Combining Integer Programming and the Randomization Method to Schedule Employees
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Bibliographic record
Abstract
We describe a method to find low cost employee shift schedules that guarantee that the fraction of customers who wait less than a specified time (the service level) is always at or above a specified minimum. Most previous approaches used a two-step procedure: (1) determine employee requirements, and (2) find a minimum cost schedule that provides the required number of employees in every period. Due to approximations used in the first step, the two-step approach sometimes results in infeasible or suboptimal solutions. Our method iterates between a schedule evaluator and a schedule generator. An iteration begins with the schedule evaluator using the randomization method to calculate transient service levels and identify infeasible intervals, where the service level is lower than desired. The schedule generator solves a series of integer programs to produce schedules. One constraint is added to the integer program for every infeasible interval, in an attempt to eliminate infeasibility without eliminating the optimal solution. The procedure terminates when a feasible solution is found. We present results for 18 test problems and discuss factors that make our approach more likely to outperform previous approaches. 1.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.029 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it