Operational Research

Basic concepts of Algebra.

A learning strategy based on the experimentation of the subjects exposed in the theoretical class is used:
a) In the theoretical component, an oral presentation of the subjects is made, using the board and projections in Power-Point (the active participation of students is encouraged by asking simple questions).
b) In the theoretical-practical component, the knowledge acquired in the theoretical classes is applied
solving exercises (the exercises sheet are available on the Moodle platform and students must bring them to class).
Individual student study outside of classes is required (for better monitoring of classes).

Goals:

After attending this curricular unit, students must: know and understand the fundamental characteristics of the most representative optimization and decision problems; be able to translate simple optimization and decision problems into mathematical models of linear programming (LP); understand the LP algorithms and know to apply the appropriate ones to solve this kind of problems; be able to interpret the solutions obtained by the application of these algorithms to the mathematical models; and to analyse the sensitivity of this (these) solution(s) to variations in model’s parameters.

The knowledge acquired in this course can be applied in solving similar algorithms/problems in a real context.

Skills:

After attending this course, students must:

– Be able to identify the different types of problems that can be studied with the use of operational research techniques.

– Be able to translate simple optimization and decision problems into mathematical models of linear programming (LP);

– Understand the LP algorithms and know to apply the appropriate ones to solve this kind of problems;

– Be able to interpret the solutions obtained by the application of these algorithms to the mathematical models;

– Be able to analysis the sensitivity of the optimal solution(s) obtained due to variations in model’s parameters.

– Application of the concepts learned in this curricular unit in the resolution of more complex similar problems in a professional context.

Theoretical content:
1 – Introduction to Operations Research
2 – Linear Programming
3 – Introduction to Post-Optimization and Sensitivity Analysis
4 – Multi-Objective Linear Programming
5 – Goal Programming

Theoretical-Practical content:
– Resolution of theoretical-practical exercises involving the various chapters of the theoretical program (exercises sheets available on Moodle).

NAO

Main Bibliography:

– Documentation that supports classes (Notes and slides, available in moodle)

– Hillier, F. S., & Lieberman, G. J. (2010). Introduction to Operations Research (6^th ed.). New York: McGraw-Hill. [available at ISEC’s Library the 5th edition = Cota ISEC: 3-9-31 (ISEC) – 08145]. The 10th edition (2015) of this book is available for download in: https://pt1lib.org/book/3426899/3de006

– Clímaco, J. N., Antunes C. H., & Alves M. J. (2003). Programação Linear multiobjectivo: do modelo de programação linear clássico à consideração explícita de várias funções objectivo. Coimbra – Imprensa da Universidade de Coimbra. [Cota ISEC: 3-9-95 (ISEC) – 13356; 3-9-96 (ISEC) – 13392]

– Ramalhete, M., Guerreiro, J., & Magalhães, A. (1984-1985) Programação Linear (vol. I e vol. II)  (6a ed.). Lisboa: McGraw-Hill. [Cota ISEC: 3-9-22 (ISEC) V.1º v. – 05262; 3-9-23 (ISEC) V.2º v. – 07016; …]

– Hill, M. M.; Santos, M. M. (2009) – Investigação Operacional (vol.I e vol.II) (2th ed.). Lisboa: Edições Sílabo [Cota ISEC: 3-9-111 (ISEC) V.1º v. – 16149 ; 3-9-112 (ISEC) V.2º v. – 15173]

Additional Bibliography:

– Tavares, L.V.,   Oliveira, R. C.,   Themido, I. H.,   Correia, F.N. (1996) Investigação Operacional. McGraw-Hill.

– Ravindran, A.; Phillips, D. T.; Solberg, J. J. (1987) Operations Research: Principles and Practice. (2nd ed.). New York: John Wiley [Cota ISEC: 3-9-57 (ISEC) – 09253]

– Taha, H. A. (2007) Operations research: an introduction (8th ed.). London: Prentice-Hall [available at ISEC’s Library the 5th edition = Cota ISEC: 3-9-29 (ISEC) – 07857]

– Murthy, P. R. (2007) Operations Research (2nd ed.). New Delhi: New Age International Publishers (PDF available for download in: https://easyengineering.net/operations-research-p-ramamurthy/

– Bazaraa M.S., Jarvis J.J., & Sherali H.D. (2010) Linear Programming and Network Flows (4th ed.), Wiley

– Steuer, R. (1986) Multiple Criteria Optimization: theory, computation and application. John Wiley & Sons.