A Hybrid Approach to Solve the Periodic Home Health Care Problem

Abstract

Home health care (HHC) services provide nursing assistance to the elderly with the advantage of allowing them to continue living at their homes. Usually a HHC service has a fleet of vehicles that are used by nurses to get to the patients, where they have to perform a specified job.

The HHC problem consists of the following task: assign a nurse to each job such that several conflicting objective functions are minimized, while a number of constraints are met. From a mathematical point of view, this problem is hard to solve, since it combines two well-known NP-hard problems: the vehicle routing problem and the nurse rostering problem. Our main objective is to minimize the number of nurses that visit a patient during the schedule: the nurse-patient loyalty. We consider this loyalty as a main indicator for a good schedule. Additionally, we have a periodic model, i.e. we do not only want to assign the nurses for one day, but we usually want to plan for a whole scheduling horizon, typically a week. As a solution approach, we propose a hybrid approach that combines the strengths of constraint programming and the large neighborhood search metaheuristic.