Operational Research

Code	15620
Year	1
Semester	S2
ECTS Credits	8
Workload	TP(60H)
Scientific area	Mathematics
Entry requirements	does not apply
Learning outcomes	It is intended that students characterize, model and solve classic Linear Programming / Optimization problems and also adapt the methods addressed for these problems in the exact and/or approximate resolution of new problems. At the end of the Operational Research Curricular Unit, the student must be able to: 1) Model problems in Linear Programming; 2) Use algorithms that produce optimal solutions for these models, as support for informed decisions; 3) Model problems in Networks; 4) Distinguish elementary concepts from Graph Theory 5) Apply and distinguish Network Optimization algorithms; 6) Build models of optimization problems;
Syllabus	1. Linear Programming 1.1 Introduction; 1.2 Linear Algebra, Convex Analysis and Polyhedra; 1.3 Simplex Algorithm; 1.4 Duality; 2. Network optimization 2.1 Graphs and Networks: notation and elementary concepts; 2.2 Shortest Path Problem; 2.3 Maximum Flow Problem; 2.4 Minimum Cost Flow Problem;
Main Bibliography	- Pereira, F., Investigação Operacional, UBI, 2019 - Valério de Carvalho, J.M., Optimização Combinatória, Universidade do Minho, 2001 - Bazaraa, M., Jarvis, J., Sherali, H., Linear Programming and Network Flows. Wiley, 2010 - Wolsey, L., Integer Programming. Wiley, 1998 - Ahuja, R., Magnanti, T., Orlin, J., Network Flows: Theory, Algorithms, and Applications. Pearson, 1993 - Ramalhete, M., Guerreiro, J., Magalhães, A., Programação Linear (I e II), MacGraw-Hill, 1995
Teaching Methodologies and Assessment Criteria	Teaching/Learning Assessment • T1 - Test 1: 10 points (individual test) • T2 - Test 2: 10 points (individual test) The final grade for the UC (Course Unit) is the sum of the scores obtained in T1 and T2. A student passes the UC and is exempt from the Final Exam if the student achieves a grade equal to or higher than 9.5 points. Assessment by Exam • Exam: 20 points (individual exam) Grades higher than 18 points, whether obtained through Teaching/Learning Assessment or by Exam, must be defended in an oral examination, in accordance with the UBI Academic Regulations (Chapter IV, Article 126, items 6 and 7).
Language	Portuguese. Tutorial support is available in English.