Decomposition and distributed algorithms for home healthcare routing and scheduling problem

Many people in need of care still live in their homes, requiring the caretakers to travel to them. Assigning the people to caretakers and generating their schedules can be formulated as a mixed integer linear programming problem (MILP) that inherits many features of the well-known vehicle routing problem with time windows (VRPTW). Currently, the most successful exact algorithms for VRPTW are based on branch and price framework, which combine column generation (CG) and branching. While these methods could be successful for Home Healthcare Routing and Scheduling Problem (HHCRSP) as well, fast approximate algorithms are appealing, especially for large problems. We recently employed a heuristic distributed gossip algorithm to solve HHCRSP. The method had the potential to provide approximate solutions for relatively large problem instances, but its effectiveness was limited to the performance of its local MILP solver. In this paper, we integrate the gossip algorithm with a local solver based on CG, which makes it an effective algorithm for larger problem instances. We also provide numerical experiments and complexity evaluations of the improved gossip algorithm (gossip-CG) with the standard gossip (gossip-MILP) and CG, and show that gossip-CG outperforms the pure CG in case of large problems.