For the purpose of determining the optimum order quantity or the economic quantity of the order. There are many, many models used, on what basis we can choose the appropriate inventory model
The basic determinant of choosing the inventory model is the nature of the demande: known and fixed, specific and variable, random stable, random unstable
the model depends on many factors, the type of demand , the policy variables, the the costs may be constant or variable ( as a function) and constraints if it exist.
In general, you may get the model from the real life , so you have to transform it to mathematical model. on the other hand, you can make some assumptions and then have your model that may be restricted or not.