A cost assignment policy for home care patients

The patient assignment problem in Home care (HC) consists of allocating each newly admitted patient to his/her reference operator, chosen among a set of possible operators. The continuity of care, where pursued, imposes that the assignment is not changed for a long period. The main goal of the assignment is to balance the workload among the operators. In the literature, the problem is usually solved with numerical approaches based on mathematical programming that do not consider the stochastic aspects of the problem. We derive a structural policy to assign a newly admitted patient while balancing the workload among the operators, by minimizing the expected value of a cost function that penalizes the overtime of operators. The workloads already loaded to the operators are assumed to be random variables as they are in the practice, while the demand related to the new patient is considered both deterministic and stochastic. Results show that the variability of the new patient's demand is negligible with respect to the variability of the already assigned workloads and that similar assignments are obtained both in the presence or in the absence of this demand variability. A numerical comparison with the current practice of assigning the new patient to the operator with the highest expected available capacity shows that better balancings and cost savings can be reached by implementing the proposed policy.