Solving a hybrid batch production problem with unreliable equipment and quality reassurance
Bibliographic record
Abstract
A hybrid batch fabrication plan involving an outsourcing option is often established to deal with the in-house capacity constraint and/or meet timely demand with a reduced cycle time. Besides, the occurrences of unpredictable equipment malfunction and imperfect product quality should also be effectively managed during in-house fabrication to meet the production schedule and the required quality level. To address these concerns, we examine a hybrid economic production quantity (EPQ) problem with an unreliable machine and quality reassurance; wherein, an outside provider helps supply a portion of the batch at a requested timing and desirable quality, but at the price of a higher than in-house unit cost. Corrective action is performed immediately when a Poisson-distributed breakdown occurs. Once the equipment repairing task completes, the interrupted lot’s fabrication resumes. Random nonconforming products are identified, and the re-workable items among them are separated from the scraps. A rework task follows the regular process in each cycle at an extra cost. A portion of reworked items fails and are scrapped. A model portraying the problem’s characteristics is built, and an optimization methodology is utilized to find the optimal runtime solution to the problem. A numerical example reveals our result’s applicability, and specific managerial implications are suggested.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| 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".