Optimal Differential Pricing for Intercity High-Speed Railway Services with Time-Dependent Demand and Passenger Choice Behaviors under Capacity Constraints

Differential pricing of trains with different departure times caters to the taste heterogeneity of the time-dependent (departure time) demand and then improves the ticket revenue of railway enterprises. This paper studies optimal differential pricing for intercity high-speed railway services. The distribution features of the passenger demand regarding departure times are analyzed, and the time-dependent demand is formulated; a passenger assignment method considering departure periods and capacity constraints is constructed to evaluate the prices by simulating the ticket-booking process. Based on these, an optimization model is constructed with the aim of maximizing the ticket revenue and the decision variables for pricing train legs. A modified direct search simulated annealing algorithm is designed to solve the optimization model, and three random generation methods of new solutions are developed to search the solution space efficiently. Experimental analysis containing dozens of trains is performed on Wuhan-Shenzhen high-speed railway in China, and price solutions with different elastic demand coefficients (phi) are compared. The following results are found: (i) the optimization algorithm converges stably and efficiently and (ii) differentiation is shown in the price solutions, and the optimized ticket revenue is influenced greatly by phi, increasing by 7%-21%.