ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Student's work ECTS: 99 Hours of tutorials: 3 Expository Class: 24 Interactive Classroom: 24 Total: 150
Use languages Spanish, Galician
Type: Ordinary Degree Subject RD 1393/2007 - 822/2021
Departments: Statistics, Mathematical Analysis and Optimisation
Areas: Statistics and Operations Research
Center Faculty of Mathematics
Call: First Semester
Teaching: With teaching
Enrolment: Enrollable
Introduce the student to mathematical programming, with an emphasis on techniques for solving and analyzing linear models.
Learn the analytical procedures and algorithms to solve linear programming problems and know how to analyze the underlying mathematical structure of these problems.
Learn to use computer tools for the practical resolution of these problems.
The contents of the subject will be the same in the three scenarios considered in the "Guidelines for the development of safe face-to-face teaching, academic year 2020-2021".
Topic 1. (6 weeks)
Introduction to Operational Research. Linear programming problems. Mathematical formulation of linear programming problems. Graphical solution to linear programming problems. Simplex Algorithm. Duality and sensitivity analysis. Duality theorem.
Topic 2. (1 week)
Integer linear programming. The Branch and Bound Algorithm.
Topic 3. (1 week)
Optimization and mathematical programming: an overview. Algorithms and computational complexity. Solving optimization problems.
Topic 3. (5 weeks)
Programming in flow networks. The minimum cost network flow problem.
The transportation problem. The transportation simplex method.
The assignment problem. The hungarian method.
The shortest path problem. The Dijkstra's algorithm.
The maximum flow problem. The augmenting path algorithm.
The minimum spanning tree problem. The Prim's algorithm.
The traveling salesman problem. The Christofides's Algorithm.
Students will have the notes of the subject in the Virtual Campus. In these notes are all the contents (theoretical and practical) of the subject.
Books that students can obtain through the portal of the Library of the University of Santiago de Compostela.
Books available at Wiley Online Library:
BAZARAA, M. / JARVIS, J. / SHERALI, H. (2010): “Linear programming and networks flows”. John Wiley & Sons.
THIE, P. R. / KEOUGH, G. E. (2008): “An introduction to linear programming and game theory”. Ed. Wiley.
Book available at https://dspace.mit.edu/handle/1721.1/49424, the MIT (Massachusetts Institute of Technology) repository:
Ahuja, R.K .; Magnanti, T.L .; Orlin, J.B. (1988): "Network flows", MIT.
Books of which students can have a physical copy in the Library of the University of Santiago de Compostela:
AHUJA, R.K./ MAGNANTI, T.L./ ORLIN, J.B. (1993): "Network Flows. Theory, Algorithms and Applications". Prentice-Hall.
HILLIER, F. / LIEBERMAN, G. (2010): “Introduction to operations research”. McGraw-Hill.
SALAZAR GONZÁLEZ, J. S. (2001): "Mathematical programming". Diaz de Santos.
Ability to analyze and model real problems in the context of linear programming: recognize possible linear programming problems, identify the linear programming problems studied and formulate the mathematical model of these problems.
Be able to put the knowledge learned into practice: plan and execute algorithms and mathematical methods to solve problems. Use computer optimization tools.
After studying this subject, students will have studied in depth the following competences of the Degree in Mathematics: CG1, CG2, CG3, CG4, CG5, CE1, CE2, CE3, CE4, CE5, CE6, CE7, CE8, CE9, CT1, CT2, CT3, CT4 and CT5.
In scenario 1, the lectures and seminars will be in the classroom with a blackboard, where the theoretical contents of the subject and the procedures for solving problems will be explained (solving exercises and proposing others for their resolution by the students) .
The laboratory can be taught in a computer room, or otherwise, the students could use their laptops.
Computer tools will be used in the context of Operational Research, emphasizing the practical application of the knowledge studied in the subject, and with special interest in programming resources. The reference software will be R [http://www.r-project.org].
Exercises will be solved and proposed for students to carry out. This will allow us not only to put into practice the knowledge studied in the subject, but also to acquire the necessary resources to use the computer tools.
In scenario 2, keep the lectures in person, as long as the required conditions are met.
If it were not possible to teach the lectures in a large classroom, they would become non-face-to-face, using the telematic tools that the University of Santiago de Compostela makes available to the university community. The material of the subject would be available on the Virtual Campus and the students would also have additional videos.
If it were not possible to keep the seminars on-site, they would become non-on-site. Apart from the subject material already available on the Virtual Campus, students would have resolved exercises that would serve as a guide to carry out the assigned tasks.
If it were not possible to keep the laboratory in person, they would become non-face-to-face. In addition to the material for the laboratory, already available on the Virtual Campus, the students would have additional R scripts that would help them to carry out the assigned tasks.
If it were not possible to keep the seminars in person, they would become non-face-to-face, using the telematic tools that the University of Santiago de Compostela makes available to the university community.
In scenario 3, all teaching would be non-face-to-face. The means used in this case would be those already exposed in scenario 2.
In the lectures the CG1, CE1, CE2, CE3, CE4 and CT3 competences will be worked, mainly, while in the seminars and laboratory, the CG3, CE5, CE6, CE7, CE8 competences will be done, respectively. and CT3, and CE8 and CE9.
In the tutorials with very small groups we will work CG4 and CT3.
