Optimization and Decision Models

Knowledge on linear algebra and differential calculus are recommended.

The teaching activity takes place in face-to-face regime, with the exposition of concepts, techniques and methods, with a strong focus on practical applications. Software will be used to support the resolution of the mathematical optimization models.

Objectives:

This subject introduces some decision support techniques, using mathematical programming models. The program includes an introductory approach to decision theory and linear programming, involving mathematical modelling of some management problems. In addition to the theoretical approach to these subjects, appropriate software (Microsoft Excel and LPSolve-IDE) will be used for solving larger sized problems.

Competences:

During the course, various problems of Business Management will be raised, through which it is intended to create in the student sensitivity to the mathematical modelling of these problems, as well as critical sense regarding the different techniques of resolution and interpretation of the solutions obtained. In this context, the sensitivity analysis and parametric analysis, in the sense of its application, will be strongly discussed. The aim is to establish bridges for the use of quantitative analytical techniques to support the decision-making process, both in the probabilistic and deterministic environments.

1 – Introduction to mathematical modelling

   1.1 – Mathematical formulation of problems

   1.2 – Applications of mathematical modelling to Business Management problems

2 – Linear Programming

   2.1 – Properties of a linear model

   2.2 – Solving techniques for continuous linear programming – Simplex method and extensions

   2.3 – Dual model. Primal/Dual properties. Economic interpretation of the dual

   2.4 – Using software for solving linear programs: Microsoft Excel and lp_solve

   2.5 – Sensitivity and parametric analysis in linear programming

   2.6 – Economic interpretation of solutions and its application to the decision-making process

3 – Study of linear programming applications

   3.1 – Transportation

   3.2 – Assignment

   3.3 – Projects selection (divisible)

4 – Integer programming

   4.1 – Definitions and interpretation of integer variables. Properties

   4.2 – Some modelling techniques using binary variables

   4.3 – Using software means for solving integer linear models: Microsoft Excel and lp_solve

   4.4 – Integer programming applications

5 – Decision analysis

   5.1 – Decision-making process without and with experimentation

   5.2 – Decision trees

   5.3 – Sensitivity analysis

   5.4 – Utility theory

   5.5 – Practical applications of decision analysis

NAO

Essential Bibliography

– Teaching materials produced by the teacher.

– F.S. Hillier e G.J. Lieberman, Introdução à pesquisa operacional. McGraw Hill Brasil, 2013.

– M.C. Mourão, L. Santiago Pinto, O. Simões, J. Valente e M. Vaz Pato, Investigação Operacional: Exercícios e

Aplicações, Dashöfer Holding Ltd., Chipre, 2011.

Supplementary Bibliography

– J.J. Júdice, P.C. Martins, M.M.B. Pascoal e J.P. Santos, Programação Linear, Departamento de Matemática da Universidade de Coimbra, 2006.

– J.J. Júdice, P.C. Martins, M.M.B. Pascoal e J.P. Santos, Optimização em Redes, Departamento de Matemática da Universidade de Coimbra, 2006.

– R. Rardin, Optimization in Operations Research, Prentice Hall, 1998.

– L. Wolsey, Integer Programming, Wiley-Interscience, 1998.