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In recent years, home care (HC) service systems have been developed as alternatives to conventional hospitalization. Many resources are involved in delivering HC service, including different categories of human resources, support staff, and material resources. One of the main issues encountered while planning human HC resources is the patient assignment problem, i.e., deciding which operator(s) will take care of which admitted patient given some sets of constraints (e.g., the continuity of care). This paper addresses the resource assignment problem for HC systems. A set of mathematical programming models to balance the workloads of the operators within specific categories are proposed. The models consider several peculiarities of HC services, such as the continuity of care constraint, operators' skills, and the geographical areas which patients and operators belong to. Given the high variability of patient demands, models are developed under the assumption that patients' demands are either deterministic or stochastic. The analysis of the results obtained from a real case study demonstrates the applicability of the proposed models as well as the benefits that stem from applying them. Moreover, the obtained results show that an acceptable level of continuity of care cannot be obtained without modeling the continuity of care as a hard constraint. The analysis under continuity of care also shows the high value of information and the difficulties of fully balancing workloads with the application of standard techniques.