Operations Research
Code: 104685 ECTS Credits: 6| Degree | Type | Year |
|---|---|---|
| Business Administration and Management | OB | 3 |
| Economics | OT | 3 |
| Economics | OT | 4 |
Contact
- Name:
- Gabriela Sicilia Suárez
- Email:
- gabriela.sicilia@uab.cat
Teachers
- Claudia Sanguinetti
Teaching groups languages
You can view this information at the end of this document.
Prerequisites
Those established by the current public regulations for university degree studies.
Objectives and Contextualisation
General objective
This course is an introduction to Operations Research that provides students with the basic analytical tools to formulate, solve, and interpret quantitative models to support decision-making in business and economic contexts.
Specific objectives
- Understand the theoretical and methodological foundations of optimization and its scope for supporting decision-making.
- Identify and formulate optimization models that represent real-world situations related to the efficient allocation of resources (production planning, logistics, finance, human resource management, etc.).
- Use computer tools to efficiently implement and solve models.
- Solve, critically interpret, and use results to improve decision-making.
- Interpret the results obtained and assess their validity and usefulness in business decision-making or economic process analysis.
Competences
- Business Administration and Management
- Apply mathematical instruments to synthesise complex economic-business situations.
- Apply theoretical knowledge to improve relations with clients and suppliers, identifying the advantages and disadvantages of those relations for both sides: company and client or supplier.
- Capacity for independent learning in the future, gaining more profound knowledge of previous areas or learning new topics.
- Identify, justify and reason the appropriate decisions according to the basic parameters of a business problem.
- Select and generate the information necessary for each problem, analyse it and take decisions based on that information.
- Take decisions in situations of uncertainty, demonstrating an entrepreneurial and innovative attitude.
- Use of the available information technology and adaptation to new technological environments.
Learning Outcomes
- Apply algorithmic resolution techniques to optimisation problems.
- Apply the basic principles of modelling in business decision-making.
- Capacity to continue future learning independently, acquiring further knowledge and exploring new areas of knowledge.
- Differentiate between alternative methods of analysis, and apply the appropriate quantitative tools to resolve business management problems.
- Make decisions in situations of uncertainty and show an enterprising and innovative spirit.
- Select and generate the information needed for each problem, analyse it and make decisions based on this information.
- Solve problems optimising and obtaining forecasts through information technology applications.
- Use available information technology and be able to adapt to new technological settings.
Content
TOPIC 1. Introduction to Operations Research and Mathematical Modelling
- What is Operations Research?
- Applications of OR
- Types of problems
- Mathematical modelling
- Formulating optimization problems
- Methods for solving optimization problems
TOPIC 2. Introduction to Linear Programming
- Basic principles of LP
- Ways to express an LP
- Transformations
- Graphical solution of LPs
- Types of solutions
TOPIC 3. The Simplex Algorithm
- Extreme points and optimality
- Basic feasible solutions
- The algebra of the simplex method
- Tableau representation
- Unbounded and infeasible LPs
TOPIC 4. Sensitivity Analysis and Duality
- The role of duality
- Economic interpretation
- Basic concepts of sensitivity analysis
- Changes in available resources
- Changes in coefficients
TOPIC 5. Transportation and Assignment Problems
- The transportation problem
- Balanced transportation problems
- Integer problems and totally unimodular matrices
- Assignment problems
- Matching problems
TOPIC 6. Software for Solving LP Problems Numerically
- Basic programming in LINGO
- Syntax
- Interpretation of results
Activities and Methodology
| Title | Hours | ECTS | Learning Outcomes |
|---|---|---|---|
| Type: Directed | |||
| Problem solving classes | 17 | 0.68 | 2, 1, 3, 4, 5, 7, 6, 8 |
| Theory classes | 32.5 | 1.3 | 2, 1, 4, 5, 7, 6, 8 |
| Type: Supervised | |||
| Supervised | 8 | 0.32 | 1, 4, 6 |
| Type: Autonomous | |||
| Autonomous | 88.5 | 3.54 | 2, 1, 3, 4, 5, 7 |
Teaching will be face-to-face.
Theoretical and practical sessions in which the professor will present the main concepts of the course and solve applied problems and activities to reinforce the covered content.
Classes will be complemented by students’ independent work on the material discussed in class and the recommended bibliography.
A number of weekly office hours will be available for individual student support (tutorials) and to address any questions they may have.
Annotation: Within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.
Assessment
Continous Assessment Activities
| Title | Weighting | Hours | ECTS | Learning Outcomes |
|---|---|---|---|---|
| Final exam | 50% | 2 | 0.08 | 2, 1, 3, 4, 5, 7, 6, 8 |
| Final project | 20% | 0 | 0 | 2, 1, 3, 4, 5, 7, 6, 8 |
| Midterm exam | 30% | 2 | 0.08 | 2, 1, 3, 4, 5, 7, 6, 8 |
Comprehensive assessment
This subject/module does not offer the option for comprehensive evaluation.
