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INTRODUCTION
In recent years, High-Speed Rail (HSR), with a speed of over 300 km per hour, has been introduced globally because HSR emits less CO2 than do cars and airplanes. In countries such as France, Germany, Japan and Korea, HSR has gained a leading market share in the medium to long distance transport markets. Reflecting the trend, the competition between HSR and Air invites many researchers to analyze pricing policies from a point of view of the revenue management (RM) (Park and Ha, 2006; Clever and Hansen, 2008; Adler et al , 2010, and Román et al , 2007). Under the competitive environment, the implemented pricing systems differ from HSR company to company. It can be classified into three types of selling method. (1) A ticket price is predetermined between origin and destination stations and it stays unchanged throughout the selling period. HSR companies in Japan, China and Taiwan are using this type of selling method. (2) Ticket prices are predetermined, but different prices are set depending on the day of week and time zone. This type of method is used by HSR companies in Korea, Germany and America. (3) A price is adjusted based on the sales volume in real time. It is called dynamic pricing and HSR companies in France and the United Kingdom are adapting this method. For airlines, the dynamic pricing is adapted in several low-cost carriers. The question of how such competition affects the dynamic pricing policy on the company's revenue is an important issue to the research area for RM problems. There are very few papers in the area of railway passenger RM problem. Armstrong and Meissner (2010) provide an overview of literatures for both passenger and freight rail RM and list the fundamental differences between the airlines and passenger rail. Sibdari et al (2008) havedeveloped some pricing policies for a multi-product RM problem and analyzed the optimal policies by using Amtrak's sales data.
Many customers take into account ticket prices and their schedules when they make out an itinerary by using the internet. Thus, the demand for a seat depends not only on its price, but also on the price of a similar schedule for a different mode. In this article, we study an RM problem under...