllabus coherence with the curricular unit’s intended learning outcomes:
The program covers methodological concepts of problem solving and implementation of solutions stressing the need to dominate the processes through the construction of specific models from previous knowledge in mathematics complemented with techniques taught in the discipline, applied in the context of problem solving.
Being a course in civil engineering the examples and the exercises presented are related to applied situations that the students might face in the future.

Mandatory literature

Frederick S. Hillier, Gerald J. Lieberman; Introduction to operations research. ISBN: 007-123828-X
Goodwin, P. e Wright, G.; Decision Analysis for Management Judgment, John Wiley & Sons, Ltd, 2007. ISBN: 978-0-470-86108-0
Hamdy A. Taha; Operations research. ISBN: 0-13-281172-3
Antunes, C. H., & Alves, M. J., & Clímaco, J.; Multiobjective Linear and Integer Programming. ISBN: 978-3-319-28746-1
Carlos Henggeler Antunes; Casos de aplicação da investigação operacional. ISBN: 972-773-075-2

Teaching methods and learning activities

Part of the theoretical classes will be based on the presentation of concepts and relevant results of the subjects that are being covered (processes, methodology of problem solving and theory of decision), as well as its importance on civil engineering, thorough the presentation of examples and case studies.
Other theoretical classes and theoretical-practical classes will cover the mathematical techniques of operational research to solve types of problems frequent in engineering.
The evaluation is realized by a work in group (30%) and by an exam (70%).

Evidence of the coherence between the teaching methodologies and the intended learning outcomes:
The teaching methodologies permit to apply the analytical tools of operational investigation to the approach, structure and rational resolution of decision problems, to analyse real problems that need a decision with different levels of complexity, different types and sources of information and different approaches. To organize them in models (deterministic and stochastic), where the objectives, decision variables and the different types of restrictions (physical, economic-financial, regulation, etc.) are easily identified, in which the adequate decisions are reasoned. Post-optimal analysis of models to adjust their applicability conditions to the evolution of their external and internal constraints (company and processes).
The evaluation will be carried out through written exam and work in groups. Evaluation in a work in group, a problem that is always poorly structured in a theme in which they have little knowledge, allows students to develop skills in the problem-solving process of any nature, starting from the initial stages of collection of information to gain knowledge of the problem in question, through the construction of the model that represents the operating process and ends in an assessment of the decision related to the result of the model. This work aims to try the problem-solving methodology in a concrete way through practical experience.

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	70,00
Trabalho escrito	30,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Frequência das aulas	45,50
Trabalho escrito	17,00
Estudo autónomo	99,50
Total:	162,00

Eligibility for exams

Eligibility for Attendance

Approval for a course unit implies compliance with the attendance requirement. A student is considered to have met this requirement if, having been regularly enrolled, they do not exceed the maximum number of absences corresponding to 25% of the scheduled in-person classes for each type. Furthermore, group work is mandatory to obtain attendance.

In addition to the cases statutorily provided for in FEUP's current rules, students who obtained a final grade of 6 points or higher in the course in the immediately preceding academic year are exempt from the attendance requirement for the course unit.

Calculation formula of final grade

  70% Exam + 30% Group Work

Classification improvement

In accordance to Article 10th of the of the General Standards of Evaluation (Artigo 10º das Normas Gerais de Avaliação), the students who were approved at the curricular unit and wish to improve their grade, they can do so by participating in the respective appeal exam. If the appeal examination mark is lower, the marks for the distributed assessment take precedence.
The grade improvement only applies to the individual assessment (70 per cent of the final grade), with the 30 per cent component of the grade obtained previously in the group work remaining (it is not possible to improve the grade for the group work).

Observations

Notes

During any assessment period, possession of any electronic device (e.g., cell phones, tablets, headphones, smartwatches, etc.) is strictly prohibited, with the exception of those expressly indicated by the faculty (e.g., calculators).
It is the student's responsibility to anticipate this situation before the assessment period begins.