Operations Research


Introduction to the scientific area of Operational Research, both in its components of modelling and optimization.

These two components will be approached under different Operational Research thematics, namely Project Management, Inventory Control, Networks Optimization, Decision Theory, Markov Chains and Simulation.

Since this is an introductory course, some of the subjects will be (or could be, as a student option) detailed in further courses of the curricular plan.

General characterization





Responsible teacher

Maria do Carmo Proença Caseiro Brás


Weekly - 4

Total - 110

Teaching language



Available soon


1. "Elementos de apoio às aulas de Introdução à Investigação Operacional", "Enunciados de Exercícios de Introdução à Investigação Operacional", Ruy A. Costa (2007)

2. Investigação Operacional, Valadares Tavares et al, McGraw Hill (1997)

3. Wayne L. Winston, Operations Research: Applications and Algorithms, Brooks/Cole; 4th edition, 2004.

4. Introduction to Operations Research, Hillier e Lieberman, McGraw Hill (1995)

5. Operations Research - An Introduction, Taha, Prentice Hall (2011)

Teaching method

The classes will be theoretical-practical, allowing students to acquire and immediately apply knowledge. Classes would take place in a computer lab, and will use spreadsheets and aditional software when required.

Theoretical notes and a set of exercises are provided to students.

Any questions or doubts will be addressed during the classes, during the weekly sessions specially programmed to attend students or on individual sessions previously scheduled between professor and students.

Students are regularly evaluated, during semester.

Evaluation method

The Evaluation Method is fully described on the Course moodle area.

All students must attend to a minimum number of 2/3 taught lessons before being accepted to evaluation.

Contact Professor Carmo Brás for aditional information: mb@fct.unl.pt.

Subject matter

1 - Project Management (Critical Path Method; Gantt Diagram; Reducing the duration of a project; PERT technique).

2 - Inventory Control (basic deterministic models; extensions of the basic deterministic models).

3 - Networks Optimization. (Introduction to Graph Theory. Shortest Path Problem. Dijsktra Algorithm. Floyd–Warshall Algorithm. Minimal Spanning Tree. Prim Algorithm. Kruskal Algorithm. Eulerian Graphs. Chinese Postman Problem. Hamiltonian Graphs. Traveling Salesman Problem.

4 - Decision Making (Decision under uncertainty and risk; Utility. Introduction to multicriteria decision making; Sequential decisions).   

5- Markov Chains in Discrete Time (Definition; Transition probabilities; Decomposition of an homogeneous chain; Limit theorems).

6 - Simulation (Generating of pseudo-random numbers; Applications).