Continuity-skill-restricted scheduling and routing problem: Formulation, optimization and implications

As the aging population grows, the demand for long-term continuously Attended Home Healthcare (AHH) services has increased significantly in recent years. AHH services are beneficial since they not only alleviate the pressure on hospital resources, but also provide more convenient care for patients. However, how to reasonably assign patients to doctors and arrange their visiting sequences is still a challenging task due to various complex factors such as heterogeneous doctors, skill-matching requirements, continuity of care, and uncertain travel and service times. Motivated by a practical problem faced by an AHH service provider, we investigate a deterministic continuity-skill-restricted scheduling and routing problem (CSRP) and its stochastic variant (SCSRP) to address these operational challenges. The problem is formulated as a heterogeneous site-dependent and consistent vehicle routing problem with time windows. However, there is not a compact model and a practically implementable exact algorithm in the literature to solve such a complicated problem. To fill this gap, we propose a branch-price-and-cut algorithm to solve the CSRP and a discrete-approximation-method adaption for the SCSRP. Extensive numerical experiments and a real case study verify the effectiveness and efficiency of the proposed algorithms and provide managerial insights for AHH service providers to achieve better performance.