Faculdade de Ciências e Tecnologia

Quantitative Methods



Academic unit

Faculdade de Ciências e Tecnologia


Departamento de Engenharia Mecânica e Industrial



Teacher in charge

Alexandra Maria Batista Ramos Tenera, Virgílio António Cruz Machado

Weekly hours


Total hours


Teaching language



The course seeks to introduce several key analytical methods and tools useful in the analysis of productive systems (in manufacturing and services). At the end of the course, students should be able to:
- Correctly analyze  queueing systems (with and without limitations of capacity and population),

-Apply several productive network analysis techniques properly

- Properly formulate and solve production problems through dynamic programming

- Design scenarios and future behaviors with Markov chains


Is advised that students have some expertise in Statistics and Operations Research

Subject matter

1.Queueing Theory: Basic Structures; Terminology and Notation; Main Performance Measures; Little’s Equations; Deterministic and Probabilistic Models with Exponential distributions and FIFO discipline; Multiple-server;  Finite queue and finite calling population variation; Data Analysis and Goodness Fit Tests

2.Graphs and Network Analysis: Minimum Spanning Tree; Shortest-Path; Maximum Flow; Transportation;   Assignment and Transshipment Problems

3.Dynamic Programming: Graph Formulation; Main Characteristics; Contributions Types: additive, multiplicative, additive-multiplicative, max-min e min-max; Applications

4.Introduction to Markov Chains: State Characterization and classification; Transition Matrix;    Steady-State Conditions; Applications


- Hillier, F. & Lieberman, G. (2010). Introduction to Operations Research (9th ed.). USA, Mcgraw-Hill. 
Taha, H. (2010). Operations Research: An Introduction (9th ed.) Englewood Cliffs, Prentice Hall.

- Evans, J. & Minieka, E. (1992). Optimization Algorithms for Networks and Graphs (2nd ed.). USA, Marcel Dekker, Inc.

- Lapin, L.(1994). Quantitative Methods for Business Decisions with Cases (6nd ed.). USA, Dryden Press.

- Chang, Y-L (2003) WinQSB: Decision Support Software for MS/OM Version 2.0. USA, John Wiley & Sons.

- Bronson, R & Naadimuthu, G. (2001). Investigação Operacional (2ª ed.). Trad. Ruy Costa. Alfragide, Mcgraw-Hill de Portugal, Lda.

Teaching method

Lectures are carried out combining theoretical classes and applied classe

Evaluation method

The course grading shall be based on the following: