A robust stochastic approach to relief pre-positioning for earthquake response under event-wise uncertainties

The unpredictable and sudden devastation caused by earthquakes demands comprehensive disaster preparation and response operations. In this study, we propose a two-stage robust stochastic optimization model for relief pre-positioning, incorporating post-disaster relief shipment considerations under uncertain parameters that modeled in an ad hoc event-wise uncertainty set, accounting for uncertainties in earthquake occurrence and the ranges of event-associated parameters (e.g., supply, demand, shipment capacity). This approach effectively captures the epicenter-sourced nature of earthquakes, simplifying the challenge of precise parameter estimation and enabling adaptive decision-making in post-disaster operations. We further analyze the possible realizations of uncertain parameters within the event-wise uncertainty set, providing managerial insights into the impact of unused supplies on decision-makers’ attitudes toward different realizations of uncertain parameters Based on these analytical results, we develop an enumeration-based column-and-constraint generation algorithm to solve the model exactly. The model is illustrated through a case study of the Yushu earthquake. Numerical experiments show that our model outperforms benchmark methods such as stochastic programming and robust optimization. Sensitivity analysis provides additional managerial insights into the robustness of our approach under inaccurate estimations, highlighting the significant impact of handling costs for unused supplies on relief pre-positioning decisions.