Covering Routing Problem with Robots and Parcel Lockers: A Sustainable Last-Mile Delivery Approach
Bibliographic record
Abstract
This study presents the Covering Routing Problem with Robots and Parcel Lockers (CRP-R-PL), a challenge arising in sustainable last-mile delivery contexts such as e-commerce and city distribution. In this problem, trucks depart from a central depot, delivering parcels directly to a subset of customers or a subset of parcel lockers. With these parcel lockers, the remaining customers could pick up items if they prefer the pick-up delivery method. In addition, each truck is equipped with an electric-powered Sidewalk Autonomous Delivery Robot (SADR), a sustainable delivery solution used in the U.S. and Canada by Uber and Amazon. This zero-emission vehicle is deployed to get off the truck, serve one or multiple customers, and then return to the same truck for battery swap and package retrieval. For the routing of SADRs, the trucks act as a moveable satellite depot to serve the remaining customers. The CRP-R-PL seeks cost-minimizing solutions by determining optimal parcel locker locations and routes of trucks and SADRs to serve all customers. We offer a mixed-integer programming formulation and a greedy heuristic to solve it. The CRP-R-PL includes three decisions: 1) finding the location of parcel lockers, 2) routing the trucks to visit the customers and parcel lockers, and 3) routing the SADRs to serve the remaining customers. Since this problem has yet to be studied in the literature, a new set of benchmark instances is introduced for the CRP-R-PL and solved by Gurobi alongside the parameter's sensitivity analysis.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".