Max-plus Modeling of Manufacturing Flow Lines
Why this work is in the frame
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Bibliographic record
Abstract
Max-plus algebra can be used to model manufacturing flow lines using linear state-space-like equations which can be used in analysis and control. This paper presents a method for easy and quick generation of the max-plus equations for manufacturing flow lines of any size or structure. The generated equations can model flow lines with infinite as well as finite buffer sizes. A flow line to be modeled is initially assumed to have infinite buffers for all stations. The line model equations are then generated as a combination of serial and merging stations after identifying the different stages using an adjacency matrix for the flow line. In the generated equations, the dynamics of the system are captured in two matrices that are function of the processing times of the different stations in the line. After generating these equations, extra terms are added to account for the finite buffers where for each buffer size, a matrix is added multiplied by the vector of system parameters delayed by the buffer size plus one. The method is intuitive and easy to understand and code in software and thus can facilitate quick analysis of different configurations of manufacturing flow lines and assessing what if scenarios. This can also allow quick on-line reconfiguration of controllers for frequently reconfiguring flow lines.
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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 | 0.000 |
| 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