A stochastic tri-level interdiction model for relief train location and infrastructure protection

Deploying relief trains as part of disaster response plans can be a promising strategy to enhance transport capacity and potentially improve survival chances in large-scale disasters. However, the limited availability of relief trains, combined with uncertainties in demand prediction and potential infrastructure damage, necessitates both strategic positioning of relief trains and robust protective interventions for infrastructure. Addressing these challenges, we introduce a tri-level Defender-Attacker-Defender interdiction problem. In this model, the defender determines train placement and infrastructure protection, while the attacker, representing either a hostile agent or the worst-case realization of a natural disruption, interdicts unprotected network arcs. During the response phase, trains are routed to disaster sites and operational medical facilities. Considering the inherent uncertainties in disasters, our approach incorporates scenario-dependent disruptions and evaluates multiple scenarios during the attacker-stage. To solve the problem, we propose a progressive hedging-inspired algorithm. We apply it to a test set of instances and two real-world-inspired instances for the country of Austria and France and discuss the impact of algorithmic choices.