The patient assignment problem in home health care: using a data-driven method to estimate the travel times of care givers

Home health care is one of the recent service systems where human resource planning has a great importance. The assignment of patients to care givers is a relevant issue that the home health care service provider must address before generating the daily routes. The assignment decision is typically made without knowing the visiting sequence, which creates some uncertainties and disparities regarding the effective workload of care givers. However, taking into account travel times in the care giver workload while solving the assignment problem is not straightforward, because travel times can also be affected by clinical conditions of patients and their homes. Providing good travel time estimates that would be used in the assignment decision is the specific topic this paper focuses on. In particular, we propose a data-driven method to estimate the travel times of care givers in the assignment problem when their routes are not available yet. The method, based on the Kernel regression technique, uses the travel times observed from previous periods to estimate the time necessary for visiting a set of patients located in specific geographical locations. The main advantage offered by this technique is the empirical modelling of the travel routes generated by care givers. Numerical results based on realistic problem instances indicate that the proposed estimation method performs better than the average value and k-nearest neighbor search methods and can be successfully used in a two-stage approach that first assigns patients to care givers and then defines their routes.