Mixed-Integer Linear Programming Model for the Dual-Resource Flexible Job-Shop Scheduling Problem
Bibliographic record
Abstract
Scheduling is a vital function for efficiently operating flexible job-shop systems.Traditionally, that function considers assigning jobs to machines and their sequence.However, machines need to be operated by another set of resources (i.e., workers).Due to the fact that operators are skilled workers, the available pool is limited.Hence, the interaction of machines and humans needs to be studied in an integral manner to address the scheduling problem.In this article, a novel precedence variable-based, mixed-integer linear programming model is developed for the dual-resource flexible job-shop problem.The mathematical formulation deals with the optimal assignment of machines and workers to operations and the operation sequence in both resources by minimizing the makespan.The model gives an exact solution by solving both the assignment and the sequencing problems concurrently.The model was implemented in Docplex and was run on three instances of varying sizes.The model solved the three introduced examples, including a large instance involving 20 operations with 4 workers and 4 machines, using only 1662 variables and 5217 constraints in 156.43 seconds, indicating that the proposed model is adequate.The model can be used to label training examples for machine learning-based techniques as well as help track and compare models developed using heuristics.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.008 | 0.002 |
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".