Resilient emergency facilities location–allocation under cascading uncertainty: A two-stage robust optimization model

The growing complexity of disasters originating from natural phenomena, compounded by cascading uncertainty, necessitates resilient emergency facilities location planning to enhance response capabilities. To address this challenge, this study proposes a novel “reinforcement-cascading uncertainty-recovery” framework to enhance system resilience. This framework specifically addresses the cascading effect propagation mechanism (CEPM) from supply-side facility disruptions to demand-side nodes, by integrating pre-disaster reinforcement with post-disaster coordinated response. Based on this framework, we develop a two-stage robust optimization model to jointly optimize facility location, structural reinforcement, and resource allocation decisions. A distinctive feature of our model is the decision-dependent uncertainty set, which captures the endogenous effect of reinforcement strategy on facility disruptions, and the cascading effect of facility disruptions on demand fluctuations. To solve the proposed model, we develop a hybrid methodology by combining a neutralization-based uncertainty transformation method with the column and constraint generation (C&CG) algorithm to reformulate and solve the model. Through the earthquake case in Istanbul, we quantify the effect of reinforcement strategy on network resilience, conduct sensitivity analyses on key parameters, and derive critical managerial insights. Our results indicate that, in comparison to the baseline model without reinforcement strategy, the proposed model reduces the number of facilities that need to be opened by approximately 50% while maintaining the desired service level. These findings provide decision-makers with a practical and efficient strategy for enhancing disaster response capabilities under cascading uncertainty.