GRASP to minimize total weighted tardiness in a permutation flow shop environment
Bibliographic record
Abstract
This paper addresses the scheduling problem in a Permutation Flow Shop (PFS) environment, which is associated with many types of industries such as chemical, petrochemical, automobile manufacturing, metallurgical, textile, etc. Thus, this work intends to solve a PFS scheduling problem in order to minimize the total weighted tardiness, since it is an important sequencing criterion not only for on time delivery jobs but also for customer satisfaction. To solve the problem, GRASP (Greedy Randomized Adaptive Search Procedure) metaheuristic is proposed as a solution, which has shown competitive results compared with other combinatorial problems. In addition, two utility functions called Weighted Modified Due Date (WMDD) and Apparent Tardiness Cost (ATC) are proposed to develop GRASP. These are based on dynamic dispatching rules and also known for solving the problem of total weighted tardiness for single machine scheduling problem. Next, an experimental design was carried out for comparing the GRASP performance with both utility functions and against the WEDD dispatching rule results. The results indicate that GRASP-WMDD could improve the total weighted tardiness in 47.8% compared with WEDD results. Finally, the GRASP-WMDD performance for the PFS total tardiness problem was evaluated, obtaining a relative deviation index of 13.89% and ranking the method over 26 heuristics and metaheuristics.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".