Multi-Item Online Order Fulfillment: A Competitive Analysis

Abstract

The boom of e-commerce around the globe in recent years has expedited the expansion of fulfillment infrastructures by e-retailers. While e-retailers are building more warehouses to offer faster delivery service than ever, the associated fulfillment costs have skyrocketed over the past decade. In this paper, we study the problem of minimizing fulfillment costs, in which an e-retailer must decide which warehouse(s) will fulfill each order, subject to warehouses’ inventory constraints. The e-retailer can split an order, at an additional cost, and fulfill it from different warehouses. Making effective real-time fulfillment decisions at the occurrence of order split is notoriously challenging, which has become a major problem for e-retailers. We focus on an RDC-FDC distribution network that major e-retailers have implemented in practice. In such a network, the upper layer contains larger regional distribution centers (RDCs) and the lower layer contains smaller front distribution centers (FDCs). We analyze the performance of a simple myopic policy that does not rely on demand forecasts and has been widely implemented in practice. We provide theoretical bounds on the performance ratio of the myopic policy compared with an optimal clairvoyant policy. We also empirically estimate our upper bound on the ratio by using FedEx shipping rates and demonstrate the bound can be as low as 1.13 for reasonable scenarios in practice. Moreover, we extend our study to the setting in which demand forecasting is available and prove the asymptotic optimality of a linear program rounding policy. Finally, we complement our theoretical results with a numerical study.