GRASP for the Vehicle Routing Problem with Time Windows, synchronization and precedence constraints

This article addresses a new routing problem encountered in the field of Home Health Care. Researches in this emerging area share the goal of establishing fine coordination to optimize the planning of human and material resources to provide support and quality monitoring while controlling costs. Home Health Care services allow keeping patients who are not entirely dependent at home, or to facilitate the return to normal life for people who have suffered serious illnesses by permitting them to leave traditional health institutions. They often need specific cares provided by caregivers. Usually, these services must be performed at specific times, and require the intervention of several caregivers, sometimes linked by precedence constraints. By associating the patients to customers and caregivers to vehicles, the problem introduced in this study can be seen as a particular vehicle routing problem with time windows and side timing constraints, where some patients require more than one visit simultaneously or in a given priority order. To solve this problem, a mixed integer programming model is presented and a meta-heuristic method based on a Greedy Randomized Adaptive Procedure (GRASP) is proposed. Numerical results are shown on a new benchmark derived from the literature.