Teaching Methodologies
Students are required to follow the classes. Lecturing involves the exposition of concepts, techniques and methods, with a strong focus on practical applications. Software will be used to help answering large sized problems.
Learning Results
The course concentrates on mathematical programming modeling and solving, addressing decision process support techniques in management, information systems and network optimization problems. It only includes linear programming in both continuous and discrete space variables. Besides the theoretical underlying contents, appropriate software (Microsoft Excel, WINQSB, Xpress and MPL) will also be introduced in order to solve large scale problems.
Program
1 – Introduction to mathematical modeling
2 – Linear Programming
2.1 – Properties and resolution of a linear model
2.2 – Dual Model. Primal/Dual Properties
2.3 – Sensitivity analysis and parametric analysis
2.4 – Economic interpretation of solutions
2.5 – Software for solving linear formulations
3. – Network optimisation
3.1 – Concepts and properties
3.2 – Shortest path problem
3.3 – Minimum cost spanning tree
3.4 – Maximum flow problem
3.5 – Minimum cost flow problem
3.6 – Software for solving models with network structure
4. – Linear programming applications
4.1 – Transportation, assignment and projects’ planning problems
5. – Integer programming
5.1 – Definitions and interpretation of integer variables. Properties
5.2 – Some modeling techniques resorting to integer variables
5.3 – Heuristics and metaheuristics
5.4 – Software for solving integer linear programs
5.5 – Integer programming applications
Internship(s)
NAO
Bibliography
[1] J.J. Júdice, P.C. Martins, M.M.B. Pascoal e J.P. Santos, Programação Linear, Departamento de Matemática
da Universidade de Coimbra, 2006.
[2] J.J. Júdice, P.C. Martins, M.M.B. Pascoal e J.P. Santos, Optimização em Redes, Departamento de Matemática
da Universidade de Coimbra, 2006.
[3] M. Ramalhete, J. Guerreiro e A. Magalhães, Programação Linear Volume
I, McGraw Hill, 1984.
[4] M. Ramalhete, J. Guerreiro e A. Magalhães, Programação Linear Volume
II, McGraw Hill, 1985.
[5] F.S. Hillier and G.J. Lieberman, Introdução à Pesquisa Operativa, McGraw Hill, 2006.
[6] R. Bronson e G. Naadimuthu, Investigação Operacional, 2ª edição, McGraw Hill, 2000.
[7] L. Wolsey, Integer Programming, WileyInterscience,
1998.
[8] Elementos de apoio pedagógico elaborados pelo docente da disciplina.