  To solve a real-world problem, the modeler usually needs to make a trade-off
between model complexity and usefulness. This is also true for robust
optimization, where a wide range of models for uncertainty, so-called
uncertainty sets, have been proposed. However, while these sets have been
mainly studied from a theoretical perspective, there is little research
comparing different sets regarding their usefulness for a real-world problem.
  In this paper we consider a network design problem in a telecommunications
context. We need to invest into the infrastructure, such that there is
sufficient capacity for future demand which is not known with certainty. There
is a penalty for an unsatisfied realized demand, which needs to be outsourced.
We consider three approaches to model demand: using a discrete uncertainty set,
using a polyhedral uncertainty set, and using the mean of a per-commodity
fitted zero-inflated uniform distribution. While the first two models are used
as part of a robust optimization setting, the last model represents a simple
stochastic optimization setting. We compare these approaches on an efficiency
frontier real-world data taken from the online library SNDlib and observe that,
contrary to current research trends, robust optimization using the polyhedral
uncertainty set may result in less efficient solutions.
