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 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 amendable 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, 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 the Dana-Farber Cancer Institute shows that our approach makes a remarkable 27% cost reduction over practice on average.
