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The rapid development of high-speed railways (HSR) worldwide has provided a fast, convenient, safe, and comfortable mode of transportation. It is also an important public transportation tool for green travel, contributing to the reduction of carbon emissions. HSR has a strong competitive advantage in long-distance passenger transportation, but it faces significant competition from the aviation industry. Airlines attract passengers with discounted fares and differentiated pricing strategies, apart from shorter travel times. Therefore, it is necessary for railway enterprises to enhance their competitiveness through differentiated pricing methods for HSR. In this study, we focus on optimizing a long-distance origin-destination (OD) pair and creating a competitive market environment by considering all operating trains and flights for the selected OD pair. We aim to improve the realism of the study by considering passengers' fully rational travel choice behavior. To reduce the complexity of variables, passengers are grouped based on their expected departure time and income level. A mixed integer linear programing model is developed to address the problem, aiming to minimize overall travel costs for passengers while ensuring that the income of the railway enterprise does not fall below a specified value. By setting this specific value, the maximum revenue of HSR train tickets can be obtained. [ABSTRACT FROM AUTHOR]

Ticket pricing, which is critical to increasing the revenue for high-speed railways, is typically optimized with a given train stop plan. However, the passenger distributions are restricted by fixed train stop plans, and the optimal ticket price scheme may not be achieved. Therefore, a mixed-integer linear programming model is proposed to optimize collaboratively train stop planning and ticket pricing in this study. The objective is to maximize the total ticket revenue, while the total number of train stops is limited to guarantee service quality. Furthermore, equity concerns of passengers are addressed by ensuring that passengers have equitable travel costs and opportunities to access high-speed railways. Finally, numerical experiments are conducted on a hypothetical railway line and the Zhengzhou-Xi'an high-speed railway corridor to demonstrate the application of the proposed approach. The computational results indicate that the proposed method can increase the total ticket revenue by 27% through adding 14 train stops and formulating a new ticket price scheme compared to the traditional method. In addition, the equity performance can be kept at a level of 1.5. [ABSTRACT FROM AUTHOR]

Developing under-exploited passenger rail networks is emerging as an alternative for freight transport. In light of this, we investigate a long-haul freight mode in which additional railcars for carrying shipments are attached to passenger trains, and the shipments can transfer among the trains at intermediate stops. To coordinate space–time schedules of shipments and railcars, we construct a two-level space–time network: one level captures the departure, transshipment, and arrival of shipments; whereas the other level depicts the holding, reshuffling, and repositioning of railcars. Incorporating variables of space–time arc selection and constraints concerning shipment (un-) loading, locomotive pulling capacity, supply–demand coupling, and flow conservation on networks, a binary integer model is established to minimize the total travel cost of both railcars and shipments. The primal problem is decomposed using Lagrangian relaxation. Lagrangian multipliers and dual bounds are approximated by solving the Lagrangian dual. We devise a primal heuristic based on tabu search for expediting high-quality solutions. Numerical experiments demonstrate computational performance and managerial insights. • Investigation of a long-haul freight mode in which additional railcars for freight transport are attached to passenger trains. • A two-level space–time network based on prescribed timetables for shipments and railcars. • A binary model concerning constraints of shipment (un-) loading, locomotive pulling capacity, supply–demand coupling, and flow conservation. • A tabu search framework that leverages the Lagrangian multipliers and thus serves as a primal heuristic. [ABSTRACT FROM AUTHOR]