Optimization of customized bus routes considering taxi collaborative services at hubs

Yuhang GUO, Kun AN, Wanjing MA

Journal of Tsinghua University(Science and Technology) ›› 2026, Vol. 66 ›› Issue (3) : 617-626.

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Journal of Tsinghua University(Science and Technology) ›› 2026, Vol. 66 ›› Issue (3) : 617-626. DOI: 10.16511/j.cnki.qhdxxb.2025.26.034
Demand Response Customized Bus

Optimization of customized bus routes considering taxi collaborative services at hubs

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Abstract

Objective: Transportation hubs, such as airports and high-speed rail stations, frequently experience taxi shortages, especially at night, when conventional public transit is unavailable. This challenge diminishes passenger satisfaction and reduces the efficiency of passenger dispersal from these hubs. To address this issue, this study proposes an optimization framework for static customized shuttle bus routes that incorporates collaborative taxi services. Unlike traditional door-to-door customized bus services, the proposed approach utilizes customized shuttle buses to transport passengers from the hub to strategic stops closer to their destinations, where taxis are more accessible to complete the final leg of their journeys. Methods: A mixed-integer nonlinear programming model was developed to optimize shuttle bus routes and service frequencies. The objective function minimizes the weighted total costs, encompassing the operational costs for companies and the travel time costs for passengers. The model accounts for the possibility that passengers may depart within a 60.0 min window after making a reservation caused by delays, such as baggage claim. Route design is based on estimated passenger demand patterns. Passengers select services according to the performance level of the collaborative mode, ultimately achieving an equilibrium state. This study integrates passenger choice behavior through a mode choice model that estimates the proportion of travelers opting for either collaborative service or direct taxi service from the hub. To solve this complex model, this study developed a customized algorithm that initially relaxes the problem through fixed proportions for passenger mode choices. The algorithm then designs the customized shuttle bus system, calculates the actual passenger choice probabilities, and iteratively updates the choice proportions until convergence is reached. This study evaluated the proposed model using data from Shanghai Hongqiao Hub and analyzed the system performance under various scenarios, including different service modes, pricing strategies, and vehicle types. Results: A case study of Shanghai Hongqiao Hub revealed the following findings: (1) The optimization yielded four customized shuttle bus routes that efficiently dispersed passenger flow from the hub. The implementation of the collaborative service reduced the system's hourly comprehensive cost by 47% compared with a taxi-only service. The average taxi waiting time at the hub decreased dramatically by 71%, from 30.0 min to 8.7 min. (2) The collaborative approach demonstrated significant advantages over traditional door-to-door customized shuttle bus services, offering substantial advantages in both operational cost savings and passenger appeal. (3) Sensitivity analysis revealed an optimal price point of 1.50 yuan/km that balances operator profitability with service attractiveness to passengers. Additionally, by selecting differentiated vehicle types based on demand density, the profitability of customized shuttle bus services can be significantly increased while also improving service quality. Conclusions: The optimized collaborative service model effectively resolves taxi shortage problems at transportation hubs by integrating strategically designed customized shuttle bus routes with taxi services. This integration ensures an optimal balance between operational efficiency and passenger convenience. The optimization framework and solution algorithm developed in this study provide a practical approach for planning static customized shuttle bus routes and schedules while incorporating cooperation with taxi services. These findings offer valuable guidance for transportation planners and hub managers seeking to increase passenger dispersal efficiency and the overall travel experience through innovative intermodal solutions.

Key words

customized bus / route and frequency optimization / gradient search algorithm / taxi service

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Yuhang GUO , Kun AN , Wanjing MA. Optimization of customized bus routes considering taxi collaborative services at hubs[J]. Journal of Tsinghua University(Science and Technology). 2026, 66(3): 617-626 https://doi.org/10.16511/j.cnki.qhdxxb.2025.26.034

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