Bi-Objective Stochastic–Fuzzy Humanitarian Logistics Network Design under Disruptions with Equity Considerations: A Benders Decomposition Approach

Efficient relief logistics management following earthquakes is crucial for reducing human suffering and economic losses, particularly in megacities such as Tehran that are exposed to high seismic risk. This study develops a bi-objective stochastic–fuzzy humanitarian logistics network design model to support post-earthquake relief operations by simultaneously minimizing response time and total operational costs while incorporating equity considerations in aid distribution. The model explicitly captures uncertainty in both primary and secondary demand as well as potential disruptions affecting facilities, vehicles, and transportation routes. To address uncertainty, a hybrid stochastic–possibilistic framework combined with scenario-based modeling is employed, while a Benders decomposition algorithm is developed to efficiently solve large-scale instances. The proposed model is applied to a real-world case study of Tehran using geographic and demographic data. Computational results demonstrate that the model can significantly improve relief network performance by balancing response time and operational costs under disruption scenarios while maintaining equitable distribution of relief supplies among affected areas. In addition, the Benders decomposition approach substantially reduces computational time compared with direct optimization, making the framework suitable for large-scale disaster planning problems. The proposed framework provides practical decision support for policymakers and disaster management authorities to design resilient and efficient humanitarian logistics networks.