Linear Algebra, Probabilities and Statistics, 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.
Providing the students with methodological and application competences in the area of operations planning and management in the context of engineering problems, in order to enable them to identify types of problems, develop mathematical models that include the essential characteristics of those problems, apply algorithms to generate solutions for the models, and to perform a critical analysis of the solutions obtained.
1. Introduction to linear programming (LP). Development of LP mathematical models. The simplex method.
2. Project planning and management. Construction of project networks (activity on arc and activity on node). The PERT method. The CPM method. Project analysis in the resource space.
3. Inventory theory models. Deterministic models. Stochastic. Global and partial optimization models.
4. Forecasting. Time series. Forecasting techniques. Linear regression. Non-linear and multiple regression.
5. Decision analysis. Decision making without and with experimentation. Decision trees. Utility functions.
6. Queueing theory. Characterization of arrivals and service distributions. Birth and death processes. M/M/1 and M/M/S models. Queues with limited length. Queues with finite population.
Resolution Problems: 30.0%
- Hillier, F. S., G. J. Lieberman. "Introduction to Operations Research", McGraw-Hill, 2010 (9th 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.