A multilevel cardinality-constrained model for the nurse-to-patient assignment problem in home care

Uncertainty is a common feature of many health care optimization problems, spreading from ambulance location to operation rooms planning. In this paper, we focus on the nurse-to-patient assignment problem under continuity of care in home care (HC), where high uncertainty is associated to the number of visits required by patients in each time period. Several techniques are adopted to manage the uncertainty of the demand in this problem and, recently, a cardinality-constrained model has been proposed. However, the standard formulation of the cardinality-constrained approach only considers two values of demand for each patient and each period of the planning horizon (i.e., expected and maximum demands). In order to overcome this limitation above, we propose a new cardinality constrained model in which different levels of demands are considered. All levels are obtained by means of probability density functions obtained from a previously developed patient stochastic model. This model is able to produce solutions that are still robust, but less conservative, and therefore cheaper for the operators.