Checking date: 29/06/2020

Course: 2020/2021

Operational Research
Study: Master in Mathematical Engineering (70)


Department assigned to the subject: Department of Statistics

Type: Electives
ECTS Credits: 6.0 ECTS


Students are expected to have completed
It is recommended that students have taken courses in Linear Algebra, Calculus of Probabilities, Business Administration, and Computer Programming.
Competences and skills that will be acquired and learning results.
The course sets out to develop the following competencies: 1) Capacity to formulate deterministic and stochastic models of operations research for optimal decision making in a wide variety of applications; in particular, linear optimization, integer and combinatorial optimization, dynamic optimization and queueing theory models; 2) capacity to analyze such models, based on an understanding of their properties; 3) capacity to solve such models by computer software, finding their optimal solutions; and 4) capacity to interpret the numerical solutions obtained in terms of decisions for the originating problem.
Description of contents: programme
1. Linear optimization. 1.1. Formulations; graphical solution; sensitivity analysis; robustness. 1.2. Duality; economic interpretation; applications. 1.3. Network flow problems. 2. Integer and combinatorial optimization. 2.1. Formulations; graphical solution; linear relaxations. 2.2. Branch and bound method; valid inequalities; applications. 2.3 Combinatorial optimization problems: shortest distance, max flow, travelling salesman 3. Dynamic and stochastic optimization. 3.1. Formulations; finite-horizon models; optimality equations; recursive solution. 3.2. Infinite-horizon models; solution via linear optimization; applications. 4. Queueing theory 4.1. Simple queueing models: M/M/1, G/M/1 and /M/G/1 models, networks of M/M/1 queues.
Learning activities and methodology
Learning of theoretical concepts will be complemented with practical learning of the formulation and solution of operations research models. For such a purpose, optimization software will be used. Weekly individual tutorials will be scheduled.
Assessment System
  • % end-of-term-examination 50
  • % of continuous assessment (assigments, laboratory, practicals...) 50
Basic Bibliography
  • F.S. Hillier and G.J. Lieberman. Introduction to Operations Research. McGraw-Hill.
  • H.A. Taha. Operations Research. Prentice Hall.
Additional Bibliography
  • D.P. Bertsekas. Dynamic Programming and Optimal Control, vol. I, II. Athena Scientific.
  • L.A. Wolsey. Integer Programming. Wiley.
  • R.J. Vanderbei. Linear Programming - Foundations and Extensions. Springer.

The course syllabus and the academic weekly planning may change due academic events or other reasons.