# Various (Integer) Linear Modeling Tricks

Modeling problems with an (integer) linear program sometimes requires some experience to recognize certain structures in the problem description that can be formulated in a linear way.

At the Naval Postgraduate School, Gerald Brown and Robert Dell developed a list of formulettes, and made these available Formulating Integer Linear Programs: A Rogues Gallery from pubsonline.informs.org/doi/pdf/10.1287/ited.7.2.153 . This article demystifies the art of formulating linear and integer linear programs. This is achieved by introducing formulettes, which consist of a verbal description and the constraints and variables that model this verbal description.

The first simple example of a formulette they provide is the following:

For each unit of $$X_1$$ , there must be at least 5 units of $$X_2$$

which can be modeled with

$$5X_1 \le X_2$$

The document contains a lot more of such formulettes of varying complexity.

Furthermore, in our book Optimization Modeling you can also find various modeling tricks in the chapters 6 Linear Programming Tricks and 7 Integer Programming Tricks. The Optimization Modeling book can either be found online via the link above, or you can find it under the Help menu after you started AIMMS.