Bi-level programming model of truck congestion pricing at container terminals

  • Hao Zhang
  • Qian ZhangEmail author
  • Wenhao Chen
Original Research


Port traffic network design is different from urban traffic flow. Port truck congestion, one of the critical port traffic network design problems, is discussed in this paper. To alleviate the truck congestion in container terminals, issues of modeling truck congestion pricing are addressed. A bi-level programming model is developed to determine the optimal toll rates. The upper level model is to minimize the average truck waiting time by optimizing toll rates of different periods. The lower level is user equilibrium model in which each truck driver chooses its arrival time according to the toll strategy of upper level model. The feedback of upper-level and lower-level model forms the optimal toll strategy. To solve the model, a method based on memetic heuristic is designed. Finally, numerical experiments are provided to illustrate the validity of the proposed model and algorithm. Results indicate that congestion toll can decrease truck’s queuing time effectively. The developed toll pricing model reflects the benefit of truckers and terminal operators, which promotes the use of toll as an efficient tool to alleviate the truck congestion and improve the terminal efficiency.


Traffic network design Container terminal Congestion pricing Truck management Bi-level programming 



This research was sponsored by Project of National Social Science Foundation of China (15BGL202); project of the planning subject of “the 12th Five Year Plan” in national science and technology for the rural development in China: demonstration of key technology and equipment for safe distribution of agricultural logistics (2015BAD18B01); Project of Beijing Philosophy and Social Science (13JGC082);Project of Beijing Municipal Commission of Education (SM201410011002); Project of Innovation Ability Promotion (PXM2016 014213 000033); the Research Foundation for Youth Scholars of Beijing Technology and Business University (QNJJ2017-25).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.School of BusinessBeijing Technology and Business UniversityBeijingChina
  2. 2.School of Transportation ManagementDalian Maritime UniversityDalianChina

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