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.

Strategic drone-delivery planning couples field locations with drone assignments and customer allocations under field capacity, cumulative payload, and round-trip energy constraints. We formulate this problem as a mixed-integer linear program and derive a Lagrangian primal heuristic with capacity-aware recovery and facility-exchange search. We show that the Lagrangian dual equals the linear-programming relaxation of the original model. For divisible demand, integer drone counts yield an exact reformulation that removes interchangeable drone labels; type-specific allocation flows extend the result to heterogeneous fleets. Experiments on 45 synthetic instances assess feasible solution quality against independent bounds. A same-machine comparison shows that the count formulation solves all 15 instances with 30 customers to optimality, while the Lagrangian heuristic has a mean objective excess of 0.72%. The count formulation also supplies incumbents and bounds for all 60- and 100-customer instances. Resource experiments distinguish changes in optimal planning cost from variation in heuristic solutions: payload tightening leaves the optimum unchanged over the tested ample fleet range, whereas a restrictive battery budget increases cost in a designated random-layout instance. The computational results favor the compact formulation for the tested divisible-demand model and identify the conditions under which the Lagrangian search improves feasible plans.