This paper studies the multistage pricing and seat allocation problems for multiple train services in a high-speed railway (HSR) with multiple origins and destinations (ODs). Taking the maximum total revenue of all trains as the objective function, a joint optimization model of multistage pricing and seat allocation is established. The actual operation constraints, including train seat capacity constraints, price time constraints in each period, and price space constraints among products, are fully considered. We reformulate the optimization model as a bilevel multifollower programming model in which the upper-level model solves the seat allocation problem for all trains serving multiple ODs in the whole booking horizon and the lower optimizes the pricing decisions for each train serving each OD in different decision periods. The upper and lower are a large-scale static seat allocation programming and many small-scale multistage dynamic pricing programming which can be solved independently, respectively. The solving difficulty can be significantly reduced by decomposing. Then, we design an effective solution method based on divide-and-conquer strategy. A real instance of the China’s Wuhan-Guangzhou high-speed railway is employed to validate the advantages of the proposed model and the solution method.

Urban rail crew scheduling problem is to allocate train services to crews based on a given train timetable while satisfying all the operational and contractual requirements. In this paper, we present a new mathematical programming model with the aim of minimizing both the related costs of crew duty and the variance of duty time spreads. In addition to iincorporating the commonly encountered crew scheduling constraints, it also takes into consideration the constraint of arranging crews having a meal in the specific meal period of one day rather than after a minimum continual service time. The proposed model is solved by an ant colony algorithm which is built based on the construction of ant travel network and the design of ant travel path choosing strategy. The performances of the model and the algorithm are evaluated by conducting case study on Changsha urban rail. The results indicate that the proposed method can obtain a satisfactory crew schedule for urban rails with a relatively small computational time.

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