Optimal and Compromise Policies for Home Care: Scheduling Strategies of Local Government and Home Care Agency

Abstract

We introduce a mixed integer programming model for home care schedules allocating home care workers to users’ service time. The purpose of this scheduling is to reflect objectives of both a local government and a home care agency. The interest of the local government is to minimize the waiting times for home care users to avoid lowering their satisfaction levels. Meanwhile, the home care agency prefers home care workers to be able to visit as many care users’ homes as possible each day. A formula is drawn out with the two interests in the objective function. In the numerical analysis, we use parameter values based on interviews conducted by the local government. Numerical results provide that the time window for home care service specified by home care users is the most important factor determining the home care schedule when the number of care workers available for the number of care users is sufficient. Conversely, when the number of workers is insufficient, it is the most crucial to consider the total transit time between the office of the home care agency and care users’ homes. Furthermore, since it is the best strategy for the local government and the home care agency to select different schedules, it is important for them to reach a point of mutual compromise. For the society, we provide the important points to create a home care schedule with the two interests of the local government and home care agency.