需求响应的集装箱班列时刻表优化及 Benders分解算法

充分考虑集装箱货物与集装箱班列在时间和数量方面的匹配关系，以集装箱货物送达目的站的总延误最小为目标，构建集装箱班列时刻表优化的线性混合整数规划模型.采 用Benders分解算法将原问题分解为确定集装箱货物与班列匹配方案的主问题，以及优化班列时刻表的子问题，通过求解子问题的对偶模型不断产生主问题的割平面.为克服割平面有效性较低的缺点，设计改进策略，使每次迭代产生多个割平面同时添加至主问题中.最后，通过算例验证模型和算法的有效性.结果表明：改进策略的运用有效提高了算法的计算效率，利用模型及算法得到的班列时刻表与集装箱货物的数量、时间分布之间具有较好的匹配性，制定的班列时刻表很好地响应了用户需求.

Optimization of Demand-response Container Train Timetables and Benders Decomposition

This study proposes a linear mixed integer programming model for the container train timetables to minimize the total tardiness of deliveries. The assignment between the container goods and the container trains is fully considered in terms of time and quantity. An approach based on Benders decomposition is developed to convert the model into a master problem of assignment scheme of container goods to trains as well as a timetabling subproblem. The cuts of the master problem are constantly generated by solving the dual subproblem. To overcome the disadvantage of low efficiency of the cut, an improved strategy is also proposed to produce multiple cuts and add them to the master problem in each iteration. A numerical example is provided to demonstrate the effectiveness of the model and algorithm. The results indicate that the improved strategy increases the calculation efficiency of the algorithm. The train timetables obtained by the proposed model and algorithm match well with the distribution of the quantity and times of the goods; the generated train timetables well meet the user demand.