灵活编组条件下轨道交通客货协同运输方案优化

基于灵活编组运营组织模式特点，综合考虑客流与货流之间的竞争关系，以列车编组类型及列车发车间隔为主要决策变量，以乘客等待时间和运营公司运营成本极小化为目标，构建灵活编组条件下轨道交通客货协同运输方案混合整数线性规划模型，得到系统优化的列车编组方案、 运行图和客货协同运输方案。当给定编组类型集合且没有货流输入时，本文所构建模型即可退化为传统的固定编组模式下客流运输优化模型。以北京地铁八通线为例设计数值实验，验证了所提模型的有效性，所有实验均由VB语言调用CPLEX优化软件进行求解。算例结果表明，相较于固定编组模式的单一客流运输，本文方法可在乘客平均等待时间仅增加1.1 min的情况下，降低 约41.86%的运营成本，大幅度增加运营收益，更好地实现运输服务质量和运营成本的均衡。

Optimization Methods of Combined Passenger and Freight Transportation Based on Flexible Train Composition Mode

To make full use of the resource of rail transit, this paper investigates the optimization methods for combined passenger and freight transportation based on the flexible train composition mode. The proposed method takes the selection of train types and the departure headway of consecutive trains as the main decision variables. A mixed-integer linear programming model is developed to minimize the waiting time of passengers and operation cost for metro companies. The competitive relationship between the freight and passenger demands are taken into consideration in the model. The numerical experiments based on Beijing Metro Batong Line are conducted to verify the effectiveness of the proposed methods, which are all computed by CPLEX solver code by Visual Basic (VB) programming language. The computational results show that compared to the operating mode with single type of train for passenger transportation, the proposed method reduced the operation cost by 41.86% with only 1.1 minutes increase of average passenger waiting time. The method can bring a better benefit and achieve a balance between the service quality and operation costs.