Bilevel optimization model for government mixed subsidy strategies in hierarchical healthcare

To alleviate the problem of long waiting time in general hospitals and underutilization of community hospital resources, this paper explores the effect of government mixed subsidies on patient choice and utilization of community hospital resources. Based on hospital service quality, we establish a benchmark model without government subsidy and a bilevel optimization model in which the government makes the upper-level decisions while the community hospital responds at the lower level. Although the benchmark model is a nonconvex optimization model, we are based on its special structure to propose a globally optimal algorithm. Then, we combine this globally optimal algorithm with the Gauss-Seidel method to solve the bilevel optimization model. Furthermore, we present a sensitivity analysis of some key parameters such as service quality costs, basic medical expenses in community hospitals, and government subsidy budget. Theoretical and numerical results provide the following insights: Government mixed subsidy may improve community hospital service quality and so attract more patients to choose community hospital; Government should focus on fixed fund subsidies to improve community hospital service quality, since hospital service quality is more critical than medical expenses for patient choices; Controlling service quality costs and basic medical expenses in community hospital at a low level and paying more attention to fund subsidies can promote hierarchical healthcare. Meanwhile, the government subsidy budget should be decided aligning with defined societal goals.