Optimization

Code:

M.EIC021

Acronym:

O

Keywords
Classification	Keyword
OFICIAL	Quantitative Methods and Management

Instance: 2023/2024 - 2S

Active?	Yes
Responsible unit:	Department of Industrial Engineering and Management
Course/CS Responsible:	Master in Informatics and Computing Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
M.EIC	32	Syllabus	1	-	6	39	162

Teaching language

Suitable for English-speaking students

Objectives

The aim of this course to provide the students with competences to:

•  identify and address decision problems in a structured way; 
• build models of decision problems; 
• identify and use analytical methods to obtain solutions for the models, that should act as a support for informed decisions; 
• use optimization solvers to analyse and obtain solutions for the models.

Learning outcomes and competences

At the end of this course in Operations Research the students should be able to:

- identify a decision problem, 

- justify the need for the application of an optimization technique

- build an appropriate mathematical model,

- select and apply a suitable method or algorithm, 

- be able to analyze critically the obtained results

- apply sensitivity analysis and 

- be able to justify the applied technique and quantify the gains for the organization

The main objective of this course is, through the creation of models, develop skills for analysing a wide range of real situations. These competencies are based on the ability to recognize the key problem in a non-structured situation and develop a framework for analysing and treating the problem, and on the application of analytical methods for its resolution.

Taking into account that Optimization is the fundamental discipline of Operational Research, looking at the definition of operational research available at the UK Operational Research Society’s website, we find a perfect match between this scientific field and the declared objectives:

“Operational research is the discipline of applying advanced analytical methods to help make better decisions. By using techniques such as problem structuring methods […] and mathematical modeling to analyze complex situations, operational research gives executives the power to make more effective decisions and build more productive systems”.

Working method

Presencial

Program

1. Linear Programming
1.1 Formulating Linear Problems
1.2 Solving LP using the Simplex Method
1.3 Solving LP problems using optimization software
1.4 Discussing: Sensitivity Analysis
1.5 Duality

2. Integer Programming
2.1 Formulating Integer and Mixed Integer Linear Problems
2.2 Solving IP & MILP: Branch & Bound
2.3 Solving IP & MILP problems using optimization software
2.4 Discussing: Comparing alternative formulations

3. Decision Theory
3.1 Decision trees and the value of information
3.2 Behavioural economics

Mandatory literature

Frederick S. Hillier, Gerald J. Lieberman; Introduction to operations research. ISBN: 0-07-118163-6

Complementary Bibliography

Luís Valadares Tavares, ... [et al.]; Investigação operacional. ISBN: 972-8298-08-0
coord. Carlos Henggeler Antunes, Luís Valadares Tavares; Casos de aplicação da investigação operacional. ISBN: 972-773-075-2

Teaching methods and learning activities

The themes are presented using active learning methods. The problems are illustrated with examples. The problems from a list of proposed problems are discussed and solved by the students.
Assessment will include a continuous assessment component (quizzes at clases, homeworks, presentation of papers) with a weight of 40%, a group project with a weight of 20% and a short test with a weight of 40%.

Software

IBM CPLEX Studio
Excel Solver

keywords

Physical sciences > Mathematics > Applied mathematics > Operations research

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Participação presencial	40,00
Exame	40,00
Trabalho prático ou de projeto	20,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	60,00
Frequência das aulas	56,00
Trabalho escrito	46,00
Total:	162,00

Eligibility for exams

The weighted average of the various evaluation components must be positive.

Calculation formula of final grade

The final classification is calculated based on the grades obtained in the exam, in the group project and in the evaluation of continuous assessment component.

The test has a weight of 40%, the group project has a weight of 20% and the continuous assessment component has a weight of 40%.

 

Examinations or Special Assignments

Not applicable

Special assessment (TE, DA, ...)

Special evaluation will be performed through an individual test with a duration of 2 hours that will cover all the syllabus of the course.

Classification improvement

 A final test will be available to improve the short test grade.