Linear Algebra, Calculus.
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.
- 3 assignments [4/20]
- Exam [16/20].
Providing the students with methodological and application competences in the context of optimization in engineering problems, in order to enable them to identify types of problems, develop adequate mathematical models that include the essential characteristics of those problems, and apply algorithms to generate the optimal solutions for the problems. Special attention is paid to the use of software packages to obtain the optimal solutions, as well as sensitivity analysis of optimal solutions in face of changes in the model data and parameters.
0. Origin and nature of Operational Research (OR).
1. Linear Programming (LP). Graphical resolution of LP models. The simplex method. Duality theory. Sensitivity analysis. Goal programming.
2. Special LP problems. The transportation, assignment and transshipment problems.
3. Network optimization problems. Shortest path. Minimum spanning tree. Shortest path with fixed costs in nodes. Maximum flow problem. Max flow -min cut theorem. Minimum cost flow problem.
4. Non-linear programming. Examples of application of non-linear mathematical models. NLP problems without and with with constraints. The Karush-Kuhn-Tucker conditions. The modified simplex method for quadratic programming.
Resolution Problems: 20.0%
- Hillier, F. S., G. J. Lieberman. "Introduction to Operations Research", McGraw-Hill, 2005 (8th ed.).
- Tavares, L. V., R. C. Oliveira, I. H. Themido, F. N. Correia. “Investigação Operacional”, McGraw-Hill Portugal, 1996.
- Bronson, R., G. Naadimuthu. "Investigação Operacional", Colecção Schaum (2ª. Ed.), McGraw-Hill Portugal, 2001.
- Clímaco, J., C. H.Antunes, M. J. Alves. "Programação Linear Multiobjectivo", Imprensa da Universidade de Coimbra, 2003.
- Chang, Y.L. "WinQSB, Decision Support Software for M/OM (ver 2.0)", Wiley, 2003.
- Antunes, C. H., L. V. Tavares (Coord.). "Casos de Aplicação da Investigação Operacional", McGraw-Hill, 2000.