Operational Optimization of the Intelligent Bi-Directional Suspended Monorail System for Sea-Rail Intermodal Transportation

The innovative application of the Intelligent Bi-directional Suspended Monorail System (IBSMS) in automated container terminals has significantly advanced sea-rail intermodal transportation, effectively addressing the connection challenges between terminal yards and railway stations. As an emerging infrastructure, the IBSMS lacks a well-defined operational framework and faces the dual challenge of enhancing operational efficiency and reducing costs. To address this issue, this study develops a bi-objective integer linear programming model aimed at minimizing the makespan and the number of rolling stock deployment, thereby achieving integrated optimization for import/export container transshipment, suspended monorail train scheduling, track allocation, and rolling stock connection. To tackle the complex operational optimization problem, a two-stage $\epsilon $ -constraint logic-based Benders decomposition (2- $\epsilon $ -LBBD) algorithm is proposed. In the first stage, the container transshipment problem is solved, while the second stage focuses on optimizing suspended monorail train scheduling, track allocation, and rolling stock connection. The $\epsilon $ -constraint method addresses the problem’s bi-objective nature, and its combination with LBBD, in which a Strengthened Benders Cut is introduced, substantially improves computational efficiency for large-scale scenarios. Numerical experiments validate the effectiveness of the proposed model and demonstrate the superior performance of the 2- $\epsilon $ -LBBD algorithm. Compared to directly solving the problem with Gurobi, the proposed algorithm reduces the average computation time by 68.65% while still achieving optimal solutions. Consequently, this study contributes both theoretically and practically to the operational of IBSMS.