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 models. 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. Introduction to Operational Research (OR). Components of an OR study. Mathematical modeling.
1. Linear Programming (LP). Prob. formulation and development of LP mathematical models. Graphical resolution of LP models. The simplex method. Duality theory. Sensitivity analysis. The goal programming model.
2. Special LP problems. The transportation problem. Alg. to solve the transportation problem. The assignment problem. The Hungarian algorithm. The transshipment problem.
3. Network optimization problems. The shortest path prob.. Algorithms: Dijkstra, Floyd, Minimum spanning tree and Prim. Shortest path with fixed costs in nodes. Maximum flow problem. Max flow-min cut theorem. The Ford-Fulkerson algorithm. The minimum cost flow prob.
4. Non-linear programming (NLP). Ex. of application of NLP. Complementarity. Unconstrained NLP prob.. Gradient search procedures. Newton method. Constrained NLP problems. Karush-Kuhn-Tucker conditions. 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, (11th ed.), 2021.

- Hillier, F., M. Hillier. Introduction to Management Science and Business Analytics: A Modeling and Case Studies Approach with Spreadsheets (7th ed.), McGraw-Hill, 2023.

- H. A. Taha, Operations Research: An Introduction (11th edition), Pearson, 2023.

- R. C. Oliveira, J. S. Ferreira. Investigação operacional em ação: casos de aplicação. Imprensa da Universidade de Coimbra, 2014

-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.

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