Collaborative optimization of train schedule and circulation plan

In this paper, an integrated model is proposed to optimize train schedules and circulation plans simultaneously according to a given service pattern. The objective of our model is to minimize the headway deviations and the number of required rolling stocks. In particular, the headway deviations are the deviations between headways that between two successive train services and that given by service pattern. The optimization problem is transformed into a mixed-integer linear programming (MILP) problem, which can be efficiently solved by existing solver, e.g. CPLEX. A case study is implemented based on the data of the Beijing Yizhuang line to evaluate the effectiveness of the proposed model and solution approach.