This paper investigates the optimization of multistage dynamic pricing for high-speed railway (HSR) considering flexible pre-sale period division scheme. To address the variability of daily demand during the booking horizon, an elastic demand function for each day is developed. Considering various constraints, including train capacity constraints, passenger demand constraints, price-related constraints, a non-linear mixed integer optimization model is formulated for the multistage dynamic pricing optimization problem to maximize railway revenue. The complicated capacity-sharing relationship for HSR and flexible pre-sale period division increase the problem’s scale. Thus, a comprehensive optimization approach is proposed based on decomposing the optimization problem into two subproblems. Subproblem 1 solves multistage dynamic pricing and ticket allocation based on a known period division scheme generated by subproblem 2, while subproblem 2 adjusts the boundaries between two consecutive periods to generate a period division neighborhood scheme. Subproblem 1 is solved by formulating as a bi-level programming problem. The numerical examples are conducted to evaluate the proposed model and solution methods, providing valuable decision support for railway operators.

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Optimization of Multi-stage Dynamic Pricing for High-Speed Railway Considering Flexible Pre-sale Period Division Scheme

  • Jing Xu,
  • Lianbo Deng

摘要

This paper investigates the optimization of multistage dynamic pricing for high-speed railway (HSR) considering flexible pre-sale period division scheme. To address the variability of daily demand during the booking horizon, an elastic demand function for each day is developed. Considering various constraints, including train capacity constraints, passenger demand constraints, price-related constraints, a non-linear mixed integer optimization model is formulated for the multistage dynamic pricing optimization problem to maximize railway revenue. The complicated capacity-sharing relationship for HSR and flexible pre-sale period division increase the problem’s scale. Thus, a comprehensive optimization approach is proposed based on decomposing the optimization problem into two subproblems. Subproblem 1 solves multistage dynamic pricing and ticket allocation based on a known period division scheme generated by subproblem 2, while subproblem 2 adjusts the boundaries between two consecutive periods to generate a period division neighborhood scheme. Subproblem 1 is solved by formulating as a bi-level programming problem. The numerical examples are conducted to evaluate the proposed model and solution methods, providing valuable decision support for railway operators.