Continuous assessment
The course will be assessed based on the following criteria:
- Final project carried out in groups (20% of the final grade).
- Midterm exam (not exempting and 30% of the final grade).
- Final exam (50% of the final grade), covering all course content. A minimum score of 4/10 on the final exam is required to pass the course.
Additional information:
- To pass the course, students must obtain a final mark of 5 or higher and a minimum of 4/10 on the final exam.
- If the final mark is below 3.5, the student must retake the course in the following academic year. The final grade recorded will be the one obtained.
- Students who obtain a final mark equal to or above 3.5 but below 5, or those who obtain a final mark equal to or above 5 but score below 4/10 in the final exam, will be allowed to take the resit exam. The teaching staff will decide the format of the resit, which will be the same for all students. If the resit exam grade is 5 or higher, the final course grade will be "PASS" with a maximum numerical score of 5. If the resit grade is below 5, the final course grade will be "FAIL" with a numerical score of 3.5 (regardless of the score obtained in the resit).
- The student will receive a final grade of "Not assessable" if they have not participated in any of the evaluation activities.
Retake process
“To participate in the retake process, students must have been previously assessed in activities representing at least two-thirds of the final grade for the course or module.” (Article 112 ter, section 3, UAB Academic Regulations). Students must also have obtained a final grade between 3.5 and 5. The resit exam date will be included in the Faculty’s official exam calendar. Students passing the resit will receive a final grade of 5. Otherwise, they will retain their final exam grade.
Assessment calendar
The dates of all assessment activities (midterms,in-class exercises, project deadlines, etc.) will be announced well in advance during the semester.
The final exam date is published in the Faculty’s official exam calendar.
IMPORTANT: “The schedule for assessment activities cannot be modified unless there is an exceptional, well-justified reason. In such cases, the program coordinators, in consultation with the teaching staff and affected students, will propose a new date within the academic term.” (Article 115, section 1, UAB Academic Regulations). Students at the Faculty of Economics and Business who need to reschedule an assessment must submit the request using the Assessment Rescheduling Form.
Review of grades
The publication date and medium of final grades will be announced along with the final exam. Students will also be informed of the procedure, date, time and location for exam reviews in accordance with university regulations.
Irregularities in assessment activities
Without prejudice to any disciplinary measures deemed appropriate and in accordance with current academic regulations:
“If a student commits any irregularity that may significantly affect the grade of an assessment activity, this activity will be graded with a 0, regardless of any disciplinary process that may follow. If multiple irregularities occur in the same course, the final course grade will be 0.” (Article 116, section 10, UAB Academic Regulations)
Bibliography
Basic bibliography
- Hillier, F. and Lieberman, G. (2020): Introduction to Operations Research, 11th ed. McGraw-Hill; chs. 1-5; 9-10 and 12.
- Winston, W.L. (2005): Operations Research: Applications and Algorithms, 4ª ed., Thomson; chs. 1-9.
Further bibliography (latest editions)
- Taha, H (2016): Operations Research: An introduction, 10 ª ed., Pearson; chs. 1-5.
Other resources
- Association of European Operational Research Societies (EURO): www.euro-online.org
- International Federation of Operational Research Societies (IFORS): www.ifors.org
- Institute for Operations Research and the Management Sciences (INFORMS): www.informs.org
- The Operations Research Society (Or): www.theorsociety.com
- Sociedad Española de Estadística e Investigación Operativa (SEIO): www.seio.es
Note: Professors can recommend different bibliography in their own groups, in exercise of their academic freedom. Changes will be communicated to students in the first lecture.
Software
LINGO and others.
Groups and Languages
Please note that this information is provisional until 30 November 2025. You can check it through this link. To consult the language you will need to enter the CODE of the subject.
| Name | Group | Language | Semester | Turn |
|---|---|---|---|---|
| (PAUL) Classroom practices | 2 | Spanish | first semester | morning-mixed |
| (PAUL) Classroom practices | 4 | English | first semester | morning-mixed |
| (PAUL) Classroom practices | 52 | Spanish | first semester | afternoon |
| (PAUL) Classroom practices | 60 | Spanish | first semester | morning-mixed |
| (TE) Theory | 2 | Spanish | first semester | morning-mixed |
| (TE) Theory | 4 | English | first semester | morning-mixed |
| (TE) Theory | 52 | Spanish | first semester | afternoon |
| (TE) Theory | 60 | Spanish | first semester | morning-mixed |