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.

To better meet the qualitative and quantitative requirements of customers or relevant sector managers, workshop environments are implementing increasingly complex task management systems. The job shop scheduling problem (JSSP) involves assigning each task to a single machine while scheduling many tasks on different machines. Finding the best scheduling for machines is one of the challenging optimizations of difficult non-deterministic polynomial (NP) time problems. The fundamental goal of optimization is to shorten the makespan (total execution time of all tasks). This paper is interested in the joint resolution of scheduling and transport problems and more particularly the Job-shop problem with Routing (JSSPR) as opposed to the Job-shop problem with Transport (JSSPT). These two problems are modeled in the form of a disjunctive graph. For the JSSPT, the solution to the transport problem is not linked to any quality of service (QoS) criterion and the solution is therefore often semi-active. The Job-shop with Routing explicitly considers transport operations and uses algorithms from the transport community to solve the transport problem. It is shown that the routing part of the JSSPR is a problem of the vehicle routing family and of the Pickup and Delivery Problem family. QoS in the JSSPR is defined by the duration of tours, the duration of transport of parts and the waiting time for them. A new evaluation function – named Time-Lag Insertion Heuristic (TLH) – is proposed to evaluate a disjunctive graph by simultaneously minimizing the makespan and maximizing the quality of service. Thus, the solution obtained is not semi-active, but a compromise between the different criteria. This evaluation function is included in a metaheuristic. Our numerical evaluations demonstrate that, on the one hand, the TLH evaluation can find almost optimal solutions regarding the QoS criterion; and on the other hand, the TLH evaluation is not very sensitive to the order of insertion of the maximum time-lags during the different minimization steps.