Spatial-Data-Driven Facility Location Planning

The placement of facilities in service regions with continuously distributed demand poses a difficult problem, often requiring discretization methods that can potentially introduce approximation errors. This study presents a robust approach to address this challenge of continuous spatial distribution by considering the problem of facility placement under the spatial uncertainty associated with future demand locations, without resorting to discretization and its associated errors. We propose a spatial-data-driven optimization approach to deal with the key challenges, namely the continuous region of potential demands, sparse historical demands, and nonstationarity of the spatial distribution of demands. To this end, we model the spatial uncertainty using a Wasserstein distance based spatial ambiguity set, wherein we leverage popular clustering algorithms to form subregions to explicitly capture the spatial structure of demand occurrences. This proposed spatial ambiguity set does not require the discretization and demand aggregation approach commonly employed in the literature, while still maintaining the optimization tractability. Following a distributionally robust optimization framework with the proposed spatial ambiguity set, the problem is reformulated as a mixed integer semi-infinite optimization problem, which is then solved by our row-and-column generation algorithm. To study the practical performance, we conduct a numerical study in the emergency response context with the real data of fatal road traffic accidents in the city of Leeds, UK. Numerical results suggest that our proposed approach outperforms the benchmarks and attains facility locations that can potentially provide shorter response times to future demand occurrences. In particular, our proposed approach attains an out-of-sample performance improvement of 7–9% over the sample average approximation approach and an improvement of 5–8% over the discretization and demand aggregation approach under higher future spatial uncertainty.