An Approach for Train Stop Planning With Variable Train Length and Stop Time of High-Speed Rail Under Stochastic Demand

This paper studied the train stop planning problem with variable train length and stop time under stochastic demand (TSPPWVTLSTSD). As we know, stop time and train length were often considered in a fixed manner in train stop planning for high-speed rail (HSR). One obvious disadvantage was that it often resulted in insufficient time for passengers to get on or get off a train. In addition, fixed train length may cause a waste of train capacity. And travel demand was usually assumed to be deterministic, although travel demand usually was stochastic. In this paper, we presented an optimization model that simultaneously optimized the stop-schedule, the stop time schedule and the train length schedule for each train trip under stochastic demand. By formulating deterministic equivalents to the chance constraints, we obtained a deterministic mixed integer model. To solve the problem, a novel column generation-based heuristic solution technique based on Dantzig-Wolfe decomposition principle and column generation procedure was proposed. Some numerical experiments and a case study based on real-world data were used to demonstrate that the proposed solution method can yield a service plan within a reasonable time compared with ILOG Cplex. Besides, the variable train length and stop time model needed fewer carriages and also gave rise to less total time loss compared with the fixed scenario.