Exact Branch-Price-and-Cut for a Hospital Therapist Scheduling Problem with Flexible Service Locations and Time-Dependent Location Capacity
Bibliographic record
Abstract
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".