Cursos / 1º Ciclo / / Faculty of Economy and Business Management :: Business Management

Versao Portuguesa

INVESTIGAÇÃO OPERACIONAL - 2021/2022

2º curricular year
Semestralidade: 1st semester
ECTS: 6

Teachers

Leading Teacher: Prof. Doutor Paulo Aguiar
Assistant Professor: Prof. Doutor Paulo Aguiar

Class type and School hours

Orientação Tutorial : 1 Horas
Teórico-prática : 2 Horas

Teaching Language

Portuguese

Main Aims/Objectives

It is intended to:
a) Bringing to attention the importance of operations research across different areas;
b) Promoting the development of the skill of translating into a mathematical language problems presented in a non-mathematical language;
c) Promoting the development of the skill of performing mathematical analysis of problems in the areas of economy and management, with the aim of obtaining the best solutions.

Specific Aims/Objectives

It is intended that the students understand and know how to apply the methods of linear programming to solve optimization problems in management.

Skills to be acquired

By the end of the course the student should be capable of:
a) Identifying problems from different areas that are prone to being formulated, and indeed formulate them, in the mathematical language of linear programming;
b) Applying graphical and simplex methods to solve those problems;
c) Performing sensitivity analysis and reoptimization, using matrix methods.

Teaching Procedures

The contents are presented following an expository methodology. When appropriate, texts are made available that further develop the subjects. The student is presented with problems that he or she must solve, being assisted during the tutorials.

Programme

1. Introduction to Operations Research (OR)
1.1 Mathematical modelling and optimization
1.2 Methodology of OR
2. Introduction to Linear Programming (LP)
2.1 Typical examples
2.2 Mathematical Formulation of LP problems
2.3 Graphical representation and solution of LP problems
2.4 Particular cases
2.5 Additional examples
3. The simplex method
3.1 Standard form of LP problems
3.2 Fundamentals of the simplex method
3.3 The primal simplex algorithm
3.4 Geometrical interpretation
3.5 Resource classification
3.6 Artificial initial solution: two-phase method
3.7 Special cases
4. Sensitivity analysis
4.1 The dual problem and sensitivity analysis
4.2 Changes in the independent terms
4.3 Changes in the variable coefficients
4.4 Introduction of new variables
4.5 Introduction of new constraints
4.6 Changes in the objective function coefficients

Evaluation Type

The Continuous Assessment is based on 2 written tests each containing complementary parts of the program. If the written tests are to be carried out online on the Moodle platform, students who obtain a grade higher than 14.0 on the online platform will need to take an oral test that will more accurately assess their knowledge. Those who do not need this oral exam will get 14 in this exam. Each test will last for 1 hour.

Teaching Resources

The didactic resources that should be available to the students are the books in the course bibliography and room for study, individually and in small groups.
The proposed exercises and other relevant content will be placed on the Moodle platform. This platform may come to be used in online examinations.

Sustainability Objectives

Keywords

Operations Research
Operational Research
Linear programming
Mathematical Programming

Main Bibliography

Author Hill, Manuela
Title Investigação Operacional - Vol. 1
Edition 3.ª edição
Place Lisboa
Editor Sílabo
Year 2015
Author Hillier, Frederick; Lieberman, Gerald
Title Introdução à Pesquisa Operacional
Edition 9.ª edição
Place Lisboa
Editor McGraw-Hill
Year 2012
Author Vanderbei, Robert J.
Title Linear Programming: Foundations and Extensions
Edition 4.ª edição
Place New York
Editor Springer
Year 2014

Complementary Bibliography

Author Bazaraa, Mokhtar; Jarvis, John; Sherali, Hanif
Title Linear Programming and Network Flows
Edition 4.ª edição
Place New York
Editor John Wiley
Year 2010
Author Rardin, Ronald L.
Title Optimization in Operations Research
Edition 2.ª edição
Place Harlow, United Kingdom
Editor Pearson
Year 2016