Optimal Design of Metro-Based Urban Logistics Networks via a Bi-level Programming Model

As urban traffic congestion intensifies and freight demand continues to rise, fully tapping the capacity potential of urban subway systems has become a critical pathway to alleviate pressure on urban logistics operations. This study first constructs a bi-level programming model for urban subway logistics networks: the upper-layer model minimizes the total cost of the subway logistics network as its objective function, comprehensively incorporating two core elements—freight transportation costs and logistics distribution center construction costs. The lower-level model, grounded in System Optimum (SO) theory, constructs a freight flow allocation sub-model to optimize cargo distribution within the network. For model solution, a hybrid approach is employed: a Genetic Algorithm (GA) serves as the primary framework, internally embedding the Frank-Wolf (FW) algorithm to solve the bi-level model. Finally, the proposed model and algorithm are validated through a design case study. The case analysis results demonstrate that the constructed model and network can effectively reduce urban logistics costs.