A stochastic programming approach for dynamic allocation of bed capacity and assignment of patients to collaborating hospitals during pandemic outbreaks

We consider a region containing several hospitals collaborating to treat patients during an infectious outbreak. Collaboration occurs through the dynamic allocation of hospital bed capacity to infectious patients and by assigning infectious patients to specific hospitals. Scaling up capacity for infectious patients means that beds are removed from regular care, which can only be done simultaneously for all beds in a room. Moreover, as opening rooms for infectious patients takes some lead time, we have to decide on preparing to open rooms for infectious patients ahead of time. We apply a stochastic direct lookahead approach. Each day, we make decisions on room allocation and patient assignment based on the solutions of two stochastic programs with scenarios using short-time forecasts of the number of infectious hospitalizations in the region and the bed occupancy in each collaborating hospital. We aim to balance costs for bed shortages and unutilized beds for infectious patients and opening and closing rooms. We demonstrate that a stochastic lookahead is superior to a deterministic one. We furthermore compare our solution approach with two heuristic strategies in a simulation study based on historical COVID-19 data of a region with three hospitals in the Netherlands. In one strategy, hospitals decide on their capacity allocation individually. In another strategy, we assume a pandemic unit, where one hospital is designated to take all regional infectious patients until full. The numerical results show that our stochastic direct lookahead approach considerably outperforms these heuristics.