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Conformal Predictive Distributions for Contextual Order Fulfillment Optimization
Optimization and Control · Submitted 27 Oct 2026
abstract compiled · 2026-10-30 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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%.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Ship-to-home fulfillment requires a retailer to select a fulfillment location and carrier before the delivery time is known. | background 1.00 | 0.05 | 0.01 | asserted 1.00 |
| s1 | These decisions often rely on static transit-time estimates, which cannot represent how delivery-time uncertainty varies across orders and fulfillment options. | gap 0.73 | 0.07 | 0.02 | asserted 0.90 |
| s2 | 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. | method 0.50 | 0.95 | 0.13 | asserted 1.00 |
| s3 | The model is solved by contextual sample-average approximation (C-SAA). | method 1.00 | 0.88 | 0.03 | asserted 1.00 |
| s4 | 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. | contribution 0.55 | 0.82 | 0.11 | asserted 1.00 |
| s5 | The forecast term depends on how well calibration residuals or class probabilities represent the current order. | interpretation 0.72 | 0.62 | 0.04 | asserted 0.99 |
| s6 | On more than five million proprietary order records, CVAP raises exact-day accuracy from 49.5% for the rule-based estimate to 64.1%. | result 1.00 | 0.94 | 0.11 | asserted 1.00 |
| s7 | 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%. | result 1.00 | 0.93 | 0.12 | asserted 1.00 |
| s8 | Residual-based CPS distributions also meet or slightly exceed nominal interval-coverage targets. | result 1.00 | 0.93 | 0.06 | asserted 0.95 |
| s9 | 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. | result 1.00 | 0.95 | 0.33 | asserted 1.00 |
| s10 | Both cut the late-delivery rate from 5.7% to below 4.0%. | result 1.00 | 0.94 | 0.22 | asserted 1.00 |
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The paper
Original 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%.
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