Stochastic Models for the Dispatch of Consolidated Shipments
Bibliographic record
Abstract
Most studies on supply chain management have taken an “inventory” point of view: The chain, supplier → manufacturer → major manufacturer, is thus analyzed as a series of production-inventory decisions. Although correct, that approach neglects issues on the transportation between nodes, thereby missing important opportunities for cost savings and optimization.Here we focus on the substantial economies of scale in transportation. These occur when merchandise is shipped in one’s own truck (private carriage), or when transport is performed by a public, for-hire trucking company (common carriage). As a result, better inventory replenishment between successive echelons may have less impact than improved transportation decisions. This is especially true when the latter include a strategy for shipment consolidation, the policies whereby several small orders will be held as they accumulate, then dispatched as a single, combined load.In the present paper, we apply renewal theory to two strategies commonly utilized in practice. For the case of a quantity policy we obtain the optimal target weight before dispatch, while for a time policy, we calculate the optimal length of each consolidation cycle (maximum holding time for any order). These strategies are analyzed for private carriage and then for common carriage. Particular situations are studied graphically and numerically; general results are expressed in the form of propositions.
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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 | 0.004 | 0.013 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.005 | 0.002 |
| Research integrity | 0.004 | 0.004 |
| Insufficient payload (model declined to judge) | 0.014 | 0.002 |
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".