Distributional robustness based on Wasserstein-metric approach for humanitarian logistics problem under road disruptions

Humanitarian logistics plays a vital role in disaster management. However, it often faces the challenge of unpredictable road conditions when solving relief prepositioning problems to effectively respond to natural disasters. This study examines the location–allocation problem in humanitarian logistics for disaster relief supplies. The research focuses on determining the optimal number and locations of supply distribution points and developing an efficient allocation scheme for relief items. Herein, we propose a two-stage programming model utilizing the distributionally robust optimization (DRO) approach for the location–allocation problem when considering uncertain road conditions. The DRO approach optimizes the expectation value of worst-case across all distributions within a specified ambiguity set. Relief facility locations, inventory levels, and relief supply distribution plans are all determined simultaneously. By utilizing the Wasserstein metric, an ambiguity set is created to characterize the link-wise uncertainties. This metric can capture uncertainties based on finite sample information, ensuring with high probability that the true distribution is contained within the constructed set. To address the problem, We develop an algorithm based on Benders decomposition. To validate the efficacy of the model and methodology, we conduct a real-life case study on the threats posed by hurricanes occurring in the Gulf of Mexico region. We evaluate the performance of our proposed model by comparing it to the scenario-based stochastic programming model and the traditional robust model. Furthermore, we offer managerial insights based on the application of distributionally robust optimization methodology in humanitarian logistics.