Spatial-Data-Driven Drone Placement for Emergency Response

Abstract

With recent technological advancements, there is a growing interest in deploying unmanned aerial vehicles (UAVs), commonly known as drones, in providing assistance, delivering supplies, and rescue operations during emergency situations. To ensure a quick response to a future emergency, it is crucial to strategically deploy the drones. In this work, we consider the drone placement problem as a facility location problem under the spatial uncertainty associated with future emergency locations. We propose a spatial-data-driven model to deal with the key challenges, namely the continuous region of potential emergencies, sparse historical incidents, and non-stationarity of spatial distribution. Specifically, our solution approach involves three steps - First, leveraging the historical data or forecasts about emergency locations, we partition the studied region into several disjoint convex subregions; From a reference spatial distribution obtained from data or forecasts, we then construct a spatial ambiguity set about the future spatial distribution such that it lies within a certain Wasserstein distance of the reference distribution; Finally, under L1 Wasserstein distance, we derive a robust optimization formulation for drone placement as a mixed-integer second-order cone program based on the vertices of those subregions. In our approach, the clustered pattern of spatial distribution can be easily incorporated and, more importantly, the challenges in dealing with a continuous region in facility optimization can be well circumvented via spatial ambiguity set modeling by adopting the robust optimization framework. In a case study on Arizona wildfire fighting, our numerical results suggest that our model produces robust drone base station locations that hedge against the spatial uncertainty, and outperformed the sample average approximation approach in terms of quick response and fair accessibility.