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Mathematical programming formulations for transit network design

Author

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  • Cancela, Héctor
  • Mauttone, Antonio
  • Urquhart, María E.

Abstract

In this work, we study the transit network design problem from the perspective of mathematical programming. More precisely, we consider the problem of defining the number and itinerary of bus routes and their frequencies, for a public transportation system. In this problem, the routes should be defined in terms of a given infrastructure of streets and stops and should cover a given origin–destination demand. The solution (routes and frequencies) should be convenient for the users and the operators. We review existing mathematical programming formulations and propose a new one, paying attention to the following aspects of public transportation systems, that are identified as key elements in order to have a realistic model: (a) the interest of the users, (b) the interest of the operators, (c) the behavior of the users, and (d) constraints regarding transfer, infrastructure and bus capacity. First, we discuss the formulations existing on the literature, in terms of the aspects mentioned above. Second, we propose a mixed integer linear programming (MILP) formulation, that incorporates the waiting time and the existence of multiple lines in the behavior of the users. We validate the proposed formulation using several cases, including a real one. Also, we compare the obtained results against results from the existing literature. In order to include transfer, infrastructure and bus capacity constraints, we propose an extension to the formulation and we discuss its impact in the structure of the model, based on concepts of bi-level mathematical programming. The mathematical formulations developed contribute towards a more realistic modeling effort, taking into account important aspects of the real system which were not included in previous proposals in the literature.

Suggested Citation

  • Cancela, Héctor & Mauttone, Antonio & Urquhart, María E., 2015. "Mathematical programming formulations for transit network design," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 17-37.
    • Handle: RePEc:eee:transb:v:77:y:2015:i:c:p:17-37
    DOI: 10.1016/j.trb.2015.03.006
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    as
    1. Zhao, Fang & Zeng, Xiaogang, 2008. "Optimization of transit route network, vehicle headways and timetables for large-scale transit networks," European Journal of Operational Research, Elsevier, vol. 186(2), pages 841-855, April.
    2. Spiess, Heinz & Florian, Michael, 1989. "Optimal strategies: A new assignment model for transit networks," Transportation Research Part B: Methodological, Elsevier, vol. 23(2), pages 83-102, April.
    3. Zhao, Jiamin & Dessouky, Maged, 2008. "Service capacity design problems for mobility allowance shuttle transit systems," Transportation Research Part B: Methodological, Elsevier, vol. 42(2), pages 135-146, February.
    4. Cepeda, M. & Cominetti, R. & Florian, M., 2006. "A frequency-based assignment model for congested transit networks with strict capacity constraints: characterization and computation of equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 40(6), pages 437-459, July.
    5. T. L. Magnanti & R. T. Wong, 1984. "Network Design and Transportation Planning: Models and Algorithms," Transportation Science, INFORMS, vol. 18(1), pages 1-55, February.
    6. Szeto, W.Y. & Jiang, Y., 2014. "Transit route and frequency design: Bi-level modeling and hybrid artificial bee colony algorithm approach," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 235-263.
    7. Farahani, Reza Zanjirani & Miandoabchi, Elnaz & Szeto, W.Y. & Rashidi, Hannaneh, 2013. "A review of urban transportation network design problems," European Journal of Operational Research, Elsevier, vol. 229(2), pages 281-302.
    8. Gao, Ziyou & Sun, Huijun & Shan, Lian Long, 2004. "A continuous equilibrium network design model and algorithm for transit systems," Transportation Research Part B: Methodological, Elsevier, vol. 38(3), pages 235-250, March.
    9. Quentin K. Wan & Hong K. Lo, 2009. "Congested multimodal transit network design," Public Transport, Springer, vol. 1(3), pages 233-251, August.
    10. Nguyen, S. & Pallottino, S., 1988. "Equilibrium traffic assignment for large scale transit networks," European Journal of Operational Research, Elsevier, vol. 37(2), pages 176-186, November.
    11. Enrique Fernández L., J. & de Cea Ch., Joaquin & Malbran, R. Henry, 2008. "Demand responsive urban public transport system design: Methodology and application," Transportation Research Part A: Policy and Practice, Elsevier, vol. 42(7), pages 951-972, August.
    12. Schmid, Verena, 2014. "Hybrid large neighborhood search for the bus rapid transit route design problem," European Journal of Operational Research, Elsevier, vol. 238(2), pages 427-437.
    13. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    14. Asadi Bagloee, Saeed & Ceder, Avishai (Avi), 2011. "Transit-network design methodology for actual-size road networks," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1787-1804.
    15. José R. Correa & Andreas S. Schulz & Nicolás E. Stier-Moses, 2004. "Selfish Routing in Capacitated Networks," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 961-976, November.
    16. Guihaire, Valérie & Hao, Jin-Kao, 2008. "Transit network design and scheduling: A global review," Transportation Research Part A: Policy and Practice, Elsevier, vol. 42(10), pages 1251-1273, December.
    17. Belgacem Bouzaïene-Ayari & Michel Gendreau & Sang Nguyen, 2001. "Modeling Bus Stops in Transit Networks: A Survey and New Formulations," Transportation Science, INFORMS, vol. 35(3), pages 304-321, August.
    18. Jose L. Walteros & Andrés L. Medaglia & Germán Riaño, 2015. "Hybrid Algorithm for Route Design on Bus Rapid Transit Systems," Transportation Science, INFORMS, vol. 49(1), pages 66-84, February.
    19. Joaquín de Cea & Enrique Fernández, 1993. "Transit Assignment for Congested Public Transport Systems: An Equilibrium Model," Transportation Science, INFORMS, vol. 27(2), pages 133-147, May.
    20. Nielsen, Otto Anker, 2000. "A stochastic transit assignment model considering differences in passengers utility functions," Transportation Research Part B: Methodological, Elsevier, vol. 34(5), pages 377-402, June.
    21. Claude Chriqui & Pierre Robillard, 1975. "Common Bus Lines," Transportation Science, INFORMS, vol. 9(2), pages 115-121, May.
    22. Lownes, Nicholas E. & Machemehl, Randy B., 2010. "Exact and heuristic methods for public transit circulator design," Transportation Research Part B: Methodological, Elsevier, vol. 44(2), pages 309-318, February.
    23. Homero Larrain & Juan Muñoz, 2008. "Public Transit Corridor Assignment Assuming Congestion Due to Passenger Boarding and Alighting," Networks and Spatial Economics, Springer, vol. 8(2), pages 241-256, September.
    24. Ceder, Avishai & Wilson, Nigel H. M., 1986. "Bus network design," Transportation Research Part B: Methodological, Elsevier, vol. 20(4), pages 331-344, August.
    25. Guan, J.F. & Yang, Hai & Wirasinghe, S.C., 2006. "Simultaneous optimization of transit line configuration and passenger line assignment," Transportation Research Part B: Methodological, Elsevier, vol. 40(10), pages 885-902, December.
    26. Leiva, Carola & Muñoz, Juan Carlos & Giesen, Ricardo & Larrain, Homero, 2010. "Design of limited-stop services for an urban bus corridor with capacity constraints," Transportation Research Part B: Methodological, Elsevier, vol. 44(10), pages 1186-1201, December.
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