A two-stage adaptive robust optimization model for the location-routing problem with drone delivery and uncertainty in humanitarian relief

The facility location problem and routing problem, two critical components of humanitarian operations management, are integrated into the location-routing problem. Given that disasters are characterized by an exceptionally high degree of uncertainty, this study focuses on addressing supply-side uncertainties, such as the disruption probability of relief facilities, and receiver-side uncertainties, including demand fluctuations in affected areas and deadlines for receiving relief supplies. To develop a reliable location scheme that mitigates potential disruptions, a two-stage adaptive robust optimization formulation is constructed. It requires determining location, allocation, and routing plans across a set of disaster scenarios. A hybrid exact algorithm incorporating column-and-constraint generation, integer Benders decomposition, and branch-and-price algorithms is developed, along with advanced acceleration strategies to improve the solution process. Comprehensive numerical studies using randomly generated datasets evaluate the algorithm’s performance, demonstrating its superiority over both the CPLEX solver and an algorithm without column-and-constraint generation. Additionally, the study examines the influence of key model parameters on the solution structure and performance metrics. Furthermore, a real-world case study in Ya’an City, Sichuan Province, validates the model’s applicability, showing that it outperforms conventional deterministic and stochastic optimization models.