Checking date: 10/07/2020

Course: 2020/2021

Mathematical optimization for business
Study: Bachelor in Management and Technology (351)

Coordinating teacher: NIÑO MORA, JOSE

Department assigned to the subject: Department of Statistics

Type: Electives
ECTS Credits: 6.0 ECTS


Students are expected to have completed
Students are expected to have completed courses with contents in linear algebra, multivariable differential calculus, statistics, business administration and computer programming.
Competences and skills that will be acquired and learning results. Further information on this link
CORE COMPETENCES: 1. Formulating optimization models for decision-making in diverse application areas. 2. Analyzing and solving optimization problems of linear, integer and nonlinear types, through the formulation and solution of their optimality conditions. 3. Using software tools for formulating and solving optimization models. 4. Interpreting the numerical solutions of optimization models in decision-making terms. TRANSVERSAL COMPETENCES: 1. Capacity for analysis and synthesis. 2. Problem solving and mathematical modeling. 3. Oral and written communication.
Description of contents: programme
Topic 1.1. Linear optimization (LO). Operations research; LO models; formulations and applications; computer-based solution. Topic 1.2. Graphical solution; sensitivity analysis. Topic 1.3. The fundamental theorem of LO; basic feasible solutions and vertices; the simplex method. Topic 1.4. The two-phase simplex method; interior point methods. Topic 1.5. Optimal network flow models. Topic 1.6. More applications and examples. Topic 2.1. Integer optimization models; linear relaxations; optimality gap; graphical and computer solution. Topic 2.2. The Branch and Bound method. Topic 2.3. Combinatorial optimization models; strengthening formulations; valid inequalities. Topic 2.4. More applications and examples. Topic 3.1: Unconstrained non-linear optimization (NLO). Motivation and examples; local and global optima; convexity; optimality conditions; numerical solution. Topic 3.2. Equality-constrained NLO. Motivation and examples; Lagrange multipliers; optimality conditions; numerical solution. Topic 3.3. Inequality-constrained NLO. Motivation and examples; Karush-Kuhn-Tucker multipliers; optimality conditions; numerical solution. Topic 3.4. More applications and examples.
Learning activities and methodology
Theory (3 ECTS). Theory classes with supporting material in Aula Global. Practice (3 ECTS). Model formulation and problem-solving classes. Computing classes. The teaching methodology will have a practical approach, being based on the formulation and solution of problems drawn from diverse application areas, both in the practical classes and in the theory classes, as motivation and illustration of the theory. There will be a weekly individual tutoring session.
Assessment System
  • % end-of-term-examination 0
  • % of continuous assessment (assigments, laboratory, practicals...) 100
Basic Bibliography
  • F.S. Hillier, G.J. Lieberman. Introduction to operations research. McGraw-Hill.
  • H.A. Taha. Operations research : an introduction. Prentice Hall.

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