Finally, for the non-face-to-face dedicated to this subject, it is convenient to promote the work of CG5, CT1, CT2 and CT5.
Coursework: the coursework will be carried out throughout the semester. It will consist of the resolution of exercises or works in which the student will use the techniques and knowledge acquired in the lectures, seminars and laboratory.
Final exam: the final exam will consist of theoretical-practical questions about the contents of the subject.
The final mark, both in the first and in the second opportunity, will be the maximum of the theoretical-practical final exam mark, on the one hand, and the weighted average between the coursework (25%) and the theoretical-practical exam mark (75%), on the other hand.
Students who do not take the theoretical-practical exam will have “no presentado".
For courseworks, students will carry out team and individual work to strengthen CG2, CG3, CE6, CE7, CE8, CE9, CT1 and CT2. Additionally, team work is also good for skills CT3, CT4 and CT5. The theoretical-practical final exam will allow to train and assess, especially, the skills CG1, CG2, CG3, CG4, CE2, CE6, CE7 and CE8.
In scenario 1, the tests would be face-to-face.
In scenario 2, keep the tests in which the conditions required by the University regulations can be met.
If there was any test and it could not be done in person, it would become not face-to-face. These tests, if applicable, would be similar to those carried out in-person. The Virtual Campus would be used for the download of the task and the delivery of the completed task.
If the first opportunity exam could not be attended face-to-face, it would be online. The exam would be similar to the one that would be done in-person, using the telematic tools that the University of Santiago de Compostela makes available to the university community for its execution and supervision.
They would take place on a fixed schedule, the same for all students, and with limited time. The Virtual Campus would be used to download the exam and deliver it once completed by the student.
It would be the same if the second chance exam could not be attended face-to-face.
In scenario 3, all tests will be not face-to-face. These tests would be as described in scenario 2.
Indication referring to plagiarism and the improper use of technologies in the performance of tasks or tests: For cases of fraudulent performance of exercises or tests, the provisions of the “Regulations for the evaluation of the academic performance of students and of the review of the qualifications ”.
It is recommended to dedicate at least an hour and a half of additional work for each hour of expository and interactive class, in addition to the hours of tutoring.
Assistance (face-to-face or virtual) to all teaching activities.
Consult the references.
It is advisable to have studied the subject "Vector Spaces and Matrix Calculus" (Espacios Vectoriales y Cálculo Matricial).
This guide and the criteria and methodology described here are subject to the modifications arising from the regulations and guidelines of the University of Santiago de Compostela.
Contingency plan if required by the health situation:
In accordance with the indications established by the academic authorities, the methodology and evaluation will be adapted to the scenarios 2 or 3, as explained above.
Balbina Virginia Casas Mendez
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- Phone
- 881813180
- balbina.casas.mendez [at] usc.es
- Category
- Professor: University Lecturer
Maria Angeles Casares De Cal
Coordinador/a- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- Phone
- 881813183
- mariadelosangeles.casares.decal [at] usc.es
- Category
- Professor: University Lecturer
Julio Gonzalez Diaz
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- Phone
- 881813207
- julio.gonzalez [at] usc.es
- Category
- Professor: Temporary PhD professor
Brais Gonzalez Rodriguez
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- braisgonzalez.rodriguez [at] usc.es
- Category
- Ministry Pre-doctoral Contract
| Monday | |||
|---|---|---|---|
| 15:00-16:00 | Grupo /CLE_01 | Spanish | Classroom 09 |
| 17:00-18:00 | Grupo /CLIS_03 | Spanish | Classroom 06 |
| 18:00-19:00 | Grupo /CLIS_04 | Spanish | Classroom 06 |
| Tuesday | |||
| 15:00-16:00 | Grupo /CLE_01 | Spanish | Classroom 07 |
| 17:00-18:00 | Grupo /CLE_02 | Spanish | Classroom 08 |
| Wednesday | |||
| 15:00-16:00 | Grupo /CLIS_01 | Spanish | Classroom 06 |
| 15:00-16:00 | Grupo /CLIL_04 | Spanish | Computer room 3 |
| 16:00-17:00 | Grupo /CLIS_02 | Spanish | Classroom 02 |
| 18:00-19:00 | Grupo /CLIL_05 | Spanish | Computer room 3 |
| 19:00-20:00 | Grupo /CLIL_06 | Spanish | Computer room 4 |
| Thursday | |||
| 15:00-16:00 | Grupo /CLIL_01 | Spanish | Computer room 2 |
| 17:00-18:00 | Grupo /CLIL_03 | Spanish | Computer room 4 |
| 19:00-20:00 | Grupo /CLE_02 | Spanish | Classroom 07 |
| Friday | |||
| 15:00-16:00 | Grupo /CLIL_02 | Spanish | Computer room 2 |
| 01.19.2021 16:00-20:00 | Grupo /CLE_01 | Classroom 02 |
| 01.19.2021 16:00-20:00 | Grupo /CLE_01 | Classroom 03 |
| 01.19.2021 16:00-20:00 | Grupo /CLE_01 | Classroom 06 |
| 01.19.2021 16:00-20:00 | Grupo /CLE_01 | Ramón María Aller Ulloa Main Hall |
| 06.30.2021 16:00-20:00 | Grupo /CLE_01 | Classroom 06 |