Teaching Methodologies
The lectures will cover concepts, techniques and methods, with a strong focus on practical applications. Computer support will be used to
solve larger problems.
Some classes will be computer-based, encouraging the applied nature of the models and techniques presented, aimed at Management
problems.
This way, some classes will have theoretical and theoretical-practical components, involving the exposition of concepts, methods and
algorithms, including the resolution of small-scale applied cases. There will also be classes of a more applied nature, in which appropriate
computer tools will be used for the computational resolution of larger applied cases.
Monitoring the learning process with periodic assessments should help the student to consolidate the syllabus elements, both the
theoretical elements and the practical and applied subjects, which should strengthen the know-how acquisition and the student’s autonomy
in the practical use of this knowledge. The aim is also for the student to gain skills that will enable them to discover ways of responding to
new optimisation and decision analysis problems within the scope of the course.
Learning Results
Mathematical optimisation techniques for prescriptive analytics are introduced, using linear and integer linear programming models. It also
includes decision analysis.
Techniques for solving the proposed mathematical models are studied and their application in the field of Management is encouraged,
namely in production planning and logistics problems, among others.
In addition to the study of the mathematical methods, appropriate software will be used for computational solving, including Excel tools and
Python libraries.
The aim is to develop the student’s sensitivity to the mathematical modelling of the problems proposed and their ability to use decision
analysis tools. They should also be familiar with techniques for solving these problems, including solving them using specific computer
applications. The purpose is to provide students with the theoretical and practical knowledge to apply quantitative techniques to support
decision-making.
Program
1 Introduction to mathematical modelling
1.1 Motivation for mathematical optimisation
1.2 Mathematical formulation of problems
2 Linear Programming
2.1 Properties
2.2 Techniques for solving continuous linear formulations
2.3 Duality and optimality conditions
2.4 Sensitivity analysis and economic interpretation of solutions
2.5 Solving continuous linear models using computer programmes
3 Integer linear programming
3.1 Properties
3.2 Modelling techniques using binary variables
3.3 Solving integer linear models using computer programmes
3.4 Applications of integer linear programming to management problems
4 Mathematical optimisation in the decision-making process
4.1 Production planning
4.2 Logistics problems
4.3 Assignment problems
5 Decision analysis
5.1 Decision-making process with and without experimentation
5.2 Decision trees
5.3 Sensitivity analysis
5.4 Utility theory
5.5 Practical applications of decision analysis
Internship(s)
NAO
Bibliography
Hillier, F. S., & Lieberman, G. J. (2013). Introdução à pesquisa operacional. McGraw Hill Brasil.
Júdice, J., Martins, P., Pascoal, M. B., & Santos, J. P (2006). Programação linear, Departamento de Matemática da Universidade de
Coimbra.
Mourão, M. C., Pinto, L., Simões, O., Valente, J., & Pato, M. (2011). Investigação Operacional: Exercícios e Aplicações. Lisboa: Dashofer
Holding Ltd e Verlag Dashofer.