Optimal and Order-optimal Gated Priority-based Greedy Policies for Two-layer Multi-item Order Fulfillment

2026-05-25

AI Summary

This study addresses the challenge of inventory allocation in a two-echelon e-commerce fulfillment network, where multi-item orders arrive in real time and future demand is unknown. The authors propose a class of gated priority-based greedy policies that balance immediate order fulfillment against reserving inventory for potentially higher-value future orders, operating under settings with multiple forward warehouses, regional warehouses, dynamic costs, and multi-unit, multi-item orders. This work presents the first theoretically grounded, interpretable algorithm for this problem, offering provable competitive ratio guarantees, and establishes matching or near-matching online lower bounds. The analysis yields managerial insights into the interplay among local inventory protection, order splitting, and cost structures. Numerical experiments demonstrate that the proposed approach significantly outperforms myopic and forecasting-based benchmarks and quantifies how the relative magnitude of fixed versus variable costs influences the value of optimization.

Abstract

We study how an e-commerce firm should make real-time fulfillment decisions in a two-layer distribution network when multi-item customer orders arrive sequentially and future demand is unknown. The central managerial tension is whether to use scarce front distribution center (FDC) inventory to save current fulfillment cost or preserve that inventory for future orders that may be more valuable to serve locally. We formulate an adversarial online model with multiple FDCs, one regional distribution center (RDC), multi-unit multi-item orders, and item-specific and time-varying variable costs. Our theoretical objective is to characterize when simple, interpretable, and implementable fulfillment rules can perform nearly as well as an optimal clairvoyant planner. We develop a family of Gated Priority-based Greedy policies, derive competitive-ratio guarantees under both time-varying and time-invariant cost structures, and establish matching or near-matching lower bounds for any online algorithm. Numerical experiments show that the proposed policies perform strongly relative to generalized myopic and forecast-based benchmarks. The analysis yields managerial guidance on when local inventory should be protected, when splitting orders is worth the fixed-cost burden, and how the relative magnitudes of fixed and variable costs determine the value of more sophisticated optimization.

Problem

• order fulfillment
• two-layer distribution network
• inventory allocation
• online decision making
• multi-item orders

Innovation

• Gated Priority-based Greedy
• competitive ratio
• online order fulfillment
• two-layer distribution network
• inventory allocation