关键词: 铁路运输, 快递定价, Benders分解算法, 高铁快运, 货流分配, 随机需求

Abstract: To fully utilize the capacity of high-speed railway during off-peak periods, high-speed railway express delivery (HSReD) emerged as a new trend in the development of railway express delivery. However, pricing and freight flow allocation problems are intertwined to determine the operational efficiency and profitability of the HSReD system. To address the challenges posed by the elastic relationship between freight price and demand, as well as stochastic demand, this paper studies the integrated optimization of pricing and freight flow allocation for HSReD by using passenger trains. A two-stage stochastic nonconvex nonlinear programming model is constructed to maximize the expected net profit of the HSReD system, considering the elastic and stochastic demand, pricing constraints, train capacity and station loading and unloading capacities. This model is reformulated into a convex quadratic constrained programming model using outer piecewise approximate linearization and bilinear linearization techniques. A benders decomposition algorithm combined with primal search strategy is developed for efficient solution. Numerical results show that: 1) Compared with the deterministic model, the proposed model achieves higher profits and revenues while reducing transportation costs, and has lower standard deviations for all indicators, demonstrating stronger robustness. 2) The comparative experiments with the solver show that the proposed algorithm has a superior performance in terms of solution efficiency and quality: in the five groups of medium and small-scale cases, the relative gap values between the objective value obtained by the proposed algorithm and the solver are all within 1×10-4 ; in the large-scale case, the proposed algorithm obtained the result within 683.6 seconds, while the solver failed to complete the solution within the specified time. 3) In the application verification on the Zhengzhou-Xi'an high-speed railway line, the proposed method achieves an expected net profit of 14.653 5 million yuan. This verified that the proposed method can attract more express delivery demands and reasonably allocate the expresses to the trains with limited transportation capacity. It achieves efficient matching between demand and capacity resources, thereby significantly increasing the operational profit of the system.

Key words: railway transportation, express delivery pricing, Benders decomposition algorithm, high-speed railway express delivery, freight flow allocation, stochastic demand