Optimization and Decsion Support Methods

Recommended Prerequisites

Calculus, Linear Algebra, Probabilities and Statistics.

Teaching Methods

Theoretical and methodological concepts are presented in tutorial lectures, being motivated by real-world problems and illustrated with application examples.

Software (commercial and public domain) packages are used to obtain solutions to the mathematical models, thus freeing the students for the more creative tasks of problem formulation, model building and critical analysis of results.

Learning Outcomes

Providing the students with methodological and application competences in the area of models and methods for optimization and decision support, mainly in the context of planning or operational problems in which environmeantal impacts are relevant, including: to identify types of problems, develop mathematical models that include their essential characteristics, apply algorithms to generate solutions for the models, and to perform a critical analysis of the solutions obtained. 

Work Placement(s)

No

Syllabus

.1. Introduction to linear programming. Model building. The simplex method.

2. Integer programming. Model building. The branch and bound method.

3. Multiobjective linear and integer programming.

4. Multicriteria decision analysis: Choice, ranking and sorting problems; Notion of preferences; Outranking relations; Value functions.

Assessment Methods

Assessment
Project: 30.0%
Exam: 70.0%

Bibliography

- Henggeler Antunes, C., M. J. Alves, J. Clímaco. "Multiobjective Linear and Integer Programming", EURO Advanced Tutorials on Operational Research, Springer, 2016.

- Hillier, F. S., G. J. Lieberman. "Introduction to Operations Research", McGraw-Hill, 2015 (10th ed.).

- Dias, L. "Avaliação Multicritério em Processos de Decisão". Imprensa da Universidade de Coimbra, 2022.