Operational Research

Recommended Prerequisites

The students should have previous knowledge of linear algrebra 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 to 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 obtained results. 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

1. Linear Programming: formulation of Linear Programming models and applications. Geometry of linear programming. The Simplex method. Sensitivity analysis. Duality theory.

2. Integer Programming: models, applications, and solution methods. The branch-and-bound method and the cutting-plane method.

3. Network flow optimization: models and applications. Transportation problem, Assigning problem, Shortest path problem, Minimum-cost flow problem.

Head Lecturer(s)

Telmo Miguel Pires Pinto

Assessment Methods

Assessment
Project: 40.0%
Frequency: 60.0%

Bibliography

-H. A. Taha, Operations Research: An Introduction, 10th edition, Pearson, 2017

-F. Hillier, G. Lieberman. Introduction to Operations Research. McGraw-Hill, 10th Edition, 2015.

- 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.

- W. Winston, J. Goldberg. Operations Research: Applications and Algorithms, 4th edition, Cengage Learning, 2003.

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