A joint replenishment problem with the (T,ki) policy under obsolescence
Bibliographic record
Abstract
Companies are frequently confronted with the need to order different types of items from a single supplier or to manufacture the items in a production line. Indeed, coordinated ordering of multiple items may lead to important savings whenever a family of items can be ordered from a common supplier, produced in a common facility, or use a common mode of transportation. The Joint Replenishment Problem (JRP) tackles the coordinated replenishment of multiple items by minimizing the total cost, composed of ordering (or setup) costs and holding costs, while satisfying the demand. On the other hand, when items are subject to obsolescence, they may face an abrupt decline in demand as they are no longer needed. This decline can be caused by reasons such as rapid advancements in technology, going out of fashion, or ceasing to be economically viable. The present article develops an extension of the JRP where the items may suddenly become obsolete during an infinite planning horizon. The point at which an item becomes obsolete is uncertain. The lifetimes of the items are assumed to follow independent negative exponential distributions. A model is proposed by using the total expected discounted cost as the minimization criterion. The time value of money is considered through an appropriate discount rate. Extensive tests were performed to assess the impact of obsolescence rates and discount rates on the ordering policies. The progressive increase of the obsolescence rates determines smaller periods between successive replenishments, while the progressive increase of the discount rate determines smaller lot sizes.
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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 | 0.006 | 0.010 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.004 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.004 | 0.003 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 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".