A robust optimization framework for two-echelon vehicle and UAV routing for post-disaster humanitarian logistics operations

Providing first aid and other supplies (e.g., epi-pens, medical supplies, dry food, water) during and after a disaster is always challenging. The complexity of these operations increases when the transportation, power, and communications networks fail, leaving people stranded and unable to communicate their locations and needs. The advent of emerging technologies like uncrewed autonomous vehicles can help humanitarian logistics providers reach otherwise stranded populations after transportation network failures. However, due to the failures in telecommunication infrastructure, demand for emergency aid can become uncertain. To address the challenges of delivering emergency aid to trapped populations with failing infrastructure networks, we propose a novel robust computational framework for a two-echelon vehicle routing problem that uses uncrewed autonomous vehicles (UAVs), or drones, for the deliveries. We formulate the problem as a two-stage robust optimization model to handle demand uncertainty. Then, we propose a column-and-constraint generation approach for worst-case demand scenario generation for a given set of truck and UAV routes. Moreover, we develop a decomposition scheme inspired by the column generation approach to generate UAV routes for a set of demand scenarios heuristically. Finally, we combine the decomposition scheme within the column-and-constraint generation approach to determine robust routes for both trucks (first echelon vehicles) and UAVs (second echelon vehicles), the time that affected communities are served, and the quantities of aid materials delivered. To validate our proposed algorithms, we use a simulated dataset that aims to recreate emergency aid requests in different areas of Puerto Rico after Hurricane Maria in 2017.