E-Commerce Middle-Mile Network Design with Delivery Speed Choices and Service Level Constraints.

This article focuses on the middle-mile network design problem for e-commerce companies aiming to meet heterogeneous customer delivery speed preferences and service level requirements. It formulates the problem as a mixed-integer linear program (MILP) that allows regional distribution centers (RDCs) to fulfill demands using longer delivery times than requested, incurring penalties, while ensuring a minimum fraction of demands are met within the requested times. The authors develop an exact Lagrangian relaxation–based branch-and-bound (LRBB) algorithm enhanced with a custom Benders decomposition approach to efficiently solve large-scale instances. Computational experiments on 220 instances, based on real U.S. geographic and demographic data, demonstrate that the best LRBB variant outperforms the commercial solver CPLEX by solving more instances to a 0.5% duality gap and reducing average CPU time by over 63%. Sensitivity analyses reveal that tighter service level requirements increase network costs and facility dispersion, while increasing delivery speed options yields diminishing returns in cost savings and delayed deliveries.