Operational Research

Recommended Prerequisites

It is recommended that students have prior knowledge of linear algebra and mathematical analysis.

Teaching Methods

Mainly, two teaching methodologies are adopted. The explanation method focuses on the presentation of the main concepts, mathematical programming models, their applications, and optimization techniques. In the experimental methodology, the students are motivated to solve, alone and within a group, application exercises and real case studies, using optimization package and modeling languages. It is also expected that the experimental issue promotes both the critical analysis and the discussion while interpreting the obtained solutions.

Learning Outcomes

The main objective of this unit is to provide the students the knowledge of mathematical modeling and optimization tools for real and complex problems in systems engineering, with applications in industry, economics, health, environment, among other areas.

With the knowledge acquired within this unit, students should be able to understand the importance of the mathematical programming models and the most suitable and efficient solution methods. Particular emphasis is given to the solution of real case studies using modeling languages and optimization software, as well as to the critical analysis of the results obtained. Students should acquire skills to identify and formulate optimization problems, as well as to select which quantitative methods and analytical tools to be used to solve problems according to their specificities.

Work Placement(s)

No

Syllabus

Linear Programming: formulation of Linear Programming models and applications.

Geometry of linear programming. The Simplex method. Sensitivity analysis.

Duality theory.

Integer Programming: models, applications, and solution methods.

The branch-and-bound method and the cutting-plane method.

Head Lecturer(s)

Samuel de Oliveira Moniz

Assessment Methods

Assessment
Project: 40.0%
Frequency: 60.0%

Bibliography

-Hillier, F. S., G. J. Lieberman. Introduction to Operations Research, McGraw-Hill, (11th ed.), 2021.

- Hillier, F., M. Hillier. Introduction to Management Science and Business Analytics: A Modeling and Case Studies Approach with Spreadsheets (7th ed.), McGraw-Hill, 2023.

- H. A. Taha, Operations Research: An Introduction (11th edition), Pearson, 2023.

- R. C. Oliveira, J. S. Ferreira, Investigação operacional em ação: casos de aplicação. Imprensa da Universidade de Coimbra, 2014.

- H. Williams. Model building in mathematical programming, 5th edition, John Wiley & Sons, 2013.

- C. H. Antunes, L.V. Tavares, "Casos de Aplicação da Investigação Operacional", McGraw-Hill, 2000.