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How to start learning mathematical modeling ?

A word to begin

Mathematical modeling for real problems is not easy. You need certain competences that can be learnt, but first of all you need power of endurance and perseverance.
More then any other intellectual occupation, modeling is a highly creative activity, and nothing is more rewarding than having found a good model for a real problem.
This site of MatMod offers a lot of mostly free material to learn modeling. Dive into it and enjoy!

Start with this

Regardless of whether you have some knowledge in the subject, it is recommended to begin with the two introductional papers:
What is modeling? and How to model?. You should at least retain the definition of what a mathematical model is, respectively, and how I define this subject. In the second paper try to solve (by any method) some problems before you look up the solution.

Next Step I

It is relatively easy to create models with a few variables and constraints. The difficulties begin when you must build large models with a lot of data. This is mostly the case in practical applications. You need concepts to break the many elements of your model down into categories and groups. In mathemaics, we use a brilliant concept for that, it is indexing. Learning well this concepts is of abolute importance to be able to create relevant models. I wrote an introductory paper on indexing:
Index Notation that includes also some exercises.
There are many different model types used in practice. A selection of them is described in the paper Model Types an it contains executable models for illustartion.

Next Step II

Now you are ready for some real exercises. My modeling book Puzzles and Games contains 120 problems. They range from easy once like math01 to more complicated like Social Golfers. The modeling of every problem is explained step by step in the textbook and can be executed directly through the Internet, no need to install any software. Alternatively, you can download Williams' Models or others, free of charge.
The short introductory text to the LPL Language or the Reference Manual may help to understand the syntax of LPL. Simultaneously, you may also look through some Tutorial Examples.

Next Step III

You did actively something on every step above? You begin to be a pro! I have collected many classical models of the operations research (shortest path, traveling salesman (TSP), covering location, cutting, production planning, scheduling, etc.) in my two Case Studies books. Many problems in this realm are difficult to solve, hence, for some models several modeling approaches are exposed.

Next Step IV

You do not want to model with LPL? That's fine! You have the basics now. Very popular today are (free) Python or Julia packages, or commercial software like AMPL, GAMS, Matlab, AIMMS, Mosel, LocalSolver and many others. The paper Modeling Tools gives you a first list and a short flavor of a number of tools and software.


Do you have questions? Please email to: info@matmod.ch

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