This paper is devoted to designing a mixed-integer linear programming to solve the simultaneous line planning and timetabling problem. A directed graph is first constructed to represent the combinational travel network for both candidate trains and passengers. Through this graph, it is easy to simultaneously describe trains’ operation choices, passengers’ travel choices, and their restrictive relations. Based on it, a mixed-integer linear programming model with many binary and non-negative integer decision variables is built to simultaneously optimize the line plan, timetable, and passenger travel choices, which can be efficiently solved using commercial solver CPLEX for small-scale network, while a decomposition strategy is required to combine with CPLEX for large-scale network. A set of numerical experiments are carried out to analyse the impacts of flow sub-units, number of candidate trains, and weight factors. Finally, we conduct two case studies for testing the practicability of our proposed method.

中文翻译：

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基于火车和乘客组合旅行网络的同步线路规划和时间表：混合整数线性规划方法

本文致力于设计一个混合整数线性规划来解决同时进行的线路规划和时间表问题。首先构建一个有向图来表示候选列车和乘客的组合旅行网络。通过这张图，很容易同时描述列车的运行选择、乘客的出行选择以及它们之间的约束关系。在此基础上，构建了具有多个二元和非负整数决策变量的混合整数线性规划模型，同时优化线路规划、时刻表和旅客出行选择，可以使用商业求解器CPLEX对小规模有效求解网络，而大规模网络需要分解策略与 CPLEX 结合。进行了一组数值实验来分析流子单元、候选列车数量和权重因子的影响。最后，我们进行了两个案例研究来测试我们提出的方法的实用性。