In the face of the third wave of the coronavirus epidemic, a critical imperative emerges: to maximize the availability of hospital beds. Home Health Care (HHC) stands out as a viable alternative to conventional hospitalization, offering a means to alleviate the strain on hospital occupancy rates. In this transformative approach, care is administered by a multi-professional team comprising doctors, nurses, and oxygen therapy providers. However, a significant challenge faced by healthcare decision-makers revolves around the need to minimize costs while optimizing workforce scheduling. This research delves into the intricacies of the HHC optimization problem, specifically addressing the routing and scheduling of medical staff. The problem at hand is an extension of the multiple Traveling Salesman Problem (mTSP), requiring the identification of the shortest path for a group of employees delivering services to patients' homes. Consequently, we propose a Mixed Integer Programming (MIP) model designed to minimize overall service times by effectively distributing the workload among employees. To tackle this model, we introduce a novel genetic algorithm (GA-mTSP) incorporating a learning curves approach (LC). The core concept behind integrating LC is to balance the workload among employees based on their experiences. The effectiveness of this approach is validated using mTSP benchmark data, with a comparative analysis against results obtained from GA-mTSP without LC. The simulation results underscore the significant impact of LC on workload balancing and its efficacy in minimizing service times.