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 distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 teacher head, 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".