A multi-objective consistent home healthcare routing and scheduling problem in an uncertain environment

Home health care (HHC) companies serve as the alternative to hospitals aiming to provide customers with medical care at home. A crucial challenge for HHC providers is to optimize routes and schedules for their caregivers to serve customers. Inspired by the practices in the HHC industry, this paper addresses a multi objective home healthcare routing and scheduling problem (HHRSP) with several conflicting objectives: minimizing routing cost and improving service consistency and workload balance. We refer to the problem as a multi-objective consistent home healthcare routing and scheduling problem (MoConHHRSP). To be more practical, uncertain travel and service times are also considered and defined based on uncertainty theory. Next, the uncertain programming model for the proposed MoConHHRSP is formulated and then reduced to its deterministic equivalent. Due to the NP-hard essence of the problem, an improved multi-objective artificial bee colony (IMOABC) metaheuristic, integrating the large neighborhood search heuristic and an adapted non dominated solution set update strategy into the multi-objective artificial bee colony (MOABC) framework, is developed. Finally, a series of numerical experiments are conducted to illustrate the competitive performance of the designed algorithm by comparing it with other multi-objective algorithms from multiple evaluation metrics. Furthermore, the trade-off analysis reveals that a better caregiver consistency can be achieved at a high price of total costs and workload balance, while a great improvement on the workload balance can be provided with little deterioration in caregiver consistency. In many cases, low total costs and a high level of workload balance can be achieved simultaneously.