Multi-warehouse package consolidation for split orders in online retailing - Zhang, Yuankai; Lin, Wei-Hua; Huang, Minfang; Hu, Xiangpei (European journal of operational research, 2021)
•Formulated a new variant of package consolidation problem in online retailing.•Proposed a network flow model to determine splitting-vs.-consolidation tradeoff.•Developed an enhanced logic-based Benders’ decomposition algorithm.•Revealed conditions under which consolidation is more beneficial than splitting. With the rapid growth of the online market in recent years, order splitting has become a great challenge to online retailers for fulfilling multi-item orders in a multi-warehouse storage network. Order splitting can lead to higher shipping costs, the use of more packages, and possible dissatisfaction from customers. This paper presents a multi-warehouse package consolidation approach aimed at consolidating multiple suborders’ stock-keeping units (SKUs) through transshipments among warehouses. A combined multi-commodity network flow model is proposed to determine the consolidation warehouses for each order and make transshipment decisions for individual SKUs. An enhanced logic-based Benders’ decomposition algorithm is proposed to decompose the model into a general multi-commodity network flow master problem and a set of bin packing with conflicts sub-problems. Two proposed Benders’ cuts guarantee the algorithm to converge to optimality. The proposed algorithm can generate the near-optimal result with only about 25% of the CPU time required by CPLEX to solve the proposed model. Numerical experiments reveal that the proposed package consolidation approach outperforms the order splitting fulfillment approach in reducing the total costs, the number of packages, and the delivery times, especially for cases with a small number of SKUs in each suborder which are typical for online retailers. Sensitivity analyses are performed to provide managerial insights of adopting the proposed approach in the real world where order splitting is a common phenomenon.