Technical Note—Error Noted in “Order-Based Cost Optimization in Assemble-to-Order Systems” by Lu and Song (2005)
Bibliographic record
Abstract
Discrete convexity, which extends submodularity to integer vectors, has been used in the economics and management literature to characterize the behavior of optimal policies. One of its variants, called L♮-convexity, has enabled recent advances in various operations management systems. In a paper published by Operations Research in 2005, an assemble-to-order inventory system was shown to have the L♮-convexity property, which was used to motivate an efficient algorithm. In a technical note, “Error Noted in ‘Order-Based Cost Optimization in Assemble-to-Order Systems’ by Lu and Song (2005)” by Bolandnazar, Huh, McCormick, and Murota, the authors show that the proof in that paper is incorrect and L♮-convexity may not hold. Despite this error, the authors credit Lu and Song for introducing this useful concept to the operations management community.
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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 | 0.006 | 0.065 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.004 | 0.006 |
| Insufficient payload (model declined to judge) | 0.022 | 0.018 |
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".