A Variant of L<sup>♮</sup>-Convexity and its Application to Inventory Models with Batch Ordering
Bibliographic record
Abstract
Previous studies show that the concept of L♮-convexity is helpful in characterizing the optimal policy for some inventory models with positive leadtimes. Such examples include the lost-sales inventory model by Zipkin (2008). On the structure of lost-sales inventory models. Operations Research, 56(4) 937–944. and the inventory-pricing model by Pang et al. (2012). A note on the structure of joint inventory-pricing control with leadtimes. Operations Research, 60(3), 581–587. However, when taking batch ordering into account, L♮-convexity does not work anymore. In this paper, we extend L♮-convexity to a more general concept termed as Q-jump-L♮-convexity and apply it to batch ordering inventory models including a lost-sales inventory model and an inventory-pricing model with batch ordering and positive leadtimes. By utilizing this new concept, we can partially characterize the structure of the optimal policies for both the models. Moreover, we are able to evaluate the sensitivity of the optimal decisions with respect to system states. Our results can also be applied to the serial and the assembly inventory systems with lost-sales and batch ordering.
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 | 0.005 | 0.010 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.004 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.006 |
| 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".