Checking date: 22/05/2022

Course: 2022/2023

Operational Research
Study: Bachelor in Statistics and Business (203)

Coordinating teacher: NIÑO MORA, JOSE

Department assigned to the subject: Department of Statistics

Type: Compulsory
ECTS Credits: 6.0 ECTS


Requirements (Subjects that are assumed to be known)
Students are expected to have completed courses with contents in linear algebra, statistics, business administration and computer programming.
1. Modeling decision optimization problems in the framework of Operations Research models. 2. Formulating, analyzing and solving linear optimization models, by the graphical method, the simplex method and computer software (in particular, spreadsheets). 3. Formulating, analyzing and solving integer optimization models, by the graphical method, the branch and bound method, and computer software. 4. Formulating, analyzing and solving queueing models of M/M/m type. 5. Designing and performing computer simulation experiments by the Monte Carlo method. 1. Capacity for analysis and synthesis. 2. Mathematical modeling and problem solving. 3. Oral and written communication.
Skills and learning outcomes
Description of contents: programme
-Topic 1. Linear optimization (LO). 1.1. Introduction to Operations Research; LO models, formulations, applications and computer-based solution. 1.2. Graphical solution and sensitivity analysis. 1.3. The fundamental theorem of LO; basic feasible solutions and vertices; the simplex method. 1.4. Problems with unbounded objetive; the two-phase simplex method. 1.5. Duality in LO; economic interpretation and application to sensitivity analysis. 1.6. Optimal network flow models. -Topic 2. Integer optimization (IO). 2.1. IO models and applications; linear relaxations; optimality gap; optimality test; graphical and computer-based solution. 2.2. The Branch and Bound method. 2.3. Combinatorial optimization models. Strengthening formulations with valid inequalities. -Topic 3. Queueing theory (QT). 3.1. QT models and applications; performance metrics; utilization factor and stability; Little's law; PASTA property. 3.2. The M/M/1 model; calculation of performance metrics. 3.3. The M/M/m model; calculation of performance metrics. -Topic 4. Simulation. 4.1. Simulation models; Monte Carlo method and applications; computer generation of pseudo-random numbers. 4.2. Computer generation of discrete and continuous probability distributions.
Learning activities and methodology
Theory (3 ECTS). Theory classes with supporting material available in the course web page. Practical classes (3 ECTS). Problem-solving classes. Computer labs. Weekly individual tutoring sessions.
Assessment System
  • % end-of-term-examination 0
  • % of continuous assessment (assigments, laboratory, practicals...) 100
Calendar of Continuous assessment
Basic Bibliography
  • F.S. HILLIER, F.S., G.J.LIEBERMAN. Introduction to Operations Research. McGraw Hill.
  • H.A. TAHA. Operations Research. Pearson.
  • J. NIÑO MORA. Introducción a la optimización de decisiones. Pirámide. 2021
Additional Bibliography
  • J. PRAWDA. Métodos y Modelos de Investigación de Operaciones / Methods and models of operations research. Limusa.
  • M.S. BAZARAA, J.J. JARVIS y H.D. SHERALI. Programación Lineal y Flujo en Redes / Linear Programming and Network Flows. Limusa.

The course syllabus may change due academic events or other reasons.