An approximate periodic review stochastic inventory control system with both fixed cost and random yield
Bibliographic record
Abstract
We study a periodic review stochastic inventory control system for a single product at a single location with both fixed cost and random yield. If the random yield follows either two-point or uniform distribution, then some research works have been done in the literature. For other random yield distributions, the structure of the optimal inventory control policy has been an open problem for over three decades. A Negative Dominance (ND) property has been identified for the expected total cost function, which is approximated by a piecewise linear function, in each period. Under some very mild requirements about the random yield distribution and the single-period cost function, a period-dependent lower bound for initial inventory levels in any period is provided such that the expected total cost function indeed has the ND property at any initial inventory level below this lower bound and a period-dependent upper bound for initial inventory levels in any period is also provided such that the optimal order quantity is zero at any initial inventory level above this upper bound. We are able to show that these two bounds will not tend to infinity when the number of periods tends to infinity and, through numerical experiment, we show that the gap between these two bounds is quite small. Even further, with the help of this ND property, the search of the optimal order quantity at any initial inventory level below this lower bound in any period is as simple as the case with zero fixed cost even if the random yield follows neither uniform nor two-point distribution.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".