©2022, Tony Hürlimann
Mathematical Modeling is an art and a skill to translate a problem into mathematical notation. This skill is on high demand and it can be learnt. This site give you a guidance by presenting many examples. Modeling can be as easy as in this exercice or more complicated as in this game With perseverance and patience you can learn the art of modeling. So let's start from the easy to the complicated! A gently introduction to mathematical modeling is presented in this paper.
LPL is a full-fetched mathematical modeling system with a point-and-click user interface and a powerful modeling language. The language is a structured mathematical and logical modeling and programming language with an extended index mechanism, which allows one to build, maintain, modify, and document large linear, non-linear, and other mathematical (optimization) models. An example in LPL syntax is given by this small model. A larger model is this LP with 2000 varibales.
| What is Modeling? | A short paper of an informal introduction to the concept of model, and a formal definition |
| How to Model? | A paper that explains the process of modeling, and a set of small instructive example problems |
| What is a Model Language? | A paper explains my ideas of a modeling language and compares it to programming languages |
| Indexing | An introduction of the use of indexing in mathematical modeling |
| Model Types | This paper collects various model classes (LP, IP, NLP) and gives examples and implemented applications |
| Pivot Table | This paper is an brief introduction into multi-dimensional datacubes, their operations and their representation as pivot tables |
| Logical Modeling | This paper is an introduction of using Boolean operations in modeling. It also gives some hints on how to translate logical expressions into linear constraints using binary variables |
| My Modeling Books | My Modeling Books containing together more than 200 modeling problems with solutions |
All the material here has mainly be compiled in order to teach mathematical modeling in Operations Research courses. Yet many examples are simple enough to treat them also in high school. Especially, the puzzles and games may be motivating examples to teach mathematical modeling. The material is also useful for self-study. However, the modeling system LPL cannot only be used in an educational environment, large models have been implemented in a commercial context (as p.e. for Rostering Planning at SwissPort at the Airport of Zurich or Power Management at ATT Finnland).
More than 400 models are formulated in the modeling language LPL and most of them can be solved directly through the Internet using free solvers such as CBC, GLPK, lp_solve and others or commercial solvers such as Gurobi, Cplex, Xpress or Knitro. Many models come with a complete description and modeling text compiled in PDF together with exercises and ready-to-learn modeling explanations. The complete PDF documentation of all the models has been generated using LPL's own automatic modeling documentation tool together with the MikTeX distribution of LaTeX.
| An Introduction | Short description of the LPL software and its functionalities |
| README | Very quick readme for installing LPL |
| Install LPL | Installation manual of LPL |
| Tutorial | A Collection of tutor examples |
| Reference Manual | The reference manual of the LPL modeling language |
| User Manual | User Manual of the Windows Interface version of the LPL modeling system |
| Download LPL | Download the complete LPL Modeling System |
| License Key | Get an Academic License for LPL valid for one month free of charge |
| Julia Notebook | A Jupyter Notebook for calling LPL from Julia through Internet. No LPL installation needed |
| Python Notebook | A Jupyter Notebook for calling LPL from Python through Internet. No LPL installation needed |
The following free textbook contains many models from various famous textbooks in operations research. All models are formulated in the modeling language LPL. To learn from these models the reader is invited to refer to the corresponding book.
The text contains all 30 models from the famous Williams book, it also contains all 65 interesting models from the French modeling book Gu�ret a.l., and a collection of many small models from various sources, all fully available.
| The Book | A Collection of many models from classical OR books (PDF). |
| William's Models | All 30 model examples are from the modeling book: "Williams H.P., Model Building in Mathematical Modelling, Wiley, 5rd edition, 2013." |
| Gueret's Models | All 65 model examples are from the modelling book: ." Guéret Ch., Prins Ch., Sevaux, M., Programmation linéaire, Eyrolles, 2000". (in French). The book has been translated to English and is available at Xpress |