Checking date: 22/05/2022


Course: 2022/2023

Mathematical optimization for business
(17674)
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

Course:
Semester:




Requirements (Subjects that are assumed to be known)
Students are expected to have completed courses with contents in linear algebra, multivariable differential calculus, statistics, business administration and computer programming.
Objectives
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.
Skills and learning outcomes
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. Duality in LO. Topic 1.5. Optimal network flow models. 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 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.
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
Calendar of Continuous assessment
Basic Bibliography
  • F.S. Hillier, G.J. Lieberman. Introduction to operations research. McGraw-Hill.
  • H.A. Taha. Operations research : an introduction. Prentice Hall.
  • J. Niño Mora. Introducción a la optimización de decisiones. Pirámide. 2021
Recursos electrónicosElectronic Resources *
Additional Bibliography
  • R. J. Vanderbei. Linear Programming: Foundations and Extensions. Springer. 2020
(*) Access to some electronic resources may be restricted to members of the university community and require validation through Campus Global. If you try to connect from outside of the University you will need to set up a VPN


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