Operational Research

Code:

1GE208

Acronym:

IO

Keywords
Classification	Keyword
OFICIAL	Management Studies

Instance: 2021/2022 - 2S

Active?	Yes
Responsible unit:	Management
Course/CS Responsible:	Bachelor in Business Administration

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
LGES	260	Bologna Syllabus since 2012	2	-	6	42	162

Teaching language

Portuguese and english

Objectives

• Provide an introduction to Operational Research and its applications.


• Describe the main characteristics of Linear Programming models.


• Describe the main concepts regarding the solution methods for Linear Programming models.


• Describe the main concepts regarding duality.


• Describe the main concepts regarding sensitivity analysis and post-optimization in Linear Programming.


• Illustrate the economic interpretation of some Linear Programming models.


• Describe the main concepts regarding discrete time Markov chains, both without and with absorbing states.


• Describe the main concepts regarding continuous time Markov chains.

Learning outcomes and competences

After completing this course unit, the student should be able to:

• Formulate a problem using a linear programming model.


• Solve a linear programming model using the graphical method, as well as Excel's Solver.


• Write the dual of a linear programming problem.


• Gather and interpret relevant data / information from the solution and sensitivity reports generated by Excel's Solver.


• Formulate a problem using a Markov chain.


• Gather and interpret relevant data / information from the outputs provided by the software used for Markov chains.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Previous knowledge of Linear Algebra and of probability distributions.

Program

1. Introduction to Operational Research

2. Linear Programming
2.1. Modelling
2.2. Solution Methods
2.3. Duality
2.4. Economic Interpretation and Sensitivity Analysis

3. Stochastic Processes
3.1. Discrete Time Markov Chains
3.2. Discrete Time Markov Chains with Absorbing States
3.3. Continuous Time Markov Chains

Mandatory literature

Hillier Frederick S.; Introduction to operations research. ISBN: 978-007-126767-0
Mourão S.; Pinto L.; Simões O.; Valente J., Pato M.; Investigação Operacional - Exercícios e Aplicações, Escolar Editora, 2018. ISBN: 978-972-592-536-2

Teaching methods and learning activities

• Theretical exposition.


• Examples and exercises.

Software

Microsoft Excel

Evaluation Type

Distributed evaluation without final exam

Assessment Components

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

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	120,00
Frequência das aulas	42,00
Total:	162,00

Eligibility for exams

All students enrolled in the course may take the final exam. However, and naturally, students who complete the distributed assessment evaluation in the regular examination period (by handing in the final test) will not be able to take the regular examination period exam.

The distributed assessment consists of two tests. The first test will be in the midle of the semestre and the second test on the exam date.

Calculation formula of final grade

Regular Examination Period

In the regular examination period there are two assessment types: 1) distributed evaluation; 2) evaluation via final exam.

1) Distributed assessment.

The distributed assessment consists of two tests. The first test has a weight of 60% in the final grade, while the second test has a weight of 40%.

This type of assessment is only available for students placed in the course's sessions. That is, the student must not only be enrolled in the course, but also registered for the classes / sessions.

If a test takes place during the sessions' schedule, students may only take the test in the schedule of the session in which they are registered.

A student who completes this assessment type, by handing in the final test, cannot take the regular examination period exam.

There is a minimum score of 6.0 in each test. Therefore, if a student scores lower than 6.0 on any test, she / he will fail the distributed assessment, regardless of the overall weighted score of the tests.

2) Assessment via final exam.

This type of assessment consists of a final exam.

Reassessment Examination Period and Special Examination Period

In the reassessment examination period and in the special examination period assessment is via final exam only.

Classification improvement

Students may improve their grade only via final exam.

Observations

In tests, students may consult the contents of one A4 sheet of paper they prepared themselves. In exams, students may consult the contents of two A4 sheets of paper they prepared themselves.

Students may only use their own calculator.