2025
Operational Research
Name: Operational Research
Code: MAT13638L
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area:
Mathematics
Teaching languages: Portuguese
Languages of tutoring support: Portuguese
Regime de Frequência: Presencial
Sustainable Development Goals
Learning Goals
This course aims primarily to provide students with fundamental concepts of linear optimization applied to economics and management.
In the first part of the course, the Simplex algorithm is presented, which allows the solution of linear programming problems with n decision variables. This algorithm is used to solve various linear programming problems and to interpret the results, including sensitivity analysis with respect to the independent terms and the coefficients of the objective function. The resolution of these problems using specific open-source software is also presented.
In the second part of the course, some special models of linear optimization are studied, namely transportation and assignment models. An introduction to Graph Theory and Project Management (CPM) is also provided, including the analysis of randomness in activity durations (PERT) and project duration reduction to achieve the minimum possible cost.
In the first part of the course, the Simplex algorithm is presented, which allows the solution of linear programming problems with n decision variables. This algorithm is used to solve various linear programming problems and to interpret the results, including sensitivity analysis with respect to the independent terms and the coefficients of the objective function. The resolution of these problems using specific open-source software is also presented.
In the second part of the course, some special models of linear optimization are studied, namely transportation and assignment models. An introduction to Graph Theory and Project Management (CPM) is also provided, including the analysis of randomness in activity durations (PERT) and project duration reduction to achieve the minimum possible cost.
Contents
- Introduction to the methodology of Operations Research.
- Linear Programming models.
- Geometry of the solution set. Graphical solution.
- Simplex Algorithm: principles, algorithm steps, and solution analysis.
- Duality in Linear Programming: concepts of primal and dual problems, relationships, and applications.
- Sensitivity analysis.
- Transportation and assignment problems.
- Optimization in networks and graphs: flow models and shortest paths.
- Project Management: PERT/CPM techniques for project planning and control.
- Software for solving Linear Programming problems.
- Linear Programming models.
- Geometry of the solution set. Graphical solution.
- Simplex Algorithm: principles, algorithm steps, and solution analysis.
- Duality in Linear Programming: concepts of primal and dual problems, relationships, and applications.
- Sensitivity analysis.
- Transportation and assignment problems.
- Optimization in networks and graphs: flow models and shortest paths.
- Project Management: PERT/CPM techniques for project planning and control.
- Software for solving Linear Programming problems.
Teaching Methods
The theoretical?practical classes are mainly taught using the board, while specific open-source software is occasionally used to support the solution of the linear programming problems presented.
The exercises are designed for the field of Economics and Management, focusing on solving current and real-world problems, with the aim of fostering students? interest in the subject and demonstrating its relevance and practical applicability.
The exercises are designed for the field of Economics and Management, focusing on solving current and real-world problems, with the aim of fostering students? interest in the subject and demonstrating its relevance and practical applicability.
Assessment
Students may choose between continuous assessment or final examination assessment (regular examination period).
Continuous assessment: this consists of two written tests, each requiring a minimum grade of 8 points. The final grade corresponds to the arithmetic mean of the two tests. Students may also complete four quizzes and/or short tests conducted in class, each graded between 0 and 2 points. The average of these four assessments is added to the average of the written tests, up to a maximum overall grade of 20 points.
Final examination: assessment is carried out through a final exam covering the entire content of the course unit.
Continuous assessment: this consists of two written tests, each requiring a minimum grade of 8 points. The final grade corresponds to the arithmetic mean of the two tests. Students may also complete four quizzes and/or short tests conducted in class, each graded between 0 and 2 points. The average of these four assessments is added to the average of the written tests, up to a maximum overall grade of 20 points.
Final examination: assessment is carried out through a final exam covering the entire content of the course unit.
Teaching Staff
Accreditations and Certifications
