Operational Research (Engineering Courses)


In this course Engineering students are introduced to the first concepts of Operations Research. The course will introduce students to the following O.R. subjects: Linear Programming, Project Management, Decision Theory and Simulation.

General characterization





Responsible teacher

Maria do Carmo Proença Caseiro Brás


Weekly - 4

Total - 56

Teaching language



Students should have strong knowledge of Probability Theory and matrix calculus.


1. F. S. Hillier e G. J. Lieberman, Introduction to Operations Research, 2015, 10ª Ed., McGraw-Hill.

2. L. V. Tavares, F. N. Correia, I. H.l Themido e R. C. Oliveira, Investigação Operacional, 1996, McGraw-Hill.

3. Wayne L. Winston, Operations Research, 2003, Duxbury Press.

Teaching method

Any non-Portuguese student should contact the Professors if (s)he requires any assistance. 

Basic concepts will be introduced in lectures ("aulas teóricas") and problems will be solved in problem solving classes ("Aulas práticas").

Evaluation method

Students should attend at least 2/3 of the practical lessons.There are 2 Tests during the semester and one Exam afterwards.

For further information, you should contact Prof. Carmo Brás, mb@fct.unl.pt .

Subject matter

1. Introduction to Linear Programming
1.1.Linear Programming Formulations
1.2.The Simplex method
1.3.The Revised Simplex method
1.5. Sensitivity Analysis

2.Project Management
2.1.Critical Path Method (CPM)
2.2.Construction of the Time Chart and Resource Leveling
2.3.Reduction of the project duration
2.4.Program Evaluation and Review Technique (PERT)

3. Decision Theory
3.1. Decisions under risk and under uncertainty
3.2 .Utility. Introduction to the multicriteria decision
3.3. Decision Trees

4. Simulation
4.1.Generating random numbers: mixed congruential method, inverse transformation, acceptance-rejection method
4.2.Duration of the simulation/Results precision
4.3.Applications: project management, inventory management, Markov chains, models of visual simulation, introduction to the simulation of queuing systems.