Computational risk management techniques for fixed charge network flow problems with uncertain arc failures

We consider a formulation for the fixed charge network flow (FCNF) problem subject to multiple uncertain arc failures, which aims to provide a robust optimal flow assignment in the sense of restricting potential losses using Conditional Value-at-Risk (CVaR). We show that a heuristic algorithm referred to as Adaptive Dynamic Cost Updating Procedure (ADCUP) previously developed for the deterministic FCNF problem can be extended to the considered problem under uncertainty and produce high-quality heuristic solutions for large problem instances. The reported computational experiments demonstrate that the described procedure can successfully tackle both the uncertainty considerations and the large size of the networks. High-quality heuristic solutions for problem instances with up to approximately 200,000 arcs have been identified in a reasonable time.