Distributionally robust hospital capacity expansion planning under stochastic and correlated patient demand

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 root mean square error. 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.