Existence and Properties of Optimal Production and Inventory Policies
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
It is an important and fundamental question whether an optimal inventory policy exists for a general deterministic multi-item, multistage (GDMM) production and inventory model. We show that an inventory model with a nonsubadditive ordering cost function could have no optimal policy over a finite horizon. However, when the ordering cost is a subadditive function an optimal policy exists for a GDMM production and inventory model over both a finite horizon and an infinite horizon. Properties of optimal inventory policies are crucial to investigating an inventory problem. We present four properties of optimal policies: (1) nonpositive inventory ordering, (2) last-minute ordering, (3) extended last-minute ordering, and (4) nonnegative filling properties. They have been explicitly or implicitly used in analyzing many different inventory models. The last two properties have been used but not proved before.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it