An Improved MILP Modeling of Sequence-Dependent Switchovers for Discrete-Time Scheduling Problems
Bibliographic record
Abstract
This paper presents a new mixed-integer linear program (MILP) formulation for modeling sequence-dependent switchovers for uniform discrete-time scheduling problems. The new formulation provides solutions faster than the formulation found in the paper by Kondili et al. ( Comput. Chem. Eng. 1993, 17, 211) and scales more efficiently. The key to this formulation is the use of memory operation logic variables that track the temporal unit-operation events occurring within the scheduling horizon for each unit. Four auxiliary dependent binary transition variables are required for every unit-operation independent binary variable, called the mode-operation setup variable. In this paper, “dependent” means that these variables are derived from the unit-operation variables and are integral at the solution without explicitly declaring them as binary search variables in the MILP formulation, hence reducing the computational effort. The four dependent variables are the startup, shutdown, switchover-to-itself, and memory operation logic variables. The sequence-dependent switchover relationships between different operations on the same unit can be derived from these variables, whereby maintenance operations can be activated and placed between the mode operations where appropriate, depending on the repetitive maintenance or cleaning requirements. The new formulation for sequence-dependent switchovers can be applied to both batch- and continuous-process units. Three illustrative examples are provided that show its advantage in terms of solution times over current state-of-the-art methods. In addition, effective integer cuts are derived, which are based on the asymmetric traveling salesman problem with costs equal to the sequence-dependent transition times.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".