Multi-Item Online Order Fulfillment in a Two-Layer Network

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 in real-time 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. 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, which chooses the least expensive fulfillment option for each order without considering the impact on future orders. Perhaps surprisingly, myopic policies (and their variations) are standard in the implementation of a typical order-management system. 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.

Keywords: online retailing, multi-item order, order split, fulfillment, myopic policy, online algorithm, LP rounding, competitive ratio, front distribution center (FDC)