APPROXIMATION ALGORITHMS FOR FLEXIBLE JOB SHOP PROBLEMS
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Bibliographic record
Abstract
The Flexible Job Shop problem is a generalization of the classical job shop scheduling problem in which for every operation there is a group of machines that can process it. The problem is to assign operations to machines and to order the operations on the machines so that the operations can be processed in the smallest amount of time. This models a wide variety of problems encountered in real manufacturing systems. We present a linear time approximation scheme for the non-preemptive version of the problem when the number m of machines and the maximum number μ of operations per job are fixed. We also study the preemptive version of the problem when m and μ are fixed, and present a linear time approximation scheme for the problem without migration and a (2+ε)-approximation algorithm for the problem with migration.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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