Arc-Flow Optimization Model for Multi-Modal Transportation
With the rapid growth of e-commerce logistics demand, transportation networks have become increasingly complex, making multi-modal transport a critical strategy for improving efficiency and reducing costs. We propose a cargo routing model grounded in arc-flow optimization to address the problem of multi-modal freight route planning and scheduling optimization. The objective function integrates weighted sums of transportation cost and time, while multiple constraints,including vehicle capacity limits, flow balance, transfer consistency, and path structure requirements, are incorporated to ensure practical feasibility. To enhance computational efficiency, nonlinear transfer logic constraints are linearized using the McCormick method. A case study is conducted on an integrated freight network comprising rail, road, and air transport modes across the Yangtze River Delta and surrounding major cities, using the 2023 "Singles’ Day" e-commerce peak season as the simulation scenario. Numerical results demonstrate that, compared with single-mode transport, the proposed multi-modal approach significantly reduces both transportation cost and time, improves resource utilization, enhances network flexibility and reliability, and effectively supports regional freight coordination and decision-making. The model exhibits strong adaptability and scalability, offering theoretical and methodological support for logistics operators in complex logistics environments.