Bilevel Programming for Evaluating Revenue Strategy of Railway Passenger Transport Under Multimodal Market Competition

Document Type

Journal Article

Publication Date


Subject Area

ridership - mode choice, economics - revenue, economics - pricing, organisation - competition, mode - rail


Travel time, Travel costs, Railways, Railroads, Railroad transportation, Rail transportation, Pricing, People's Republic of China, Passenger transportation, Operating speed, Operating revenues, Multimodal transportation, Multimodal systems, Mode choice, Modal choice, Level of service, Journey time, Competition, Choice of transportation, China, Bilevel programming


A bilevel programming approach is used to study the strategies of increasing revenue of the railway agency running between Beijing and Tianjin, China. Bilevel programming approaches have been used in many studies to tackle a variety of transportation problems, but rarely for railway revenue strategy analysis. In this paper, the upper-level problem of the bilevel programming is to determine optimal pricing, speed, and level-of-service (LOS) strategy that maximizes the revenue of the railway agency. The lower-level problem describes passengers’ mode choice behavior under a transportation market with three competing modes: bus, rail, and car. The lower-level problem is to minimize the traveler’s cost in terms of money, time, and other related factors such as comfort and safety. A generalized cost function, considering these factors together with a logit model, is used to simulate travelers’ mode choice behavior. Study results clearly show that the bilevel programming is appropriate for the problem studied here. The results indicate that, to increase its revenue, the railway agency should focus on not only the pricing but also travel time and LOS. A pricing breakpoint of about ¥31 (¥7 = US$1) is found, as it results in the highest revenue for all traveling speeds and LOS. Further increase of the price leads to reduced revenue. A consistent revenue increase trend is observed for all higher traveling speeds and LOS, which emphasizes that the railway agency should pay attention to a combined revenue strategy.