Joint Optimization of Multistage Pricing and Seat Allocation for High-Speed Railways Integrating Pre-Sale Period Division

This paper studies the joint optimization problem of multistage pricing and seat allocation integrating pre-sale period division in high-speed railways (HSRs), taking the fluctuation of daily demand and the interaction between pricing and seat allocation into account. To maximize railway revenue, we establish an elastic demand function for each day, and then formulate a non-linear mixed integer optimization model, which considers real-life constraints, including price time and space relationships. The complex capacity sharing in HSRs and multistage pricing increase the scale of the optimization problem; the inclusion of pre-sale period division further complicates this. Therefore, we propose a multi-level comprehensive optimization method that decomposes the joint problem into two subproblems. The first subproblem optimizes multistage pricing and seat allocation under the given pre-sale period division scheme obtained from the second subproblem, while the second subproblem optimizes the pre-sale period division scheme by adjusting the period boundary between two adjacent periods to generate a new pre-sale period division scheme. Then, three algorithms are designed.
Algorithm 1
optimizes the first subproblem based on a divide-and-conquer strategy.
Algorithm 2
optimizes the pre-sale period division scheme, with a high-quality initial solution given by
Algorithm 3
. Two numerical examples are presented to demonstrate the high quality and efficiency of the proposed model and algorithms, which could provide decision support for railway ticket pricing. When there are five periods, the total revenue increases by 3.11% and 2.59% for small and large-scale instances, respectively; the total passenger kilometers increase by 21.21% and 19.42%, respectively.