Cluster-based healthcare network design problem with referral system using a hybrid genetic algorithm

Addressing the unbalanced distribution of demands and medical resources is a particularly important issue in many healthcare systems. To achieve the equitable and efficient utilization of medical resources across regions, various medical alliances with tiered hospitals have been proposed and promoted to implement patient referrals. However, no formal analysis has been conducted on the implementation and management of medical alliances, especially over large geographical areas. This paper proposes the cluster-based healthcare network design problem with a referral system that provides a framework for integrating healthcare districting and patient referral problems within a hierarchical healthcare network design. It partitions the healthcare network into several clusters based on administrative features and designs diverse referral strategies for heterogeneous patients. To address the proposed problem, a mixed-integer linear programming model is formulated, and a hybrid genetic algorithm framework is developed to solve it efficiently. This algorithm considers the cluster-based nature of the healthcare networks and incorporates local search strategies to guarantee convergence performance. To demonstrate the efficiency of the proposed method, a case study is conducted involving 93 hospitals in Hebei, China. The results reveal that the proposed model can be extensively used to help decision-makers make informed decisions about constructing effective healthcare networks containing multiple medical alliances to reduce costs and improve efficiency. Furthermore, it suggests that a healthcare system equipped with a multi-hub configuration, diverse referral strategies, and a more relaxed capacity setting exhibits excellent performance in terms of costs and resilience. Finally, our study demonstrates that the proposed algorithm performs well in terms of efficiency and robustness.