Planning For Edge Failure in Fixed-Charge Flow Networks

The Fixed-Charge Network Flow problem is a well-studied NP-hard problem that has the goal of finding a flow in a network where fixed edge costs are incurred, regardless of the amount of flow hosted by the edge. In this paper, we consider scenarios where a designated edge in the network has the potential to fail after edges have already been purchased. If the edge does fail, procurement of additional edges may be required to repair the flow and compensate for the failed edge so as to maintain the original flow amount. We formulate a multi-objective optimization problem that aims to minimize the costs of both the initial flow as well as the repaired flow. We introduce an algorithm that finds the Pareto front between these two objectives, thereby providing decision makers with a sequence of solutions that trade off initial flow cost with repaired flow cost. We demonstrate the algorithm's efficacy with an evaluation using real-world CO2 capture and storage infrastructure data.