In this study, we propose a new multi-objective mathematical model for designing compact, balanced, and contiguous districts in healthcare systems. The objective functions minimize districting heterogeneity and the implementation cost of monitoring plans for promoting hygiene and public health. Expert teams perform these plans periodically by maximizing the coverage area. The purpose of the districting problem is to specify how teams are formed and allocated based on their service provision capacity and type of expertise. Improper team allocation and unsuitable service provision cause an increase in time and costs, fostering an adverse effect on the promotion of public health in the area. Compliance of the plan with the specified requirements and its implementation cost are the main factors impacting the districting problem decisions. We define two meta-heuristic algorithms including a multi-objective genetic algorithm II (NSGAII) and a multi-objective grey wolf optimizer (MOGWO) for solving the mathematical model in a real-scale because districting problems are NP-hard problems. We also present a case study taking place at a university medical centre in Iran to demonstrate the applicability and efficacy of the proposed model.
