Optimal Train Dispatching by Benders’-Like Reformulation
将列车调度问题建模为混合整数线性规划，采用类Benders分解方法求解，在意大利和挪威铁路线上实际应用，效果优于已有启发式系统。
Train movements on railway lines are generally controlled by human dispatchers. Because disruptions often occur, dispatchers make real-time scheduling and routing decisions in an attempt to minimize deviations from the official timetable. This optimization problem is called train dispatching. We represent it as a mixed integer linear programming model, and solve it with a Benders’-like decomposition within a suitable master/slave scheme. Interestingly, the master and the slave problems correspond to a macroscopic and microscopic representation of the railway, recently exploited in heuristic approaches to the problem. The decomposition, along with some new modeling ideas, allowed us to solve real-life instances of practical interest to optimality. Automatic dispatching systems based on our macro/micro decomposition—in which both master and slave are solved heuristically—have been in operation in several Italian lines since 2011. The exact approach described in this paper outperforms such systems on our test bed of real-life instances. Furthermore, a system based on another version of the exact decomposition approach has been in operation since February 2014 on a line in Norway.