Quantitative Methods


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 graph theory and network analysis

- Properly formulate and solve production problems through dynamic programming

General characterization





Responsible teacher

Alexandra Maria Batista Ramos Tenera, António Carlos Bárbara Grilo


Weekly - 5

Total - 70

Teaching language



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


- 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 will be based on the following:

- Individual Evaluation: 2  course subject tests or 1 global Exam (EX)

Course frequency is achieved with test T1 participation and a 2/3 pratical class participation

In order to obtain an UC approval, a minimum grade of 9.5 is required.

FINAL Grade (CF) = 0,5 T1 + 0,5 T2 or Ex

with  test average or Final Exam (EX) ≥ 9,5 v

if CF>= 18 /20 => Grade check required

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


Programs where the course is taught: