This study proposes a model for the balanced assignment of patients to healthcare centers in a region. In the suggested model, it is supposed that patients want to go to the nearest center, which causes an imbalance in the workloads of resources between centers. This disproportion is undesirable not only for the centers but also for the patients. Thus, balancing assignments is targeted. This goal is expressed in a model with a multi-objective function. Since balancing is one of the main goals of the sectorization concept, we characterize the model based on it. Unlike studies in the literature, we do sectorization employing dispatching rules. This diminishes the problem's complexity and makes it suitable for solving actual, large, and dynamic problems. We simulated the system using the Rockwell Arena software. We consider the effect of different seasons, days, and hours on the system. The dispatching rule used for sectorization is optimized using the OptQuest software. The numerical results demonstrate that by optimizing the dispatching rule, it is possible to enhance the objective function significantly.