Collaborative optimization of differential pricing and seat allocation for multiple high-speed trains considering passenger demand

Differential pricing and seat allocation of multiple high-speed trains were jointly optimized considering with travel demand characteristics of high-speed railways in China. The preference of the passenger demand regarding departure times were analyzed. The departure time deviation, travel time and ticket fare were considered simultaneously in the travel cost function. The multinomial Logit model was employed to simulating passenger choice behaviors. A collaborative optimization model was constructed with the aim of maximizing the ticket revenue and the decision variables for pricing train legs and allocating seats for multiple high-speed trains. New solutions were constructed in two stages. In the first stage, three methods of generating new solutions were used to search new solutions randomly within the price constraints, which were respectively the method based on the Cauchy distribution with a variable scale parameter, the method by combining randomly and the method based on the standard normal distribution. In the second stage, the collaborative optimization model was translated into a seat allocation optimization model with the same optimized objective. Based on the above two stages, a modified direct search simulated annealing algorithm was designed to solve the optimization model. The experimental analysis containing dozens of trains is performed on Wuhan-Shenzhen high-speed railway. The results are drawn as follows. (1) The ticket revenue of the optimized solution increases obviously by 9%～27%, influenced greatly by the elastic demand coefficient, and more than 97% of the passenger demand is satisfied. (2) Over 97% of the optimization objective is obtained while the temperature of the algorithm falls 200 times, and the algorithm converges efficiently. (3) Differentiation is reflected for trains with different departure periods and the seat allocation of each train leg is highly matched with the passenger demand, illustrating that passenger demand are fully considered in the optimization method. © 2022, Central South University Press. All rights reserved.