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 several productive network analysis techniques properly

- Properly formulate and solve production problems through dynamic programming

- Design scenarios and future behaviors with Markov chains

General characterization





Responsible teacher

António Carlos Bárbara Grilo, Radu Godina


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: Exam (EX) or Tests (Test in the midddle (T1) and at the end of the semester (T2): if the average of the test Ts >= 9,5 then the student can optionally skip the exam.

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

Final Grade (FG) = 0.5T1 + 0.5T2

or Final Exam (EX) ≥ 9,5

Graphing calculators are not allowed during tests.

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


Programs where the course is taught: