Inventory control of an item with a probabilistic replenishment lead time and a known supplier shutdown period
Bibliographic record
Abstract
In this paper, we address an important practical situation, namely where the usual replenishment lead time (when the supplier's production facility is operating) is a random variable and the supplier shuts down for an interval of known duration (for maintenance, vacation, etc.) each year. The demand rate is constant and any demand when out of stock is assumed to be lost. Under such circumstances we develop a heuristic procedure to decide when to initiate replenishment as well as the associated order-up-to-levels. Through the use of simulation (which accurately estimates the average costs per unit time), the heuristic is shown to perform excellently in a selection of small size problems when one can find the optimal solution. For a large number of problems of more realistic size, the use of simulation reveals that the heuristic achieves substantial cost savings when compared with a simpler, baseline approach. The heuristic itself does not require the use of simulation. The sensitivity of total expected costs to various parameters (such as the length of the shutdown interval and characteristics of the lead time distribution) is discussed.
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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 | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 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) | 0.001 | 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".