Integrating evacuation and relief redistribution into last-mile relief network design: A two-stage distributionally robust optimization approach

Abstract

Last-mile relief networks (LMRNs) play a critical role in disaster response, as they directly connect relief supplies to affected populations and determine the timeliness and effectiveness of emergency operations. Consequently, an efficient and reliable LMRN is essential for post-disaster management, ensuring that evacuation and relief distribution processes are seamlessly integrated and effectively executed. However, current approaches often neglect the varying severity of disasters, which is essential for tailoring evacuation networks, shelter planning, and relief distribution to real-world post-disaster needs. This paper investigates the design of a last-mile relief network that jointly integrates emergency evacuation and relief redistribution in post-disaster scenarios. The objective is to provide effective evacuation plans for severely affected areas while ensuring equitable relief allocation, even in cases where distribution centers are damaged. To capture the dual uncertainties of disaster environments and varying severity levels, we propose a two-stage distributionally robust optimization (DRO) model, where distinct ambiguity sets describe uncertain parameters. In the first stage, we determine the locations of candidate distribution centers (CDCs), local distribution centers (LDCs), and shelters. In the second stage, we optimize the evacuation plan and the allocation of relief supplies in response to the realized post-disaster conditions. To address the computational complexity of the two-stage DRO, we derive a tractable robust counterpart based on partial probability information and design a tailored solution algorithm to efficiently obtain optimal strategies. The proposed approach is validated using a real-world case study of the Nepal earthquake, demonstrating improvements in evacuation efficiency and relief distribution reliability, while sensitivity analyses further yield practical insights for disaster response planning.