Home health care faces new challenges day by day and it has become increasingly legitimate in the face of an aging population. Home healthcare centers are exposed to cumulative demands and academics are paying attention to the routing and scheduling matter, which is offered in literature as a Technician Routing and Scheduling Problem (TRSP) where the aim is to minimize the total cost subject to the time windows constraints to serve the patients respecting their priorities. In this paper, we develop a new distributed algorithm to resolve the home health care routing and scheduling problem (HHRSP). The principal idea of this algorithm is to apply artificial intelligence techniques in a distributed optimization method. The integration of automatic learning and search methods are applied to optimize the assignment of appointments to home caregivers. It allows us to gain time, effort, especially cost, and while complying with the problem constraints. The comparison results prove the efficacy of the recommended approach, which can offer decision support for medical executives of home health care.

The Health Care system is changing from the hospitalization to the home care, and the World Health Organization has announced that the rate of care-dependent elderly people in Europe will considerably increase within the next decades. Thus, scientific planning for this area is an essential factor to improve the community health. This paper aims to develop a mathematical modeling for Home Health Care Routing and Scheduling Problem and to solve it by means of Simulated Annealing (SA) algorithm considering real condition (staff vehicle traveling, conditions of patients and so forth). We permit interdependent services for patients in which they can order as many services as they want with any relation between them (Multiple Services) and supposed time window for each service. The mathematical formulation of the problem is coded in GMAS software, which is a well-known commercial software for solving optimization problems. In addition, for large-scale problems where GAMS is unable to solve, SA algorithm is applied to tackle the problems. Finally, sensitivity analysis on the most important parameters (number of services and number of patients with interdependent Multiple services) are conducted. The results reveal that when each patient can order infinite services with any relation between them, complexity of the problem increases, but SA algorithm can solve large instances with reasonable solution in the less computational time. Thus, SA algorithm shows a rational performance for large instances. Moreover, the most important factors that affect the objective value and the run time of the problems are number of patients, and number of patients with interdependent multiple services.