Multi-Warehouse Assortment Selection: Minimizing Order Splitting in E-Commerce Logistics

Abstract

Order splitting is one of the key issues in the e-commerce order fulfillment process. It increases operational costs, elevates carbon emissions, and compromises customer satisfaction. This article focuses on determining the product assortments to store within the multi-warehouse logistics network to minimize the total number of split orders subject to cardinality constraints. We show that this minimizing split orders (MSO) problem is NP-hard and demonstrate that even finding an optimal order fulfillment strategy with a given assortment selection is NP-hard. To further analyze the MSO problem, we introduce a concept termed the second-order dominant indexing rule. This indexing rule corresponds to a group of demand distributions, under which we are able to characterize the structure of the optimal assortment selection for various scenarios. In particular, when assortment overlapping is prohibited, the optimal selection can be explicitly derived. When the demand exhibits a total nested structure, an optimal selection is non-overlapping with more popular products allocated to larger warehouses. We also bridge the two-warehouse order splitting minimization problem with the single-warehouse assortment selection problem in the literature. Building upon this connection, we propose an extended marginal choice indexing (MCI) policy, which is proven to achieve optimality when the demand has a second-order dominant MCI. In addition, we propose an Iterative Improvement Heuristic that refines any existing assortment selection. The efficiency of the proposed heuristics is validated by extensive numerical experiments, demonstrating that the extended MCI policy performs near-optimally even when customer demand is not ideal, and both heuristics outperform the best benchmark in existing literature. Additional experiments on real-world data further confirm their effectiveness and scalability. Finally, we extend our findings to a two-tier multi-warehouse scenario with a back-end warehouse.