基于固定班制的地铁乘务计划一体化优化方法

针对运营中常用的固定班制轮班模式，通过加入班次数量比例和备班约束，构建排班和轮班计划一体化的乘务计划优化模型，进行乘务组数的全局优化；之后对传统列生成求解算法进行改进，在定价子问题中分别针对不同班次类型，各自生成班次以适应新的模型约束，并设计加速策略，以完成对一体化优化模型的求解；最后以轮乘站设置不同的两条地铁线路为例开展案例研究，研究了在四班三运转和六班五运转班制下的优化效果，分析了算法的求解效率. 研究结果表明:固定班制条件下，与分阶段优化方法相比，简化了轮班单元构成，乘务组数量减少了6.67%～14.29%，求解时间节约了44.2%～51.4%. 

Integrated Optimum Crew Planning in Fixed Shift System for Subways

In order to globally optimize crew members in commonly used fixed shift system, an integrated optimum scheduling that combines crew scheduling and rostering is proposed with the constraints of shift proportions and candidate shifts. Then, an improved column generation approach is developed for the proposed model in which the suitable shifts are generated according to the type of shifts in a pricing sub-problem. Meanwhile, acceleration techniques are used for solving the proposed model. Finally, the case studies with two metro lines connecting different home stations in Beijing is carried out, focusing on the optimization results under three shifts in four groups and five shifts in six groups and their algorithm efficiency. It is indicated that as for the fixed shift system, the proposed integrated optimum scheduling is able to reduce the number of drivers by 6.67%?14.29% in contrast to the separated optimization, and the computation time by 44.2%?51.4%.