PDF(1695 KB)
Bi-level programming model for differentiated toll discounts for expressway trucks
Shengyu YAN, Jiaqi ZHAO, Wenbo YOU, Yang LIU, Shijie HAO, Fuwei WU
Journal of Tsinghua University(Science and Technology) ›› 2025, Vol. 65 ›› Issue (7) : 1347-1358.
PDF(1695 KB)
PDF(1695 KB)
Bi-level programming model for differentiated toll discounts for expressway trucks
Objective: Implementing differentiated toll discounts for expressway trucks can lead to a more balanced traffic flow across the road network. Expressway operators hope to make profits by charging truck tolls, while truck groups aim to maximize profits through toll charges, whereas truck groups focus on minimizing travel costs in terms of economics and time. A balance exists between the benefits of both parties; however, determining differentiated toll discounts for expressways to reach this balance is difficult. Methods: (1) Based on consumer surplus theory, key factors affecting freight route selection are identified using the preference survey of traveling behavior, and a bi-level programming model is proposed for determining differentiated toll discounts, incorporating assumptions and constraints. (2) The upper model, considering truck cost and travel time, is a surplus maximization model for expressway operators. It is solved using a novel algorithm enhanced by combining a genetic algorithm with simulated annealing. In the upper model, a lower limit on the financial revenue targets of highway operating enterprises is included the constraints to avoid overflow of lower bound returns during the iteration process. (3) The lower model leverages a logit-based stochastic user equilibrium allocation model for multiple vehicle types under elastic demand, solved using the Frank Wolfe algorithm. A generalized impedance function considering economic and time costs is established in the lower model to demonstrate the impacts of road conditions on truck travel. Cost weighting coefficients are introduced, and calculation methods and recommended values are proposed to integrate economics and time costs. (4) Detailed execution steps are provided for solving algorithms of the upper and lower models. The model also introduces model convergence criteria to optimize the iteration efficiency of the solving algorithm. A fitness function is proposed based on the financial lower bound target, and the upper model is transformed into a minimum value problem, eliminating the constraint of discounted rates. Results: The feasibility of the model is validated using toll collection data of expressway and link traffic data of highways, with three instance highway sections. A reasonable range suitable for implementing differentiated toll discounts can attract trucks back to the expressway, and increasing the daily average traffic volume for each vehicle type. After 43 iterations, the upper model achieves a stable function value. The toll discount rates for small trucks, medium trucks, heavy trucks, and extra-heavy trucks on the instance expressway fall within the ranges of 78.68%-86.27%, 55.82%-65.82%, 47.90%-54.81% and 47.52%-48.31% respectively; consequently, the average truck flow on the expressway increases by 12.24%. Conclusions: The conclusion demonstrates that the bi-level programming model can accurately determine the toll discount range for trucks on expressways; however, even with a discount rate of 4.7% for oversized trucks on nearly 100 km of the actual expressway, attracting all oversized trucks to return to the expressway remains challenging. Fuel and toll fees remarkably impact travel path selection within the generalized impedance function; moreover, the same toll discount produces notable differences in implementation effects across truck types. The research provides support for developing differentiated toll policies for expressways, as well as their subsequent optimization and adjustment.
transportation planning / expressway / toll discounts for trucks / bi-level programming model / consumer surplus theory / solving algorithm
| 1 |
交通运输部公路局. 2021年收费公路统计公报[R]. 北京: 交通运输部, 2022.
Highway Bureau of the Ministry of Transport. Statistical bulletin on toll roads in 2021[R]. Beijing: Ministry of Transport, 2022. (in Chinese)
|
| 2 |
徐瑛, 虞明远. 基于差异化公共性的公路收费问题解析[J]. 公路交通科技, 2012, 29 (4): 149-152, 158.
|
| 3 |
|
| 4 |
|
| 5 |
|
| 6 |
|
| 7 |
ARUNOTAYANUN K, POLAK J W. Accounting for supply chain structures in modelling freight mode choice behaviour[C]//European Transport Conference, 2009 Proceedings. Leiden Leeuwenhorst Conference Centre, Netherlands: Association for European Transport, 2009: 1-19.
|
| 8 |
|
| 9 |
|
| 10 |
张戎, 李璐, 简文良. 城市货运车辆选择行为模型及应用[J]. 交通运输系统工程与信息, 2018, 18 (4): 135- 141.
|
| 11 |
周国华, 陈德捷, 周芳汀, 等. 高速铁路与公路客运竞争的市场分担率模型研究[J]. 铁道学报, 2020, 42 (1): 1- 8.
|
| 12 |
张小强, 张旭, 彭燕. 考虑容量约束的铁路货运竞争性定价策略研究[J]. 交通运输系统工程与信息, 2017, 17 (6): 1- 6.
|
| 13 |
|
| 14 |
|
| 15 |
|
| 16 |
|
| 17 |
|
| 18 |
闫晟煜, 肖润谋, 杨铭. 在地公路货物运输量统计方法[J]. 交通运输工程学报, 2020, 20 (6): 210- 217.
|
| 19 |
康凤伟, 李雪梅, 李金宇, 等. 无车承运人参与下的公铁联运主体利益博弈研究[J]. 铁道学报, 2020, 42 (11): 22- 28.
|
| 20 |
刘玮, 万燕鸣, 陈思源, 等. 基于场景模拟的公路货运新能源车成本效益分析研究[J]. 中国环境科学, 2023, 43 (10): 5624- 5632.
|
| 21 |
|
| 22 |
|
| 23 |
|
| 24 |
|
| 25 |
黄亚飞, 刘涛. 路网最优费率的双层规划模型及算法[J]. 交通运输工程学报, 2006, 6 (4): 105- 111.
|
| 26 |
魏波, 马耀兰. 随机平衡配流与次优拥挤收费的双层规划模型构建与求解[J]. 统计与决策, 2015 (2): 48- 51.
|
| 27 |
倪娜, 秦建平, 王垒. 客车专用高速公路通行能力研究[J]. 铁道科学与工程学报, 2016, 13 (9): 1864- 1871.
|
| 28 |
|
| 29 |
|
| 30 |
|
| 31 |
刘伟铭, 姜山. 基于GASA混合优化策略的双层规划模型求解算法研究[J]. 土木工程学报, 2003, 36 (7): 27- 32.
|
| 32 |
肖武, 王开锋, 姜晓滨, 等. 遗传-模拟退火算法优化设计管壳式换热器[J]. 清华大学学报(自然科学版), 2016, 56 (7): 728- 734.
|
| 33 |
中华人民共和国交通运输部. 公路工程技术标准: JT/G B01-2014[S]. 北京: 人民交通出版社股份有限公司, 2014.
Ministry of Transport of the People's Republic of China. Technical standard of highway engineering: JT/G B01-2014[S]. Beijing: China Communications Press, 2014. (in Chinese)
|
/
| 〈 |
|
〉 |