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

Versao Portuguesa

INVESTIGAÇÃO OPERACIONAL - 2016/2017

2º curricular year
Semestralidade: 2nd semester
ECTS: 6

Teachers

Leading Teacher: Prof. Doutor José Noronha
Assistant Professor: Prof. Doutor José Noronha

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 and duality;
d) Identifying transportation and assignment problems, choosing adequate procedures to solve them.

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. Duality
4.1 The dual problem
4.2 Primal-dual relations
4.3 Economical interpretation of the dual problem
5. Sensitivity analysis
5.1 The dual problem and sensitivity analysis
5.2 Changes in the independent terms
5.3 Changes in the variable coefficients
5.4 Introduction of new variables
5.5 Introduction of new constraints
5.6 Changes in the objective function coefficients
6. Transportation models and their variants
6.1 The transportation problem
6.2 Properties
6.3 Simplex method for the transportation problem
6.4 The assignment problem

Evaluation Type

The continuous assessment comprises two written examinations with the duration of about one hour each. The first one covers the first half of the course contents and takes place approximately half way through the semester and the second one covers the second half of the course contents and takes place towards the end of the semester.

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.

Sustainability Objectives

Keywords

Operations Research
Operational Research
Linear programming
Mathematical Programming

Main Bibliography

Author Hill, Manuela
Title Investigação Operacional - Vol. 1
Edition 3.ª ed.
Place Lisboa
Editor Sílabo
Year 2015
Author Hillier, Frederick; Lieberman, Gerald
Title Introdução à Pesquisa Operacional
Edition 9.ª ed.
Place Lisboa
Editor McGraw-Hill
Year 2012
Author Vanderbei, Robert J.
Title Linear Programming: Foundations and Extensions
Edition 4. ed.
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 ed.
Place New York
Editor John Wiley
Year 2010
Author Rardin, Ronald L.
Title Optimization in Operations Research
Edition 2.ª ed.
Place Harlow, United Kingdom
Editor Pearson
Year 2016