A Comparison of Data-Driven 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 actually construct two common models of uncertainty set, discrete and polyhedral uncertainty, using data-driven techniques on real-world data. We employ clustering to generate a discrete uncertainty set, and supervised learning 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 literature, are less effective than discrete models both in terms of computational burden and solution quality regardless of the performance measure considered (worst-case, conditional value-at-risk, average).