Quantifying the air-rail intermodal fares based on dynamic connection times

Air and rail intermodal services (AHISs) are transforming the competitive landscape by bridging gaps in medium- and long-haul markets, thereby fostering the development of a modern, integrated transportation system. Despite their potential, current air-rail intermodal transportation remains largely underexplored, particularly in terms of connections and fares. This paper proposes an integrated pricing strategy by quantifying the impact of fares on operator revenue and passenger connection costs under different arrival scenarios at Zhengzhou Xinzheng International Airport (ZHCC). The panel data are used including the daily data of estimated and actual times for departures and arrivals at ZHCC and its different departure and arrival airports and connected rail stations across January to July 2023. First, the distribution model of flight arrival delay times is analyzed. Then a bi-level programming model is established for different flight scenarios, i.e. early, on-time, and delayed. The upper-level aims to maximize operator revenue, while the lower-level seeks to minimize passengers’ average connection costs. A heuristic algorithm based on sensitivity analysis is then applied to solve the model. To validate the model’s feasibility, the Dalian-Zhengzhou-Fuyang line is used as a case study. The results indicate that the company can achieve maximum revenue by increasing the intermodal fare by 9.29% for early flights, although this results in a 17.54% increase in average connection costs for passengers compared to on-time arrivals. In the case of flight delays, maintaining the new fare close to the original fare, with a slight reduction of 0.55%, is recommended to incentivize passengers to stick to their original travel plans. In theory, this is for the first time in academic research that quantifies the impact of fares on operator revenue and passenger connection costs under various arrival scenarios with bi-level programming. In practice, the quantified results provide intermodal operators with a clear guideline of optimizing their pricing strategy and improving the revenue management based on the dynamic passengers’ arrival timeframes based on historical statistical data. • Based on the panel data of flight arrival times at ZHCC, this study for the first time analyzes the probability distribution of flight delays. It provides a reference and guideline for operators to optimize flight schedules and adjust pricing strategies, thereby enhancing operational efficiency and passenger satisfaction. • This study focuses on the components of actual flight connection time to identify the factors influencing passengers’ choice of travel plans. • The research prices the air-rail products as a whole and designs a bi-level pricing model based on flight arrival scenarios, i.e. early, on time, and delayed arrivals. The upper-level model aims to maximize the company’s revenue, while the lower-level model focuses on minimizing the average connection cost for passengers.