Heuristic Methods for Centralized Control of One-Warehouse, <i>N</i>-Retailer Inventory Systems
Bibliographic record
Abstract
This paper considers a periodic-review, two-echelon inventory system with one central warehouse and several retailers facing stochastic demand. The retailers replenish their stock from the warehouse, which in turn places orders at an outside supplier with infinite capacity. Transportation times and costs are constant. No ordering costs are considered, but warehouse replenishments must be multiples of a given batch quantity. The objective is to find policies that minimize holding and backorder costs. The standard approach to approximately solve this problem is to use a “balance” assumption, meaning that negative stock allocations to the retailers are possible. This approach may lead to considerable errors for problems with large differences between the retailers in terms of service requirements and demand characteristics. To handle such situations we suggest and evaluate two computationally tractable heuristics: the Virtual Assignment ordering rule for warehouse replenishments and the Two-step Allocation rule for allocating stock from the warehouse to the retailers. Numerical evidence shows that, especially when combining these heuristics, we obtain considerable improvements for many problems over the standard approach. Savings of up to 50% have been recorded.
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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 | 0.003 | 0.004 |
| 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 | 0.002 | 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".