"Operational Research" is an area of study that is originated during the second world war, basically, it consists of applying the scientific method (making use of mathematic models, statistics and algorithms) in order to model and solve complex problems.



Most of the situations try to find an optimal use of the resources, which are subjected to a series of limiting conditions. The applications are wide and include the manufacturing improvement, business management and programming.



In its current state "Operational Research" covers a wide range of topics such as linear and nonlinear programming, simulation, graph theory and so on. The aim of this academic subject is having a first approach to the problems, tools and strategies considered here, as well as acquire basic/medium competences for employing these techniques in productive contexts.



The subject is part of the module devoted to "basic training", in particular, inside the unit of "mathematics", and gives answer to the competence CM01 ("being able to solve mathematic problems in Engineering. Capability to use efficiently Algebra, Calculus, Numeric Methods, Statistics and Optimization"). It complements the rest of subjects on mathematics that are seen during the studies.

During the course, some deterministic methods concerning "Operational Research" aimed at solving lineal models will be revised.



As for the competences that students will acquire, the following ones can be stressed:



C1.- Application of the scientific method in problems related with the control of organizations or systems so as to improve the solutions.



C2.- Understanding of real problems and ability to model them mathematically under different circumstances.



C3.- Employ specific mathematic tools.



C4.- Analyzing how changes in inputs might affect to the outputs of a model (sensibility).

Chapter 1: Introduction.

Definition of the subject, stages of implantation and critical assessment of the method.



Chapter 2: Linear programming, basics.

Definition of a lineal program and graphic solution.



Chapter 3: Simplex method.

Description, uses, variations and computational issues.



Chapter 4: Duality.

Dual formulation and properties.



Chapter 5: Analysis of sensibility.

Study of the changes in the solutions due to changes in the initial conditions.



Chapter 6: Integer linear programming.

Problem solving when the variables have to take only integer values. Specific algorithms.



Chapter 7: Model of transportation.

Application to the transportation problem.

During part of the sessions, the lecturer will explain the concepts related with each chapter and propose points of discussion with students, therefore, participative sessions will be greatly encouraged. Complementarily, some sessions will be dedicated to practical exercises. The students will also work in groups developing a personal case study that will be part of the evaluation.



All teaching material will be available in the virtual classroom and students will have at their disposal a wide range of virtual tools for studying and communicating with their colleagues and with the lecturer.



NOTE: In case that the lessons and/or exams could not be done face-to-face, alternative options will be set up in order to replace them by on-line activities by means of the tools provided by the university. The characteristics of the on-line ebaluation will be published in the virtual classroom and in an ammendement of the academic guide.

• Final Assessment System
• Tools and qualification percentages:
  • Written test to be taken (%): 60
  • Team projects (problem solving, project design)) (%): 20
  • Actividades en el aula y/o en eGela (%): 20

Final exam: 60% (a minimum result of 4.5/10 is asked).



Continuous evaluation by means of exercises gathered along the semester (20%).



Work in group (20%).



Students who do not want to follow the aforementioned evaluation system will have the possibility to be evaluated only with a final exam.



Students will abide with all pertinents rules about the evaluation, in particular they will keep in mind the following norms:



- Students's regulation: https://www.ehu.eus/documents/3026289/3106907/Reglamento_Alumnado_UPV_EHU.pdf



- Regulation for students' evaluation: https://www.ehu.eus/es/web/estudiosdegrado-gradukoikasketak/ebaluaziorakoarautegia



- Code of ethics: https://www.ehu.eus/documents/2100129/0/6.-+b%29+Protocolo+plagio+cas+-.pdf/11f13960-d46acf5a-

ac13-ebfb5ad10acd





During the final exam study notes can be used provided students meet the following criteria:



a) the material for consultation is for each specific student and cannot be shared.



b) only documents in print will be allowed, no electronic devices (such as laptop, tablets or mobile phones).



c) notes will never got mixed with the exam. During the exercise, notes will be placed at the side, students will be allowed to check them at any moment but will have to let them back to the very place after consulting.



d) students cannot add to the exam any piece of material previously elaborated.



Students will carry their calculators for the exam, as well as some basic materials for drawing (e.g. a ruler) in order to improve the drawing up of charts.



NOTE: In case that the lessons and/or exams could not be done face-to-face, alternative options will be set up in order to replace them by on-line activities by means of the tools provided by the university. The characteristics of the on-line ebaluation will be published in the virtual classroom and in an ammendement of the academic guide.

By means of a written exam (100% of the mark). Previous work done along the semester will not be considered in the extraordinary call.



NOTE: In case that the lessons and/or exams could not be done face-to-face, alternative options will be set up in order to replace them by on-line activities by means of the tools provided by the university. The characteristics of the on-line ebaluation will be published in the virtual classroom and in an ammendement of the academic guide.

Materials in the virtual classroom.

Basic bibliography

"Operations research : an introduction"

Taha, Hamdy A.

Ed. Prentice-Hall



"Linear programming : foundations and extensions"

Robert J Vanderbei

Ed. Springer

In-depth bibliography

"Elementary linear programming with applications"
Bernard Kolman, Robert E Beck, Robert Edward Beck
San Diego Academic Press

Journals

https://link-springer-com.ehu.idm.oclc.org/journal/41274
https://www-sciencedirect-com.ehu.idm.oclc.org/journal/european-journal-of-operational-research

Web addresses

https://www.ehu.eus/es/web/dma