Solving Tri-criteria: Total Completion Time, Total Earliness, and Maximum Tardiness Using Exact and Heuristic Methods on Single-Machine Scheduling Problems
Bibliographic record
Abstract
Machine scheduling problems have become increasingly complex and dynamic.In industrial contexts, managers often evaluate several objectives simultaneously and attempt to identify the optimal solution that satisfies all concerns.This study proposes two heuristic methods based on SPT and dominated rules (DR) to minimize Total Completion ∑𝐶 𝑗 , Total Earliness ∑𝐸 𝑗 , and Maximum Tardiness Time 𝑇 𝑚𝑎𝑥 for multicriteria and multi-objective functions (1//(∑𝐶 𝑗 , ∑𝐸 𝑗 , 𝑇 𝑚𝑎𝑥 ) and (∑𝐶 𝑗 + ∑𝐸 𝑗 + 𝑇 𝑚𝑎𝑥 )) based on single machine scheduling problems.in addition, two exact methods Branch and Bound (BAB with and without DR) and a complete enumeration method are applied to solve the multi-criteria and multi-objective functions.According to the calculation results, the CEM is able to solve problems up to 𝑛 = 11 jobs, while BAB without DR and BAB with DR able to resolve problems from 𝑛 = 19 to 𝑛 = 50 jobs, respectively, within a reasonable time.However, heuristic methods can solve up to 𝑛 = 5000 jobs. in addition, the experimental results for a subproblem show that the heuristic methods can solve up to 𝑛 = 4000 jobs.Practical experiments demonstrate the proposed heuristic methods are the most effective of all approaches.All methods used in this work were coded with MATLAB 2019a.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".