Inventory routing with heterogeneous vehicles and hazardous material backhauling
Bibliographic record
Abstract
Efficient coordination of distribution and backhauling is a critical challenge for many industries. This paper is motivated by a real-world case study at Hydro-Québec, a large-scale utility company in North America, and introduces an inventory routing problem that integrates inventory management and vehicle routing under several operational constraints. The problem involves distributing multiple commodities to customer sites while backhauling hazardous materials to depots. The objective is to minimize delivery, collection, and inventory holding costs using a fleet of capacitated heterogeneous vehicles, while ensuring that hazardous materials are transported separately from regular delivery commodities. In each period, a customer’s delivery and backhauling can be split and satisfied by multiple vehicles. We propose a mathematical formulation, introduce valid inequalities, and solve the resulting model using a branch-and-cut algorithm. To tackle large-size instances, a two-phase decomposition matheuristic is developed. To highlight the value of split delivery and backhauling, we compare the solutions from our model with those when split delivery is prohibited and when backhauling is optimized independently. In addition, we investigate the order-up-to level policy and the case when stockout is allowed. An extensive numerical study is conducted on synthetic instances to evaluate the performance of the models and solution approaches. The heuristic algorithm solves the synthetic instances in less than two hours with an average optimality gap of less than 2 %. Finally, a case study is conducted on the Hydro-Québec network to demonstrate the real-world applicability of the model and quantify the benefits to the company. Our proposed model reduces the total routing costs by 21 % compared to the case where backhauling is not integrated and split delivery is not allowed.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| 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) | 0.004 | 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".