Modeling and
Optimization of
Linear
Systems
This site is a collection of lessons, examples, notes, etc. I use for teaching introductory courses about practical linear optimization.
The page is under continuous development, if You find any mistakes, or have suggestions, please let me know. -- Máté Hegyháti
Modeling and Optimization in Practice
14 week, 3 hour course at the Szechenyi Istvan University for 3rd year bachelors in IT
Motivational example: festivals
A discrete decision problem for motivation, and to discuss basic concepts and principles
Motivational example: fröccs
A continuous decision problem for motivation, and to discuss basic concepts and principles
Linear Programming: first steps
Constructing the first (MI)LP models for the motivational examples.
GMPL/glpk basics
An overview of tools and languages for (MI)LP problems, and a bit of introduction to GLPK and GMPL
Introduction to using sets and parameters in GMPL in order to separate data from the logic
Advanced GMPL models of the motivational examples
Default values, display statements, derived parameters, etc.
Introducing "redundant" variables to make models more transparent
Practice example: Car dealership
A practice example for GMPL skills with increasing difficulty.
General frame algorithm for solving discrete problems.
Next planned pages:
- Under the hood: the simplex method
- Advanced modelling: Nonlinear function approximation with piecewise linear functions
- GLPK API
- COIN/OR, Gurobi, CPLEX
- Special problem classes: Assignment problem
- Applications: Batch process scheduling