Heatmap Design for Probabilistic Driver Repositioning in Crowdsourced Delivery
Bibliographic record
Abstract
This paper proposes the use of heatmaps as a control lever to manage the probabilistic repositioning of independent drivers in crowdsourced delivery platforms. The platform aims to maximize order fulfillment by dynamically matching drivers and orders and selecting heatmaps that trigger the probabilistic flow of unmatched drivers to balance driver supply and delivery requests across the service region. We develop a Markov decision process (MDP) model to sequentially select matching and heatmap decisions in which the repositioning behavior of drivers is captured by a multinomial logit discrete choice model. Because of the curse of dimensionality and the endogenous uncertainty of driver repositioning, the MDP model is solved using a rolling-horizon stochastic lookahead policy. This policy decomposes matching and heatmap decisions into two optimization problems: a two-stage stochastic programming upper bounding problem for matching decisions and a mixed-integer programming problem for heatmap decisions. We also propose a simple policy for efficiently solving large-scale problems. An extensive computational study on instances derived from the Chicago ride-hailing data set is conducted. Computational experiments demonstrate the value of heatmaps in improving order fulfillment beyond the level achieved by matching alone (up to 25%) and identify conditions that affect the benefit of using heatmaps to guide driver repositioning. Funding: The authors gratefully acknowledge the support of the Natural Sciences and Engineering Research Council of Canada through Discovery Grants [Grants RGPIN-2024-04881, RGPIN-2020-04498, and RGPIN-2019-06207] awarded to the first, second, and third authors, respectively. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0418 .
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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 | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 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".