Some modified mathematical analytic derivations of the annual total relevant cost of the inventory model with two levels of trade credit in the supply chain system
Bibliographic record
Abstract
Several recent studies in supply chain system and related areas explored various economic order quantity (EOQ) models for noninstantaneous deteriorating items with imperfect quality and trade credit financing. In particular, in the year 2007, Teng et al investigated an EOQ model in which the supplier offers the retailer the permissible delay period M and the retailer, in turn, provides the trade credit period N (with ) to his/her customers. The main purpose of this article is twofold: (a) It modifies the annual total relevant cost TVC(T) in the study of Teng et al and presents the correct derivations of TVC(T) by applying mathematical analytic tools and techniques. (b) It exposes some logical and mathematical problems in the proof of Theorem 1 in Teng et al. It also corrects and overcomes all of the errors and shortcomings by systematically presenting the complete and mathematical solution procedures in order to locate all optimal solutions for the model in Teng et al.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.003 |
| 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".