A robust programming model for the assignment problem in home care services

Home Care (HC) includes medical, paramedical and social services which are delivered to patients at their domicile rather than in hospital. Managing human and material resources is a difficult task, because the HC 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 improved the quality of the assignments with respect to those actually provided by HC providers in practice. In this paper, we develop a robust assignment problem, which allows exploiting the potentialities of a programming model rather than an analytical approach, without the necessity of generating scenarios. The developed model is finally applied to a relevant HC 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 HC provider and the previously developed approaches.