We study a new variant of the vehicle routing problem, which arises in hospital-wide scheduling of physical therapists. Multiple service locations exist for patients, and resource synchronization for the location capacities is required as only a limited number of patients can be treated at one location at a time. Additionally, operations synchronization between treatments is required as precedence relations exist. We develop an innovative exact branch-price-and-cut algorithm including two approaches targeting the synchronization constraints (1) based on branching on time windows and (2) based on adding combinatorial Benders cuts. We optimally solve realistic hospital instances with up to 120 treatments and find that branching on time windows performs better than adding cutting planes. Summary of Contribution: We present an exact branch-price-and-cut (BPC) algorithm for the therapist scheduling and routing problem (ThSRP), a daily planning problem arising at almost every hospital. The difficulty of this problem stems from its inherent structure that features routing and scheduling while considering multiple possible service locations with time-dependent location capacities. We model the ThSRP as a vehicle routing problem with time windows and flexible delivery locations and synchronization constraints, which are properties relevant to other vehicle routing problem variants as well. In our computational study, we show that the proposed exact BPC algorithm is capable of solving realistic hospital instances and can, thus, be used by hospital planners to derive better schedules with less manual work. Moreover, we show that time window branching can be a valid alternative to cutting planes when addressing synchronization constraints in a BPC algorithm.

Recent research has highlighted the need for upstream planning in healthcare service delivery systems, patient scheduling, and resource allocation in the hospital inpatient setting. This study examines the value of upstream planning within hospital-wide resource allocation decisions based on machine learning (ML) and mixed-integer programming (MIP), focusing on prediction of diagnosis-related groups (DRGs) and the use of these predictions for allocating scarce hospital resources. DRGs are a payment scheme employed at patients’ discharge, where the DRG and length of stay determine the revenue that the hospital obtains. We show that early and accurate DRG classification using ML methods, incorporated into an MIP-based resource allocation model, can increase the hospital’s contribution margin, the number of admitted patients, and the utilization of resources such as operating rooms and beds. We test these methods on hospital data containing more than 16,000 inpatient records and demonstrate improved DRG classification accuracy as compared to the hospital’s current approach. The largest improvements were observed at and before admission, when information such as procedures and diagnoses is typically incomplete, but performance was improved even after a substantial portion of the patient’s length of stay, and under multiple scenarios making different assumptions about the available information. Using the improved DRG predictions within our resource allocation model improves contribution margin by 2.9% and the utilization of scarce resources such as operating rooms and beds from 66.3% to 67.3% and from 70.7% to 71.7%, respectively. This enables 9.0% more nonurgent elective patients to be admitted as compared to the baseline.