Two-stage stochastic programming for the inventory routing problem with stochastic demands in fuel delivery
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Bibliographic record
Abstract
The inventory routing problem (IRP) arises in the joint practices of vendor-managed inventory (VMI) and vehicle routing problem (VRP), aiming to simultaneously optimize the distribution, inventory and vehicle routes. This paper studies the multi-vehicle multi-compartment inventory routing problem with stochastic demands (MCIRPSD) in the context of fuel delivery. The problem with maximum-to-level (ML) replenishment policy is modeled as a two-stage stochastic programming model with the purpose of minimizing the total cost, in which the inventory management and routing decisions are made in the first stage while the corresponding resource actions are implemented in the second stage. An acceleration strategy is incorporated into the exact single-cut Benders decomposition algorithm and its multi-cut version respectively to solve the MCIRPSD on the small instances. Two-phase heuristic approaches based on the single-cut decomposition algorithm and its multi-cut version are developed to deal with the MCIRPSD on the medium and large-scale instances. Comparing the performance of the proposed algorithms with the Gurobi solver within limited time, the average objective value obtained by the proposed algorithm has decreased more than 7.30% for the medium and large instances, which demonstrates the effectiveness of our algorithms. The impacts of the instance features on the results are further analyzed, and some managerial insights are concluded for the manager.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it