Developing a mathematical model for staff routing and scheduling in home health care industries: Genetic Algorithm based solution scheme

Efficient management of providing home health care services requires many considerations. In this paper, a mathematical model for the daily staff routing and service scheduling is developed for home health care companies. In this model, both economic factors and qualitative service-oriented performance measures are simultaneously optimized. To make the model more realistic, many real situations such as considering different qualifications and diverse vehicles for staff members, different requirements and predetermined preferences for patients, possible temporal interdependencies between services, and continuity of care (CoC) are taken into account. We also added some important constraints related to blood sampling requirements, which make our proposed model more complex. The proposed model is a mixed integer linear programming model (MILP) that belongs to an NP-hard class of optimization problems. To solve such a complex mathematical model, a genetic algorithm (GA) is proposed to find near-optimal solutions. We use some randomly generated test instances with different sizes to evaluate the performance of the GA. Finally, it is demonstrated how the proposed solution scheme can end up with proper scheduling and routing policies compared to those obtained through exact methods.