A REPERTOIRE OF MODEL FORMULATION TRICKS

The models we have described in the last section rely on two quite relevant limiting assumptions:

1. They are linear, whereas in real life we deal with economies or diseconomies of scale that introduce nonlinearities in the model. Yet, the efficiency of LP solvers is so remarkable that, whenever we can, we should try to squeeze our model into a linear framework. This is rather natural when we have a piecewise linear objective function, as we discuss in full generality later, in Section 12.4.7.
2. They optimize a single objective, which amounts to say that whatever criteria we use in evaluating a solution can be aggregated into one function, usually representing cost or profit. However, we might deal with conflicting criteria that cannot be expressed in common monetary terms.

Luckily, there is an array of modeling tricks that can be used to partially overcome these difficulties. In the next sections we illustrate a few of them, in order to show that the LP modeling framework is less restrictive than it might appear. We also consider a couple of approaches to deal with multiple objectives. Then, we discuss the use of elastic model formulations, as well as a general and powerful approach, modeling by columns, which may be used to model seemingly tough problems in a very simple way.