OPtimally Balancing Large Assembly Lines: Updating Johnson S 1988 Fable Algorithm<sup>*</sup>
Bibliographic record
Abstract
In 1988 Roger Johnson published a paper entitled “Optimally Balancing Large Assembly Lines with Fable” describing a depth-tirst. branch-and-bound algorithm tor solving the type-1 line balancing problem. The Fable algorithm sought to achieve three goals. 1) The algorithm could be a heuristic that would quickly find good solutions to instances containing lOOOor more tasks. 2) After finding a good solution the algorithm could continue until it found a verifiable optimal solution. 3) The algorithm would require a small and predictable amount of computer memory. Fable did remarkably well at achieving goals 1 and 3 and reasonably well at achieving goal 2. Though unstated. Fable achieved another goal. It was easy to understand and easy to program. Over the years researchers have proposed alternatives and improvements aimed at doing better at goal 2. The objective of this paper is to apply the best of these improvements to the original Fable algorithm to see what progress has been made in 15 years and where work i.s still needed. Tbe resulting algorithm is called Fable 2003 and it seems to peribrm as well as the current best algorithms in the literature.The range of instances solved by Fable 2003 is significantly larger than what Johnson's 11988] Fable was able to solve. This is due primarily to three groups of improvements: I) Changing direction, task priorities, and running more than I trial per instance; 2) Tbe Nourie-Venta list and other fathoming methods; and 3) The C programming language. The first improvement ensures that the most promising parts of the solution space are searched. The second improvement fathoms targe parts of the branchand- bound tree. Johnson's Fable was written in Fortran. Fable 2003 is written in C and so can use pointers to make more effective use of computer memory.One group of instances is difficult for Fable 2003 and the best algorithms in the literature. These are instances having a small average number of tasks per station, say tbree or fewer. Solving these instances is the research area where work is needed most. This is the same area that Johnson identified 15 years ago.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 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".