The home health care routing and scheduling problem (HHCRSP) is an extension of the vehicle routing problem with time windows (VRPTW). It consists of providing services operations at patients’ homes in case of aging or disabling disease. In this paper, we address the HHCRSP with multiple availability periods of patients, which are considered as soft/flexible time windows. A mathematical model is proposed to define a daily planning by minimizing the total penalized earliness and tardiness of service operations, and caregivers’ total waiting time. Taking into account requested services of patients, qualifications and time windows of caregivers, patients’ preferences expressed as multiple availability periods. The model is implemented and tested using CPLEX IBM. To deal with large instances a general variable neighborhood search (GVNS) based heuristic is proposed, implemented and tested using the language C++. Computational results show that the proposed heuristic could find a good solution in a very short computational time.