  This paper investigates the optimal locations and capacities of hospital
expansion facilities under uncertain future patient demands, considering both
spatial and temporal correlations. We propose a novel two-stage
distributionally robust optimization (DRO) model that integrates a
Spatio-Temporal Neural Network (STNN). Specifically, we develop an STNN model
that predicts future hospital occupancy levels considering spatial and temporal
patterns in time-series datasets over a network of hospitals. The predictions
of the STNN model are then used in the construction of the ambiguity set of the
DRO model. To address computational challenges associated with two-stage DRO,
we employ the linear-decision-rules technique to derive a tractable
mixed-integer linear programming approximation. Extensive computational
experiments conducted on real-world data demonstrate the superiority of the
STNN model in minimizing forecast errors. Compared to neural network models
built for each individual hospital, the proposed STNN model achieves a 53%
improvement in average RMSE. Furthermore, the results demonstrate the value of
incorporating spatiotemporal dependencies of demand uncertainty in the DRO
model, as evidenced by out-of-sample analysis conducted with both ground truth
data and under perfect information scenarios.
