Shipment Consolidation by Private Carrier: The Discrete Time and Discrete Quantity Case
Bibliographic record
Abstract
This article studies the dispatch of consolidate shipments. Orders arrive to a depot at discrete time epochs following a discrete time batch Markov arrival process (BMAP). The weight of an order is measured in discrete units and may be correlated with the arrival time. As soon as the total weight of the accumulated orders reaches a threshold, which is a function of the time elapsed since the last dispatch, all orders are consolidated and a shipment is dispatched. A discrete time Markov chain for the accumulated weight of orders in the system is introduced and analyzed. The distributions of the accumulated weights at an arbitrary time, total accumulated weight in a consolidation cycle, and excess of weight per shipment are obtained. By introducing an absorption Markov chain and a terminating Markovian arrival process, we find the distributions of the consolidation cycle length, the waiting time of an arbitrary order, and the number of orders that occur in a cycle. An efficient computational procedure is developed for evaluating dispatch policies. The model with a quantity policy and a phase-type weight distribution is studied in detail. An extensive numerical analysis is conducted to test the efficiency of the algorithm and to gain insight in these shipment consolidation models.
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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 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".