Soft Computing

, Volume 22, Issue 21, pp 6995–7003 | Cite as

A minimum-cost model for bus timetabling problem

  • Haitao Yu
  • Hongguang Ma
  • Changjing Shang
  • Xiang Li
  • Randong Xiao
  • Yong DuEmail author


In urban traffic, a bus’ running speed is greatly influenced by the time-dependent road conditions. Based on historical GPS data, this paper formulates a bus’ running speed between each pair of adjacent stops as a step function. A minimum-cost timetabling model is proposed, in which the total operation cost consists of the cost for a fixed setup and that for variable fuel consumption. Furthermore, a genetic algorithm with self-crossover operation is used to optimize the proposed integer nonlinear programming model. Finally, a real-world case study of Yuntong 128 bus line in Beijing is presented. Comparisons among popular timetabling models are given, involving time-dependent running speed, minimum running speed, maximum running speed and average running speed. The results demonstrate that the consideration of time-dependent running speed is helpful to improve the prediction accuracy of the fuel consumption cost by around 12.7%.


Bus timetabling Time-dependent speed Fuel consumption Genetic algorithm 



This work was partly supported by Grants from the National Natural Science Foundation of China (No. 71722007), partly by the Welsh Government and Higher Education Funding Council for Wales through the S\(\hat{e}\)r Cymru National Research Network for Low Carbon, Energy and Environment (NRN-LCEE), and partly by a S\(\hat{e}\)r Cymru II COFUND Fellowship, UK.

Compliance with ethical standards

Conflict of interest

All authors declare that they have no conflict of interest in this research.

Human and animal rights

This article does not contain any studies with human participants or animals performed by any of the authors.

Informed consent

Informed consent was obtained from all individual participants included in the study.


  1. Department for Transport, UK (2009) Road vehicle emission factors 2009Google Scholar
  2. Do NAD, Nielsen IE, Chen G, Nielsen P (2016) A simulation-based genetic algorithm approach for reducing emissions from import container pick-up operation at container terminal. Ann Oper Res 242(2):285–301MathSciNetCrossRefGoogle Scholar
  3. Holland JH (1975) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial Intelligence. University of Michigan Press, OxfordzbMATHGoogle Scholar
  4. Hurdle VF (1973) Minimum cost schedules for a public transportation route. Transp Sci 7(2):109–137MathSciNetCrossRefGoogle Scholar
  5. Janson BN (1991) Dynamic traffic assignment for urban road networks. Transp Res Part B Methodol 25(2):143–161CrossRefGoogle Scholar
  6. Kliewer N, Mellouli T, Suhl L (2006) A time–space network based exact optimization model for multi-depot bus scheduling. Eur J Oper Res 175(3):1616–1627CrossRefGoogle Scholar
  7. Lampkin W, Saalmans PD (1967) The design of routes, service frequencies, and schedules for a municipal bus undertaking: a case study. J Oper Res Soc 18(4):375–397CrossRefGoogle Scholar
  8. Mekkaoui O, Palma AD, Lindsey R (2000) Optimal bus timetables and trip timing preferences. Traffic Transp Stud 2000:355–363CrossRefGoogle Scholar
  9. Mohaymany AS, Amiripour SMM (2009) Creating bus timetables under stochastic demand. Int J Ind Eng Prod Res 3:83–91Google Scholar
  10. Oldfield RH, Bly PH (2008) An analytic investigation of optimal bus size. Transp Res Part B 22(5):319–337CrossRefGoogle Scholar
  11. Proon S, Jin M (2015) A genetic algorithm with neighborhood search for the resource-constrained project scheduling problem. Naval Res Logist 58(2):73–82MathSciNetCrossRefGoogle Scholar
  12. Sun CJ, Zhou W, Wang YQ (2008) Scheduling combination and headway optimization of bus rapid transit. J Transp Syst Eng Inf Technol 8(5):61–67Google Scholar
  13. Sun DJ, Xu Y, Peng ZR (2015) Timetable optimization for single bus line based on hybrid vehicle size model. J Traffic Transp Eng (Engl Edit) 2(3):179–186CrossRefGoogle Scholar
  14. Van den Heuvel APR, Van Den Akker JM, Van Kooten M (2008) Integrating timetabling and vehicle scheduling in public bus transportation. Reporte Técnico UU-CS-2008-003, Department of Information and Computing Sciences, Utrecht University, The NetherlandsGoogle Scholar
  15. Weckman G (2015) Applying genetic algorithm to a new location and routing model of hazardous materials. Int J Prod Res 53(3):916–928CrossRefGoogle Scholar
  16. Xiao H, Huang HJ, Tang TQ (2017) Impacts of road conditions on the energy consumption of electric vehicular flow. Mod Phys Lett B 31(11):1750121CrossRefGoogle Scholar
  17. Yan SY, Chen HL (2002) A scheduling model and a solution algorithm for inter-city bus carriers. Transp Res Part A 36:805–825Google Scholar
  18. Yan S, Chi CJ, Tang CH (2006) Inter-city bus routing and timetable setting under stochastic demands. Transp Res Part A 40(7):572–586Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Haitao Yu
    • 1
    • 2
  • Hongguang Ma
    • 3
  • Changjing Shang
    • 4
  • Xiang Li
    • 4
    • 5
  • Randong Xiao
    • 2
  • Yong Du
    • 2
    Email author
  1. 1.School of Computer Science and EngineeringBeihang UniversityBeijingChina
  2. 2.Beijing Key Laboratory for Comprehensive Traffic Operation Monitoring and ServiceBeijing Transportation Information CenterBeijingChina
  3. 3.College of Information Science and TechnologyBeijing University of Chemical TechnologyBeijingChina
  4. 4.Department of Computer ScienceAberystwyth UniversityAberystwythUK
  5. 5.School of Economics and ManagementBeijing University of Chemical TechnologyBeijingChina

Personalised recommendations