Contextual Stochastic Optimization for Omnichannel Multi-Courier Order Fulfillment Under Delivery Time Uncertainty

TL;DR

The paper addresses omnichannel, multi‑courier order fulfillment under delivery‑time uncertainty using observational data. It develops a Contextual Stochastic Optimization ($CSO$) framework that learns a contextual distribution oracle from partial observations and feeds it into two scalable solvers: Contextual Sample Average Approximation ($C$‑SAA) and Contextual Robust Optimization ($C$‑RO). The approach enables consolidation‑aware MILP optimization that jointly selects fulfillment centers and carriers while incorporating distributional forecasts of delivery deviations via calibrated multi‑class classifiers and tree‑based quantile regression. Case study results on real, large‑scale data show meaningful reductions in expected costs and improved on‑time delivery rates, with $C$‑RO variants providing strong tail risk protection and robustness to distributional misspecification. The framework offers a practical, end‑to‑end template for data‑driven, contextually informed decision making in logistics, with potential multi‑million dollar savings and clear managerial guidance for deployment across varying risk tolerances and demand conditions.

Abstract

The paper studies a large-scale order fulfillment problem for a leading e-commerce company in the United States. The challenge involves selecting fulfillment centers and shipping carriers with observational data only to efficiently process orders from a vast network of physical stores and warehouses. The company's current practice relies on heuristic rules that choose the cheapest fulfillment and shipping options for each unit, without considering opportunities for batching items or the reliability of carriers in meeting expected delivery dates. The paper develops a data-driven Contextual Stochastic Optimization (CSO) framework that integrates distributional forecasts of delivery time deviations with stochastic and robust order fulfillment optimization models. The framework optimizes the selection of fulfillment centers and carriers, accounting for item consolidation and delivery time uncertainty. Validated on a real-world data set containing tens of thousands of products, each with hundreds to thousands of fulfillment options, the proposed CSO framework significantly enhances the accuracy of meeting customer-expected delivery dates compared to current practices. It provides a flexible balance between reducing fulfillment costs and managing delivery time deviation risks, emphasizing the importance of contextual information and distributional forecasts in order fulfillment. This is the first paper that studies the omnichannel multi-courier order fulfillment problem with delivery time uncertainty through the lens of contextual optimization, fusing machine learning and optimization.

Figures (21)

• Figure 1: The Life Cycle of the Order Fulfillment Process.
• Figure 2: A Schematic Overview of the CSO Framework for Observational Data.
• Figure 3: Out‐of‐Sample Comparison of the Joint Predicted Distribution and True Empirical Distribution for an Example Carrier.
• Figure 4: Sorted Observed Deviation Values versus 95% Prediction Intervals for an Example Carrier on Out‑of‑Sample Data.
• Figure 5: C-SAA vs. Empirical SAA Across Different Sample Sizes.