Benders decomposition for robust distribution network design and operations in online retailing

The increasingly flourishing e-commerce has prompted e-retailers to implement a two-layer distribution network consisting of regional and forward distribution centers (FDCs) to reduce the fulfillment cost. This is done at the expense of incurring construction cost and complicating the inventory management, thus may not achieve a cost-effective goal. In this paper, we study a joint network design and operations problem that first chooses the locations and assortments for FDCs before the horizon starts, then decides the replenishment, allocation, and fulfillment quantities adaptively as random demands reveal over periods. We formulate a multi-period stochastic model and propose a robustness based Benders decomposition algorithm, which first applies a linear decision rule to get a mixed-integer robust counterpart model, then solves it using a Benders decomposition. Numerical experiments suggest that our algorithm produces good-quality solutions efficiently and robustly under distributional ambiguity. A case study using real data from JD.com demonstrates the applicability of our algorithm, which yields substantial cost savings over a decentralized policy and a status quo policy. Some managerial and practical insights are derived from the results.