Fundamentals of Operational Research

Recommended Prerequisites

Linear Algebra, Calculus.

Teaching Methods

Theoretical and methodological concepts are presented in tutorial lectures, being motivated by real-world problems and illustrated with application examples.

Software (commercial and public domain) packages are used to obtain solutions to the mathematical models, thus freeing the students for the more creative tasks of problem formulation, model building and critical analysis of results.

Learning Outcomes

Providing the students with methodological and application competences in the context of optimization in engineering problems, in order to enable them to identify types of problems, develop adequate mathematical models that include the essential characteristics of those problems, and apply algorithms to generate the optimal solutions for the problems. Special attention is paid to the use of software packages to obtain the optimal solutions, as well as sensitivity analysis of optimal solutions in face of changes in the model data and parameters.

Work Placement(s)

No

Syllabus

0. Origin and nature of Operational Research (OR).

1. Linear Programming (LP). Problem formulation and development of PL mathematical models. The simplex method. Duality theory. Sensitivity analysis. Goal programming.

2. The transportation, assignment  and transshipment  problems.

3. Network optimization problems. Shortest path. Minimum spanning tree. Shortest path with fixed costs in nodes. Maximum flow. Minimum cost flow.

4. Non-linear programming. Types of non-linear programming (NLP) problems. NLP problems without constraints (single variable, multiple variables). Gradient methods. NLP problems with constraints. The Karush-Kuhn-Tucker conditions. The modified simplex method for quadratic programming.

Head Lecturer(s)

Carlos Alberto Henggeler de Carvalho Antunes

Assessment Methods

Assessment
Mini Tests: 20.0%
Exam: 80.0%

Bibliography

- Hillier, F. S., G. J. Lieberman. "Introduction to Operations Research", McGraw-Hill, 2005 (8th ed.).

- Tavares, L. V., R. C. Oliveira, I. H. Themido, F. N. Correia. “Investigação Operacional”, McGraw-Hill Portugal, 1996.

- Bronson, R., G. Naadimuthu. "Investigação Operacional", Colecção Schaum (2ª. Ed.), McGraw-Hill Portugal, 2001.

- Clímaco, J., C. H.Antunes, M. J. Alves. "Programação Linear Multiobjectivo", Imprensa da Universidade de Coimbra, 2003.

- Chang, Y.L. "WinQSB, Decision Support Software for M/OM (ver 2.0)", Wiley, 2003.

- Antunes, C. H., L. V. Tavares (Coord.). "Casos de Aplicação da Investigação Operacional", McGraw-Hill, 2000.