Conformal Predictive Distributions for Contextual Order Fulfillment Optimization
Abstract
Ship-to-home fulfillment requires a retailer to select a fulfillment location and carrier before the delivery time is known. These decisions often rely on static transit-time estimates, which cannot represent how delivery-time uncertainty varies across orders and fulfillment options. This paper constructs conformal predictive distributions (CPDs) using Conformal Predictive Systems (CPS) for regression and the cross Venn-Abers predictor (CVAP) for multiclass classification, and uses them in a contextual optimization model for fulfillment decisions. The model is solved by contextual sample-average approximation (C-SAA). The regret of each fulfillment decision, its expected cost above that of the best decision, is bounded by forecast error, scenario-evaluation error, and the candidate-generation gap. The forecast term depends on how well calibration residuals or class probabilities represent the current order. On more than five million proprietary order records, CVAP raises exact-day accuracy from 49.5% for the rule-based estimate to 64.1%. Paired with a decision rule that selects a quantile weighting late errors more heavily, the split CPS (SCPS) gives a point estimate that raises late-delivery detection from 3.8% to 79.4%. Residual-based CPS distributions also meet or slightly exceed nominal interval-coverage targets. In decision experiments with a JD.com simulator over six test dates, C-SAA with CVAP lowers mean total cost by 7.1% and C-SAA with the Mondrian CPS (MCPS) lowers it by 6.7%, relative to C-SAA with the original nonconformal forecast. Both cut the late-delivery rate from 5.7% to below 4.0%.
Related
- Retrieving predictive densities from conformal predictive distributions
- Contextual Decision Making: Predictive or Generative
- Contextual Factors Behind Income Inequality: A Predictive Analysis
- The Curvature of Regret in Contextual Linear Optimization
- Conformal ordering: Distribution-free predictive inference for orders and rank
BibTeX
@misc{ye2026conformal,
title = {{Conformal Predictive Distributions for Contextual Order Fulfillment Optimization}},
author = {Tinghan Ye and Amira Hijazi and Pascal Van Hentenryck},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38046},
eprint = {2610.38046},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38046},
}
RIS
TY - UNPB
TI - Conformal Predictive Distributions for Contextual Order Fulfillment Optimization
AU - Tinghan Ye
AU - Amira Hijazi
AU - Pascal Van Hentenryck
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.38046
UR - https://arxiv.org/abs/2610.38046
AB - Ship-to-home fulfillment requires a retailer to select a fulfillment location and carrier before the delivery time is known. These decisions often rely on static transit-time estimates, which cannot represent how delivery-time uncertainty varies across orders and fulfillment options. This paper constructs conformal predictive distributions (CPDs) using Conformal Predictive Systems (CPS) for regression and the cross Venn-Abers predictor (CVAP) for multiclass classification, and uses them in a contextual optimization model for fulfillment decisions. The model is solved by contextual sample-average approximation (C-SAA). The regret of each fulfillment decision, its expected cost above that of the best decision, is bounded by forecast error, scenario-evaluation error, and the candidate-generation gap. The forecast term depends on how well calibration residuals or class probabilities represent the current order. On more than five million proprietary order records, CVAP raises exact-day accuracy from 49.5% for the rule-based estimate to 64.1%. Paired with a decision rule that selects a quantile weighting late errors more heavily, the split CPS (SCPS) gives a point estimate that raises late-delivery detection from 3.8% to 79.4%. Residual-based CPS distributions also meet or slightly exceed nominal interval-coverage targets. In decision experiments with a JD.com simulator over six test dates, C-SAA with CVAP lowers mean total cost by 7.1% and C-SAA with the Mondrian CPS (MCPS) lowers it by 6.7%, relative to C-SAA with the original nonconformal forecast. Both cut the late-delivery rate from 5.7% to below 4.0%.
ER -