Optimization Models

There are no basic knowledge prerequisites other than those required for admission to this Master course.

Students are requested to follow the classes on site. Lecturing involves the exposition of concepts, techniques and methods, with a strong focus on practical applications. Software will be used to help answering large sized problems, mostly within the Python libraries.

Objectives:

This discipline introduces mathematical modeling techniques devoted for solving complex problems within planningand management, resorting to linear programming and linear integer programming mathematical models.

The discipline is mainly devoted to solving applied problems, focusing on: investment planning, productionmanagement, financial management, project planning and shift scheduling and rostering. Given the scale of the problems involved, computational means of optimization will be adopted for the resolution of theproposed mathematical models. These means rely mainly on Python libraries, seeking na easy use of the data and theresults of the proposed problems.

Competences:

It is intended that the student can model optimization problems within the aforementioned themes, using linear andlinear integer programming. The student should also be able to handle the data from these problems and exploit theresults generated, using Python tools.

1. Linear and linear integer programming models. Economic analysis

2. Computational tools for solving linear and linear integer programming models

     2.1. Python tools

     2.2. Other linear optimization tools

3. Economic discussion of the solutions. Sensitivity analysis and parametric analysis

4. Data processing and results processing using Python tools

5. Selected decision making problems:

     5.1. Investment planning

     5.2. Production management

     5.3. Financial management

     5.4. Project planning

     5.5. Shift scheduling and rostering

NAO

Essential bibliography:

– Teaching materials produced by the teacher.

Supplementary bibliography:

– Cornuejols, G., & Tütüncü, R. (2006). Optimization methods in finance (Vol. 5). Cambridge U Press.

– F.S. Hillier & G.J. Lieberman, Introdução à Pesquisa Operativa, McGraw Hill, 2006.

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

– Jesus, F.; & Lisboa, J.V.. Introdução à Investigação Operacional, Vida Económica, 2020.

– Online manual of the PuLP library (last version released on January 12, 2024)

– Online manual of the gurobipy library (last version released on November 28, 2023)