Efficient Mathematical Lower Bounds for City Logistics Distribution Network with Intra-Echelon Connection of Facilities: Bridging the Gap from Theoretical Model Formulations to Practical Solutions

Focusing on the dynamic improvement of the underlying service network configuration, this paper aims to address a specific challenge of redesigning a multi-echelon city logistics distribution network. By considering the intra-echelon connection of facilities within the same layer of echelon, we propose a new distribution network design model by reformulating the classical quadratic assignment problem (QAP). To minimize the overall transportation costs, the proposed model jointly optimizes two types of decisions to enable agile distribution with dynamic "shortcuts": (i) the allocation of warehouses to supply the corresponding distribution centers (DCs), and (ii) the demand coverage decision from distribution centers to delivery stations. Furthermore, a customized branch-and-bound algorithm is developed, where the lower bound is obtained by adopting Gilmore and Lawler lower Bound (GLB) for QAP. We conduct extensive computational experiments, highlighting the significant contribution of GLB-oriented lower bound, to obtain practical solutions; this type of efficient mathematical lower bounds offers a powerful tool for balancing theoretical research ideas with practical and industrial applicability.