Robust Network Enhancement: Formulations and Approximations

We study robust network enhancement problems that improve network performance through component upgrades, where both network utilities and enhancement costs are uncertain. We consider two formulations: a lower-bound problem that improves the minimum utility across feasible network structures and an upper-bound problem that improves the maximum utility. For the lower-bound problem, we develop an exact cut-generation reformulation and identify the robust separation subproblem as a key computational bottleneck. We characterize conditions under which fractional extreme points arise in the linearized robust formulation and demonstrate that such points can be optimal. For the upper-bound problem, we derive two exact reformulations and compare the strength of their linear relaxations. To improve computational tractability, we introduce a box approximation of the utility uncertainty set that preserves solution robustness and provides explicit performance guarantees for both lower- and upper-bound problems. Computational experiments on spanning tree instances show that the proposed approximation improves computational efficiency for both problems while maintaining solution quality close to that of the exact formulations.