Logic-Based Benders Decomposition and Binary Decision Diagram Based Approaches for Stochastic Distributed Operating Room Scheduling
Bibliographic record
Abstract
The distributed operating room (OR) scheduling problem aims to find an assignment of surgeries to ORs across collaborating hospitals that share their waiting lists and ORs. We propose a stochastic extension of this problem where surgery durations are considered to be uncertain. In order to obtain solutions for the challenging stochastic model, we use sample average approximation and develop two enhanced decomposition frameworks that use logic-based Benders (LBBD) optimality cuts and binary decision diagram based Benders cuts. Specifically, to the best of our knowledge, deriving LBBD optimality cuts in a stochastic programming context is new to the literature. Our computational experiments on a hospital data set illustrate that the stochastic formulation generates robust schedules and that our algorithms improve the computational efficiency. Summary of Contribution: We propose a new model for an important problem in healthcare scheduling, namely, stochastic distributed operating room scheduling, which is inspired by a current practice in Toronto, Ontario, Canada. We develop two decomposition methods that are computationally faster than solving the model directly via a state-of-the-art solver. We present both some theoretical results for our algorithms and numerical results for the evaluation of the model and algorithms. Compared with its deterministic counterpart in the literature, our model shows improvement in relevant evaluation metrics for the underlying scheduling problem. In addition, our algorithms exploit the structure of the model and improve its solvability. Those algorithms also have the potential to be used to tackle other planning and scheduling problems with a similar structure.
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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 | 0.003 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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".