A First Route Second Assign decomposition to enforce continuity of care in home health care

Home health care (HHC) is a very popular service that plays an important role in reducing hospitalization costs and improving the quality of life for patients. Human resource planning is one of the most important processes in HHC facilities, and service providers must deal with several operational problems, e.g., the assignment of nurses to patients and the nurse routing. These two problems in HHC are intrinsically related. In the literature, they are solved simultaneously or sequentially, by exploiting First Assign Second Route (FASR) decomposition approaches in which the assignment problem is solved first and the routing problem is solved second. However, on the one hand, the simultaneous approach focuses primarily on the routing component of the problem but fails to offer continuity of care to the patients. On the other hand, FASR is more adequate to enforce the continuity of care constraint but is less effective toward the routing part. In this paper, we propose a novel decomposition approach that combines the advantages of each these approaches, which is based on the First Route Second Assign (FRSA) paradigm. To validate our FRSA approach and compare with a benchmark FASR decomposition, we also develop an instance generator that is inspired by real HHC settings with different sizes and travel time ratios. Experiments show the effectiveness of the FRSA decomposition and improvements with respect to the classical FASR, especially when travel times constitute a relevant part of the workload and the routing component of the problem is predominant; moreover, continuity of care is fully respected. Thus, FRSA can be effectively implemented by HHC providers for an efficient planning of resources and visits, especially where patients are spread in a vast territory.