Generalized Hose uncertainty in single-commodity robust network design

Abstract

Single-commodity network design considers an edge-weighted, undirected graph with a supply/demand value at each node. It asks for minimum weight capacities such that each node can exactly send (or receive) its supply (or demand). In the robust variant, the supply or demand values may assume any realization in a given uncertainty set. One popular set is the well-known Hose polytope, which specifies an interval for the supply/demand at each node, while ensuring that the total supply and demand are balanced across the whole network. While previous work has established the Hose uncertainty set as a tractable choice, it can yield unnecessarily expensive solutions because it admits many unlikely supply and demand scenarios. In this paper, we propose a generalization of the Hose polytope that more realistically captures existing interdependencies among nodes in real life networks, and we show how to extend the state-of-the-art cutting plane algorithm for solving the single-commodity robust network design problem in view of this new uncertainty set. Our computational studies across multiple robust network design instances illustrate that the new set can provide significant cost savings without sacrificing numerical tractability.