Comparing two different objective functions in a cardinality-constrained model for the assignments in home care

Human resource planning in Home Care (HC) services is a difficult task, as the provider has to deal with peculiar constraints (e.g., the continuity of care) and to manage the high variability of patients' demands. Indeed, under continuity of care, one of the main issues encountered in planning HC services is the nurse-to-patient assignment. In the literature, several techniques are adopted to manage the uncertainty of the demand in such assignment problem and, recently, the problem has been solved adopting a cardinality-constrained robust model. The objective function of that robust model was the minimization of the nurses' overtime costs, which arise in case nurses work for a time larger than the contractual value. In this paper, we model a new objective function for the above mentioned problem, i.e., the fairness of the nurses' utilizations, and we compare the two objective functions.