Logistic system balancing of servicing home-care in urban areas and surrounding villages

Home care is supportive care provided in the home, mainly offered by licensed healthcare professionals who provide medical treatment needs or by professional caregivers who provide daily assistance to ensure the activities of daily living and hospice care. For these purposes, Europe is developing new long-term care systems, which include the ideas of deinstitutionalization, where provisions of services are changing place from institutional environment to homes of patients. After the study of time, available for servicing, spatial dispersion of facilities and homes of older people who are included in a home-care, such system of health and social services needs to undergo some balancing of activities for optimal allocation of nurses to the supply network. When technology is changing rapidly, the services can be provided in a more effective way and higher agility is required. The spatial dispersion of housing should be particularly considered in planning of the built environment and other new facilities for seniors. Namely, logistic costs per capita are increasing by increasing the dispersion, while there is decreasing density of homes in the functional regions where services are provided. Feasible scheduling and optimal routing are essential for an acceptable trade-off between logistic costs and satisfaction of clients. In our study, we optimize the home healthcare routing and scheduling to balance the necessary workforce and service time requirements at given clustering of homes in the given functional region. The model is based on the ideas of solving the nonlinear balancing problem developed in industrial engineering for line balancing, also known as assembly line nonlinear balancing problem. Mathematical method for line balancing is formalized on the basic idea of the Patterson and Albracht algorithm (1975), where nonlinear problem is linearized to be able to formalize it as a linear programming problem. Here fixed cycle time is relaxed, the operation time is an integer deterministic value. The method for evaluation of the precedence diagram is studied additionally while other balancing procedures follows the similar phases as at Petterson- Albracht algorithm. This mathematical programming tool enables us to study the outputs of various scenarios very rapidly, therefore it might help professionals to be prepared in advance for the coming changes caused by the growing number of seniors and changes of technologies.