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

arXiv: https://arxiv.org/abs/2605.25888 · HTML: https://mlsanity.com/paper/2605.25888/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 29 references that are in the map.
- First posted on arXiv 25 May 2026.

## Builds on (most cited first, 1 of 1)

- [Online Order Fulfillment with Replenishment](https://mlsanity.com/paper/2603.04065/) (2026)

## Abstract (arXiv)

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.