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Operational Research

Code:

MP11122

Sigla:

IO

Áreas Científicas
Classificação	Área Científica
OFICIAL	Matemática

Ocorrência: 2021/2022 - 1S (on the 11-10-2021 a 19-02-2022)

Ativa?	Yes
Página Web:	https://moodle.ips.pt/2122/course/view.php?id=357
Unidade Responsável:	Departamento de Matemática
Curso/CE Responsável:

Ciclos de Estudo/Cursos

Sigla	Nº de Estudantes	Plano de Estudos	Anos Curriculares	Créditos UCN	Créditos ECTS	Horas de Contacto	Horas Totais
MP	30	Plano de Estudos	1	-	6	0	162

Língua de trabalho

Portuguese

Objetivos

Understand and apply the most general concepts and methodologies of mathematical programming in the formulation, solving and analysis of results in different Operations Research problems

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 geometrically solve some LP problems.
(d) Understand and know how to solve LP problems by the Simplex algorithm.
(e) Being able to model LP problems in software to solve them.
(f) Understand the fundamentals to model Integer Linear Programming (ILP) problems and know how to model and solve ILP problems by Branch and Bound techniques.
(g) Being able to model ILP problems in software to solve them.
(h) Know how to solve Transportation and Assignment problems through appropriate algorithms.
(i) Understand the fundamental definitions and concepts of graphs.
(j) Understand and know how to solve the Minimum Spanning Tree, Shortest Path, Maximal Flow and Project Management problems through appropriate algorithms.

Modo de trabalho

B-learning

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

Matrix calculus and linear equations.

Programa

1. Origin and Nature of Operations Research

2. Linear Programming


3. Network Analysis

Bibliografia Obrigatória

Luz C.; Pereira A.; Investigação Operacional, Departamento de Matemática ESTSetúbal
Rodrigo C.; Sebenta de Investigação Operacional, Departamento de Matemática ESTSetúbal

Bibliografia Complementar

Bazaraa M.S.; Jarvis J.J.; Sherali H.D.; Linear Programming and Network Flows, John Wiley & sons, 1997. ISBN: 978-0-470-46272-0
Hillier F.S.; Lieberman G.J.; Introduction to Operations Research, McGraw-Hill, 1990. ISBN: 9780071139892
Tavares L.V.; Oliveira R.C.; Themido I.H.; Correia F.N.; Investigação Operacional, McGraw-Hill, 1990. ISBN: 9789728298081
Ramalhete M.; Gerreiro J.; Magalhães A.; Programação Linear . Volumes 1 e 2, McGraw-Hill, 1990. ISBN: 9789729241031
Marques dos Santos M.; Magalhães Hill M.; Monteiro A.L.; Investigação Operacional - Volumes 1,2,3, Sílabo Ed., 2008. ISBN: 978-972-618-496-6
Taha H.A.; Pesquisa Operacional, Pearson, 2007. ISBN: 9788576051503

Métodos de ensino e atividades de aprendizagem

Theoretical-practical classes (75%) present the fundamental concepts corresponding to different topics of the syllabus, with proofs and illustrating examples of the main results, through the combined application of expositive methods and resolution of practical exercises. It is intended that in these lessons students should adquire a global understanding of the different subjects and its interconnections, based on a mathematically correct and objective formulation.

Synchronous online lessons (25%) are oriented to the training in different computational tools, and the practical application in a variety of problems typical of Operations Research.

The student will, further, engage into autonomous study of the presented subjects, deepening this knowledge, using the recomended bibliography of the Curricular Unit, and the orientations given by the teacher in the scheduled tutorial support. All this knowledge will be secured by autonomous reading and problem solving activities

Software

excel with linear programming solver add-in

Tipo de avaliação

Evaluation with final exam

Componentes de Avaliação

Designation	Peso (%)
Teste	75,00
Trabalho escrito	25,00
Total:	100,00

Componentes de Ocupação

Designation	Tempo (Horas)
Estudo autónomo	92,00
Frequência das aulas	60,00
Trabalho escrito	10,00
Total:	162,00

Obtenção de frequência

The positive evaluation of the student is achieved either by continuous evaluation or by evaluation in final exam.

CONTINUOUS EVALUATION

Continuous evaluation is based on 2 tests, with open-answer questions, and the written presentation of 2 individual practical assignments.

The first test and practical assignment evaluate the achievements related with the general notions of operations research and linear programming.

The second test and practival assingment evaluate the achievements in network-related questions.

Denoting T1,T2 the scores for both written tests, and PA1,PA2 the scores for both Practical Assignments, in the range 0-20, the final score (rounded to the integer) is computed as follows:

FS = 0.125*PA1+0.375*T1+0.125*PA2+p.375*T2

Conditions to obtain a positive evaluation are the following:

If FS is greater or equal to 10, the student has a positive evaluation with the final score FS, as long as 0.25*TP1+0.75*T1 and 0.25*TP2+0.75*T2 are both greater or equal 5. In any other case the final score shall be the integer value closest to the sum FS, not higher than 9 values.

EVALUATION BY EXAM

Students that don't get positive evaluation in the continuous evaluation process have the chance to take a global exam, evaluated in the integer range 0-20, where the positive evaluation is conditioned to a final score higher or equal to 10 values.

In any of these evaluations systems, in the case that a student has a final score higher or equal to 18 values, the student will be called for an oral exam, evaluated in the integer range 0-20, and the final score is the mean of the scores obtained in the written and oral proofs. If the student doesn't appear at the oral proof, the final score will be 17 values.

Fórmula de cálculo da classificação final

The final evaluation, in the integer range 0-20, is based on the presentation of two individual written practical assignments and two written tests.

Each written assignment is evaluated (PA1,PA2) in the integer range 0-20. Each written test (T1,T2) in the number range 0-20, rounded to the decimal point.

The final score (FS) is obtained by rounding to the nearest integer the numerical value obtained by application of the following formula:

FS=0.125*PA1+0.375*T1+0.125*PA2+0.375*T2

Avaliação especial (TE, DA, ...)

Working Students, higher competition athletes, student associations leaders and students demanding application of Religious Freedom Laws should contact the Curricular Unit Responsible teacher on this subject, no later than two weeks after the start of the teaching activities, indicating the corresponding specific circumstances, as declared by the corresponding norms. The timely application is needed so that the corresponding measures can be applied, with the needed objective conditions.

Observações

Distance learning activities will be developed using the corresponding IPS MsTeams "Investigação Operacional-MEP" Team.