Optimal Cyclic Multi-Hoist Scheduling: A Mixed Integer Programming Approach
Bibliographic record
Abstract
In the manufacture of circuit boards, panels are immersed sequentially in a series of tanks, with upper and lower bounds on the processing time within each tank. The panels are mounted on carriers that are lowered into and raised from the tanks, and transported from tank to tank by programmable hoists. The sequence of hoist moves does not have to follow the sequence of processing stages for the circuit boards. By optimising the sequence of hoist moves, we can maximise the production throughput. We consider simple cyclic schedules, where the hoist move sequence repeats every cycle and one panel is completed per cycle. Phillips and Unger (1976) developed the first mixed integer programming model for finding the hoist move schedule to minimise the cycle time for lines with only one hoist. We discuss how their formulation can be tightened, and introduce new valid inequalities. We present the first mixed integer programming formulation for finding the minimum-time cycle for lines with multiple hoists and present valid inequalities for this problem. Some preliminary computational results are also presented.
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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 | 0.002 | 0.004 |
| 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 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.001 |
| 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".