Joint optimization of carriage arrangement and flow control in a metro-based underground logistics system

Under the background of developing sustainable urban freight transportation on the operation level, this study investigates a joint optimization problem of carriage arrangement and flow control in a metro-based underground logistics system, in which passengers and freights are allowable to share each service train. By introducing the carriage arrangement variable and flow assignment variables related to passengers and freights, the problem of interest is formulated as an integer linear programming model with the objective of minimizing the weighted sum of the operation cost and the total delay penalty. To handle the solution challenges posed by a large number of integer decision variables, it is proved that the proposed model can be transformed into an equivalent mixed-integer linear programming model. Then, for solving the proposed model, an improved Benders decomposition algorithm is designed based on the model characteristics. Finally, a set of numerical examples on the Beijing metro Batong line are conducted to verify the performance and effectiveness of the proposed approaches.