A New Optimization Model for Hierarchical Location and Districting Problem in Healthcare System Under Uncertainty

Health care facility systems are hierarchical as they consist of facilities at different levels such as clinics, health centers, and hospitals. Therefore, finding a proper location for the health care system can be categorized as a hierarchical location problem. Besides, partitioning a given region in a geographical area into different zones is very crucial to make sure the health services are available at their highest possible level for everyone in that region.  In this study, an optimization model for the integrated problem of hierarchical location and partitioning under uncertainty in the Iranian healthcare system is proposed. The objective function of this model maximizes the total social utility of districts while workload balance and distance limitation between the zones are considered as the main constraints. Since this study involves NP-hard problems, three metaheuristic algorithms, including Genetic, Salp Swarm Algorithm (SSA), and Grey Wolf Optimizer (GWO) were developed. The numerical results suggest that the Grey Wolf Optimizer (GWO) algorithm indicates a more appropriate level of performance in almost all responses compared to the other algorithms. Therefore, the case study was solved by the Grey Wolf Optimizer (GWO). Based on the results, 10 distrcis with their zones are identified to maximize the overall utility. A sensitivity analysis also performed to show the behavior of the model. It can be stated that the findings of this study can be utilized as a useful management tool in other organizations.