An integrated approach of train scheduling and rolling stock circulation with skip-stopping pattern for urban rail transit lines

Integrated planning for urban rail transit (URT) systems is a significant technique in URT operation to balance service level and operating cost. It is generally oriented towards transportation efficiency and solved in a sequential way due to the complexity, but ignores the service experiences among equitable passengers and the utilization balance among equal rolling stocks. This paper aims to study the integrated planning for an oversaturated URT line, incorporating the fairness in train scheduling and workload balance in rolling stock circulation that are measured by two defined min-max indexes. A mixed-integer nonlinear programming (MINLP) model is established to formulate the integrated planning of stop planning, train scheduling and rolling stock circulation, explicitly considering time-dependent origin-destination demand, first-come-first-serve principle and rigid capacity constraints. Due to the model complexity, an iterative searching approach (ISA) is proposed to solve the model, involving adjusting stop patterns, departure times and connections at the depot terminal. The performance of the ISA is evaluated by three cases with different time lengths based on the practical data from No.8 URT line in Guangzhou. The results are compared with the practical plans and the solutions solved by the two-stage approach respectively. It shows that the ISA can not only mitigate unfairness and balance workload, but also improve transportation efficiency. We also investigate the optimization effects and application conditions of different combinations of searching strategies in the ISA. Furthermore, the study on the typical case during peak hours shows more details about the optimization effects and mechanism of the ISA, which can reach a uniform state in both service level and resource utilization.