Design of Patient Visit Itineraries in Tandem Systems

Problem definition: Multi-stage service is common in healthcare. One widely adopted approach to manage patient visits in multi-stage service is to provide patients with visit itineraries, which specify individualized appointment time for each patient at each service stage. We study how to design such visit itineraries. Methodology/results: We develop the first optimization modeling framework to provide each patient an individualized visit itinerary in a tandem (healthcare) service system. Due to interdependence among stages, our model loses those elegant properties (e.g., L-convexity and submodularity) often utilized to solve the classic single-stage models. To address these challenges, we develop two original reformulations. One is directly amenable to off-the-shelf optimization software and the other is a concave minimization problem over a polyhedron shown to have neat structural properties, based on which we develop efficient solution algorithms. In addition to these exact solution approaches, we propose an approximation approach with provable optimality bound and numerically validated performance to serve as an easy-to-implement heuristic. A case study populated by data from a large infusion center shows that our approach makes a remarkable 27% cost reduction over practice on average.Managerial implications: Common approaches used in practice are based on simple adjustments to schedules generated by single-stage models, often assuming deterministic service times. Whereas such approaches are intuitive and take advantage of existing knowledge on single-stage models, they can lead to significant loss of operational efficiency in managing multi-stage services. A well-designed patient visit itinerary which carefully addresses the interdependence among stages can significantly improve patient experience and provider utilization.