Surgical Scheduling with Constrained Patient Waiting Times
Bibliographic record
Abstract
We consider a surgical case scheduling problem with the objective of minimizing the expected time span of the schedule subject to a prespecified upper bound on the expected waiting time for each patient. The problem is challenging due to its combinatorial and nonlinear nature, and we focus on developing approximate methods to solve the problem. Specifically, we study two approximation methods. In the certainty equivalent method, we approximate the expected time span of the cases by assuming that the waiting time of each surgical case is a deterministic value. In the variance bounding method, we approximate the expected time span based on upper bounds on the variance of the surgical case waiting times. We show that the certainty equivalent method leads to a lower bound on the optimal expected time span, while the variance bounding method leads to an upper bound. Both methods suggest a simple sequencing rule, which is to sort the surgical cases in the ascending order of the surgical duration variability. Based on the upper and lower bounds, we derive a closed‐form, distribution‐free relative error bound for our sequencing rule, and show that it is uniformly bounded with respect to the number of cases. We also conduct a case study based on real‐life data on hernia repair procedures at the Jewish General Hospital in Montréal, to demonstrate our analytical models and their potential benefits for improving surgical scheduling. Finally, we conclude the paper by mentioning a few future research directions.
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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 | 0.005 | 0.017 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".