A robust programming model for the assignmentproblem in Home Care services

Home Care includes medical, paramedical and social services which are delivered to patients at their domicile rather than in hospital. Managing human and material resources in Home Care services is a difficult task, because the provider has to synchronize the use of resources, to deal with peculiar constraints (e.g., the continuity of care) and to manage the high variability of patients’ demands. Under continuity of care, one of the main issues encountered in the planning is the nurse-to-patient assignment. Despite the importance of this topic, the problem is only marginally addressed in the literature, where it is solved adopting the stochastic programming or analytical policies. However, both these approaches proved to be limited, even if they improve the quality of the assignments with respect to those actually provided by providers in practice. In this paper, we develop a robust assignment model, which allows exploiting the potentialities of a mathematical programming model rather than an analytical approach, even without the necessity of generating scenarios. The developed model is applied to a relevant Home Care provider operating in Italy, in order to evaluate its capability of reducing the variable costs related to nurses’ overtimes, and to compare the results with both the real practice of the analyzed provider and the previously developed approaches.