Pattern-based decompositions for human resource planning in home health care services

Home health care services play a crucial role in reducing the hospitalization costs due to the increase of chronic diseases of elderly people. At the same time, they allow us to improve the quality of life for those patients that receive treatments at their home. Optimization tools are therefore necessary to plan service delivery at patients' homes. Recently, solution methods that jointly address the assignment of the patient to the caregiver (assignment), the definition of the days (pattern) in which caregivers visit the assigned patients (scheduling), and the sequence of visits for each caregiver (routing) have been proposed in the scientific literature. However, the joint consideration of these three levels of decisions may be not affordable for large providers, due to the required computational time. In order to combine the strength and the flexibility guaranteed by a joint assignment, scheduling and routing solution approach with the computational efficiency required for large providers, in this study we propose a new family of two-phase methods that decompose the joint approach by incrementally incorporating some decisions into the first phase. The concept of pattern is crucial to perform such a decomposition in a clever way. Several scenarios are analyzed by changing the way in which resource skills are managed and the optimization criteria adopted to guide the provider decisions. The proposed methods are tested on realistic instances. The numerical experiments help us to identify the combinations of decomposition techniques, skill management policies and optimization criteria that best fit with problem instances of different size.