Lead-Time-Constrained Middle-Mile Consolidation Network Design with Fixed Origins and Destinations

Many large e-commerce retailers move sufficient freight volumes to operate private middle-mile consolidation networks for order fulfillment, transporting customer shipments from stocking locations to last-mile delivery partners in consolidated loads to reduce freight costs. We study a middle-mile network design optimization problem with fixed origins and destinations to build load consolidation plans that minimize cost and satisfy customer shipment lead-time constraints. We propose models that extend traditional flat network service network design problems to capture waiting delays between load dispatches and ensure that shipment lead-time requirements are satisfied with a desired probability. We approximate these chance constraints using hyperparameterized linear constraints, resulting in new mixed-integer programs (MIPs) for service network design. To find high-quality solutions to the proposed MIPs, we develop an effective integer-programming-based local search (IPBLS) heuristic that iteratively improves a solution by optimizing over a smartly selected subset of commodities. For the largest problem instances, we propose a two-phase IPBLS heuristic that first utilizes a simplified, restricted MIP that constrains leg waiting delays individually. Computational experiments using data from a large U.S.-based e-commerce partner demonstrate the significant impact of tight lead-time constraints on the structure of the consolidation network designs and their concomitant operating costs. Notably, tighter constraints lead to solutions with increased shipment consolidation and higher dispatch frequencies on selected key transportation lanes. Such solutions trade off higher shipment transit times with significantly reduced shipment waiting times to meet lead-time constraints at lower cost.