ECTS credits ECTS credits: 5
ECTS Hours Rules/Memories Student's work ECTS: 85 Hours of tutorials: 5 Expository Class: 20 Interactive Classroom: 15 Total: 125
Use languages Spanish, Galician
Type: Ordinary subject Master’s Degree RD 1393/2007 - 822/2021
Departments: Statistics, Mathematical Analysis and Optimisation
Areas: Statistics and Operations Research
Center Faculty of Mathematics
Call: Second Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
In this subject, the aim is to bring the student closer to the modeling and resolution of optimization problems from real applications.
The objectives to be achieved as a result of learning are:
• Be able to identify and model complex mathematical optimization problems that arise in real applications.
• Know the appropriate software to solve mathematical optimization problems.
• Understand the implications of possible reformulations of the same optimization model.
• Know how to interpret the results for their presentation in highly multidisciplinary environments, both before specialized and non-specialized audiences.
Unit 1. Fundamentals of optimization: Review.
Unit 2. Formulating and reformulating optimization problems.
Unit 3. Solving complex problems using heuristics.
Unit 4. Modeling and problem solving under uncertainty. Robust optimization.
Unit 5. Modeling and solving multiobjective problems.
Unit 6. Modeling and solution of large problems.
Basic
- Ahuja, R.K.; Magnanti, T.L.; Orlin, J.B. (1993). "Network Flows. Theory, Algorithms and Applications". Prentice-Hall.
- Bazaraa, M.; Jarvis, J.; Sherali, H. (2010). “Linear programming and networks flows”. John Wiley & Sons.
- Papadimitriou, C.H.; STEIGLITZ, K. (1998). “Combinatorial Optimization: Algorithms and Complexity”. Prentice-Hall, Inc.
- Bazaraa, M.S.; Sherali, H.; Shetty, C. (2006). “Nonlinear programming. Theory and algorithms”. Wiley.
- Ehrgott, M.; Wiecek, M. M. (2005). “Multiobjective programming”. In: Multiple Criteria Decision Analysis. State of the Art. Surveys. J. Figueira, S. Greco and M. Ehrgott (eds.). Páginas 667-722. Springer.
- Horst, R.; Tuy, H. (2003). “Global Optimization: Deterministic Approaches”. Springer.
Complementary
- Fourer, R.; Gay, D.M.; Kernighan, B.W. (2002). “AMPL: A modeling language for Mathematical Programming”. Duxbury Press.
- Hillier, F.; Lieberman, G. (2015). “Introduction to operations research”. McGraw-Hill.
- Winston, W.L. (2005): “Investigación de operaciones. Aplicaciones y algoritmos”. Grupo Editorial Iberoamericana.
- Barbolla, R.; Cerdá, E.; Sanz, P. (2001). “Optimización. Cuestiones, ejercicios y aplicaciones a la economía”. Prentice-Hall.
- Bertsekas, D.P. (2016). “Nonlinear programming”. Athena Scientific.
- Bhatti, M.A. (2000). “Practical optimization methods”, Springer-Verlag.
- Chankong, V.; Haimes, Y.Y. (2008). “Multiobjective decision making: theory and methodology”. Dover.
- Sawaragi, Y.; Nakayama, H.; Tanino, T. (1985). “Theory of Multiobjective Optimization”. Series in Mathematics in Science and Engineering. Volume 176. Academic Press.
In this matter the basic, general and transversal competences collected in the memory of the title will be worked on. The specific competences that will be promoted in this area are indicated below:
E1 - Know, identify, model, study and solve complex statistical and operational research problems, in a scientific, technological or professional context, arising from real applications.
E2 - Develop autonomy for the practical resolution of complex problems arising in real applications and for the interpretation of results in order to aid decision-making.
E3 - Acquire advanced knowledge of the theoretical foundations underlying the different methodologies of statistics and operational research, which allow for their specialized professional development.
E6 - Acquire advanced theoretical-practical knowledge of different mathematical techniques, specifically oriented to aid in decision-making, and develop reflective capacity to evaluate and decide between different perspectives in complex contexts.
E7 - Acquire advanced theoretical-practical knowledge of different mathematical optimization techniques, both in one-person and multi-person contexts, and know how to apply them with sufficient autonomy in a scientific, technological or professional context.
E10 - Acquire advanced knowledge of methodologies for obtaining and processing data from different sources, such as surveys, the internet, or "cloud" environments.
The teaching will consist of expository and interactive classes, as well as the tutoring of the learning and the tasks entrusted to the students. In the exhibition and interactive classes, examples will be solved using specialized software, so it is convenient for students to have a computer in the classroom.
Activities will be proposed for students, which will consist of solving questions, exercises and examples related to modeling and solving applied optimization problems.
The appropriate support material will be provided to the student through the virtual campus.
The final grade will come, 100%, from the continuous evaluation, which will consist of the delivery and review of different works proposed throughout the course, including the possibility that the evaluation is based on the oral presentation of some of the works.
The exercises proposed in the continuous evaluation will be of a different nature, in order to evaluate the different competences to be developed in the subject:
- There will be works that require the student to model problems raised by the teacher, adequately arguing the suitability of the chosen modeling compared to other alternatives. This will allow to evaluate the competences CB6, CB7, CB10, CG1, CG2, E1.
- Other works will require both modeling and solving optimization problems, followed by an analysis of the solutions obtained through structured and clear reports, which will allow us to evaluate, in addition to the skills in the previous section, the following CB8, CB9, CG3, CG4, CT1, CT2, CT3, CT4, E2, E3, E6, E7, E10.
- In addition, some of these works will require the use of specific software and algorithms for their resolution, which will allow assessing CG5 proficiency and delving into E6.
- Finally, the CT5 competence will be developed by assigning some work to be done in a group.
Each ECTS credit translates into 7 classroom hours. It is estimated that the student will need, for each hour of face-to-face class, an additional hour for the global understanding of the contents. In addition, the continuous assessment work will amount to 10 hours per ECTS credit. In total 24 hours for ECTS credit will result.
It is convenient that the students have basic knowledge of mathematical optimization. It is also advisable to have average computer skills, and specifically specialized optimization problem modeling software.
It is advisable to actively participate in the learning process of the subject: attendance and participation in the theoretical, practical and computer classes, use of hours of tutoring and the realization of a responsible effort of work and assimilation
staff of the studied methods
It is recommended that the student have completed Linear and Integer Programming and/or Mathematical Programming.
The development of the contents of the subject will be carried out taking into account that the competences to be acquired by the students must meet the MECES3 level. This course will have a large practical component, with an emphasis on the identification and modeling of complex and highly specialized real problems. As a problem solving tool, you will work intensively with some algebraic modeling language (such as AMPL or GAMS). These languages allow rapid prototyping and resolution of complex models and problems.
In cases of fraudulent performance of exercises or tests, the provisions of the respective regulations of the universities participating in the Master in Statistical Techniques will apply.
This guide and the criteria and methodologies described therein are subject to modifications arising from regulations and directives of the universities participating in the Master in Statistical Techniques.
Angel Manuel Gonzalez Rueda
Coordinador/a- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- angelmanuel.gonzalez.rueda [at] usc.es
- Category
- Professor: LOU (Organic Law for Universities) PhD Assistant Professor
| 05.27.2025 10:00-14:00 | Grupo /CLE_01 | Classroom 04 |
| 07.09.2025 10:00-14:00 | Grupo /CLE_01 | Classroom 04 |