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Elements of Operational Research

Code:

TGI18

Sigla:

EIO

Áreas Científicas
Classificação	Área Científica
OFICIAL	Matemática

Ocorrência: 2022/2023 - 3T

Ativa?	Yes
Página Web:	https://moodle.ips.pt/2223/course/view.php?id=1750
Unidade Responsável:	Departamento de Matemática
Curso/CE Responsável:	Industrial Management and Techinology

Ciclos de Estudo/Cursos

Sigla	Nº de Estudantes	Plano de Estudos	Anos Curriculares	Créditos UCN	Créditos ECTS	Horas de Contacto	Horas Totais
TGI	21	Plano de Estudos 2016	3	-	4	44	108

Língua de trabalho

Portuguese
Obs.: Portuguesa

Objetivos

This curricular unit (CU) aims to present a first reference to the modeling of real problems of Operational Research, as well as to provide information about some of the techniques used in solving those problems. An approach will be taken to the various subjects according to the area of the Degree, in order to develop the capacity to apply the techniques of modeling and optimization to real situations.

Resultados de aprendizagem e competências

(a) Understand the origins, evolution and methodology of Operational Research.
(b) Understand and being able to model real problems in Mathematical and Linear Programming (LP).
(c) Understand and know how to solve LP problems by the Simplex algorithm.
(d) Being able to model LP problems in software to solve them.
(e) Understand the fundamental definitions and concepts of graphs.
(f) Understand and know how to solve the Minimum Spanning Tree, Shortest Path and Project Management problems through appropriate algorithms.

Modo de trabalho

Presencial

Pré-requisitos (conhecimentos prévios) e co-requisitos (conhecimentos simultâneos)

Previous mathematical knowledge acquired through to course unit Métodos Matemáticos I and Métodos Matemáticos II.

Programa

1. Origin and Nature of Operational Research
1.1. Components of an Operational Research (OR) study.
1.2. Mathematical modeling.
1.3. Brief reference to different OR models through illustrative examples.
2. Linear Programming
2.1. Introduction to Linear Programming (LP). Formulation of problems and construction of mathematical models of LP.
2.2. The simplex method.
2.3. Duality.
3. Network Analysis
3.1. Graphs: terminology, notation and basic concepts.
3.2. Minimum Spanning Tree problem and Shortest-Path problem.
3.3. Project management through PERT/CPM techniques.

Bibliografia Obrigatória

Pereira, Anabela; Elementos de Investigação Opracional, Departamento de Matemática, 2021

Bibliografia Complementar

Bazaraa, M.S., Jarvis J. J., Sherali H. D; Linear Programming and Network Flows, Second Edition, John Wiley & Sons, 1997
Hillier, F.S.; Lieberman, G.J.; Introduction to Operations Research, Fifth edition, McGraw-Hill, 1990
Oliveira, R.; Ferreira, J.; Investigação Operacional em ação: casos de aplicação, Imprensa da Universidade de Coimbra, 2014
Ramalhete, M.; Guerreiro, J.; Magalhães, A.; Programação Linear, Vols 1 e 2, McGraw-Hill, 1985
Tavares, L.V., Oliveira, R.C., Themido, I.H., Correia, F.N.; Investigação Operacional, McGraw-Hill, 1996

Métodos de ensino e atividades de aprendizagem

The teaching methodology has two strands:
• face-to-face, in theoretical-practical classes, combining the expository method and problem solving;
• at a distance, on the moodle platform (http://moodle.ips.pt/), where students access the contents of the CU through various materials and where weekly activities are proposed.

Tipo de avaliação

Distributed evaluation with final exam

Componentes de Avaliação

Designation	Peso (%)
Teste	100,00
Total:	100,00

Componentes de Ocupação

Designation	Tempo (Horas)
Frequência das aulas	22,00
Estudo autónomo	86,00
Total:	108,00

Obtenção de frequência

The use of this CU can be obtained through two assessment processes: Continuous Assessment or Exam Evaluation.
Continuous evaluation:
The Continuous Assessment consists of two tests.
Assigning by T1 and T2 the scores (from zero to 20 values, rounded to the hundredths) obtained in the 1st test and the 2nd test, the final classification CF (rounded to the units) will be calculated as follows:
CF = (T1 + T2) / 2
The approval conditions are as follows:
1. If CF is greater than or equal to 10 and less than 18, the student is awarded a final grade equal to CF, provided that the classification in any one of the tests was greater than or equal to 8.0 values.
2. If CF is less than 10 and one of the tests has a rating of 8.0 or more, the student can perform a recovery test on the date of the normal period exam to retrieve the other test's classification.

Assessment by Exam:
Students who have not obtained approval for Continuous Assessment may take an exam, being approved as long as they obtain a grade of 10 or higher.

NOTE: In any of the evaluation processes, whenever the final classification is greater than or equal to 18 values, the student must present an oral test, obtaining as a final mark the average of the classifications of the written test and of the said oral test . If the student does not attend the oral test, the final grade will be 17 points.


Comments:
1. Each test lasts 2 hours and the exam lasts 2 hours and 30 minutes;
2. During the tests (tests or examinations), it is allowed to consult an A4 sheet handwritten by the student himself;
3. During the tests (tests or exams), the use, manipulation or display of any electronic equipment, other than school calculators, is not permitted.

Fórmula de cálculo da classificação final

CF = (T1+T2)/2

or exam evaluation

Provas e trabalhos especiais

Working students, high-level athletes, association leaders and students under the Religious Freedom Law must address, until the second academic week of the semester, to the head of the Curricular Unit to present their pertinent specificities, in accordance with the terms of the respective diplomas under penalty of failure to enforce them for lack of objective conditions.