A Comparison of Discrete and Polyhedral Uncertainty Sets for Robust Network Design

We consider a network design and expansion problem, where we need to make a capacity investment now, such that uncertain future demand can be satisfied as closely as possible. To use a robust optimization approach, we need to construct an uncertainty set that contains all scenarios that we believe to be possible. In this paper we discuss how to construct two common types of uncertainty sets, which are discrete and polyhedral uncertainty, using real-world data. We employ clustering to generate a discrete uncertainty set, and place hyperplanes sequentially to generate a polyhedral uncertainty set. We then compare the performance of the resulting robust solutions for these two types of models on real-world data. Our results indicate that polyhedral models, while being popular in the recent network design literature, are less effective than discrete models both in terms of computational burden and solution quality with respect to the performance measure considered.