Linear optimization: Mathematical formulations of complex problems (How to) 1

Theory

In contradiction to simple optimization problems, complex problems are not to solve graphically in 2D because of containing more than 2 variables. The complexity rises with incerasing number of variables and interdependance between them.

How to formulate complex problems mathematically

First of all the problem should be regarded properly and the information should be structured. This helps not to lose the overview caused of the huge amount of information.

In the next step it could be useful to transform the text-based information into a graph if it is possible. So you can easily comprehend the processes and go through the problem step by step.

After that you should define the variables. Clear assignments like input and output factors can be set directly as well as all other arrows of the graph can be equipped with variables. Some of these variables could lead to equations in the formulation and will be cleared while setting up the restrictions.

Now you can formulate the restrictions. You have to use the information in the graph in combination with further information given in the text or additional tables.