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Frequency optimization in public transportation systems: Formulation and metaheuristic approach

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

Abstract

We study the transit frequency optimization problem, which aims to determine the time interval between subsequent buses for a set of public transportation lines given by their itineraries, i.e., sequences of stops and street sections. The solution should satisfy a given origin–destination demand and a constraint on the available fleet of buses. We propose a new mixed integer linear programming (MILP) formulation for an already existing model, originally formulated as a nonlinear bilevel one. The proposed formulation is able to solve to optimality real small-sized instances of the problem using MILP techniques. For solving larger instances we propose a metaheuristic which accuracy is estimated by comparing against exact results (when possible). Both exact and approximated approaches are tested by using existing cases, including a real one related to a small-city which public transportation system comprises 13 lines. The magnitude of the improvement of that system obtained by applying the proposed methodologies, is comparable with the improvements reported in the literature, related to other real systems. Also, we investigate the applicability of the metaheuristic to a larger-sized real case, comprising more than 130 lines.

Suggested Citation

  • Martínez, Héctor & Mauttone, Antonio & Urquhart, María E., 2014. "Frequency optimization in public transportation systems: Formulation and metaheuristic approach," European Journal of Operational Research, Elsevier, vol. 236(1), pages 27-36.
    • Handle: RePEc:eee:ejores:v:236:y:2014:i:1:p:27-36
    DOI: 10.1016/j.ejor.2013.11.007
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    1. 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.
    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. Fred Glover, 1989. "Tabu Search---Part I," INFORMS Journal on Computing, INFORMS, vol. 1(3), pages 190-206, August.
    4. Szeto, W.Y. & Wu, Yongzhong, 2011. "A simultaneous bus route design and frequency setting problem for Tin Shui Wai, Hong Kong," European Journal of Operational Research, Elsevier, vol. 209(2), pages 141-155, March.
    5. Ceder, Avishai & Wilson, Nigel H. M., 1986. "Bus network design," Transportation Research Part B: Methodological, Elsevier, vol. 20(4), pages 331-344, August.
    6. Han, Anthony F. & Wilson, Nigel H. M., 1982. "The allocation of buses in heavily utilized networks with overlapping routes," Transportation Research Part B: Methodological, Elsevier, vol. 16(3), pages 221-232, June.
    7. Luigi dell’Olio & Angel Ibeas & Francisco Ruisánchez, 2012. "Optimizing bus-size and headway in transit networks," Transportation, Springer, vol. 39(2), pages 449-464, March.
    8. 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.
    9. 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.
    10. Claude Chriqui & Pierre Robillard, 1975. "Common Bus Lines," Transportation Science, INFORMS, vol. 9(2), pages 115-121, May.
    11. 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.
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    Cited by:

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    2. Ren, Hualing & Song, Yingjie & Long, Jiancheng & Si, Bingfeng, 2021. "A new transit assignment model based on line and node strategies," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 121-142.
    3. Cinzia Daraio & Marco Diana & Flavia Di Costa & Claudio Leporelli & Giorgio Matteucci & Alberto Nastasi, 2014. "Efficiency and effectiveness in the urban public transport sector: a critical review with directions for future research," DIAG Technical Reports 2014-14, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    4. Nuri Cihat Onat & Galal M. Abdella & Murat Kucukvar & Adeeb A. Kutty & Munera Al‐Nuaimi & Gürkan Kumbaroğlu & Melih Bulu, 2021. "How eco‐efficient are electric vehicles across Europe? A regionalized life cycle assessment‐based eco‐efficiency analysis," Sustainable Development, John Wiley & Sons, Ltd., vol. 29(5), pages 941-956, September.
    5. Benjamin Otto, 2019. "Aggregation techniques for frequency assignment in public transportation," Public Transport, Springer, vol. 11(1), pages 51-87, June.
    6. Sadrani, Mohammad & Tirachini, Alejandro & Antoniou, Constantinos, 2022. "Vehicle dispatching plan for minimizing passenger waiting time in a corridor with buses of different sizes: Model formulation and solution approaches," European Journal of Operational Research, Elsevier, vol. 299(1), pages 263-282.
    7. Daraio, Cinzia & Diana, Marco & Di Costa, Flavia & Leporelli, Claudio & Matteucci, Giorgio & Nastasi, Alberto, 2016. "Efficiency and effectiveness in the urban public transport sector: A critical review with directions for future research," European Journal of Operational Research, Elsevier, vol. 248(1), pages 1-20.
    8. Ibarra-Rojas, O.J. & Delgado, F. & Giesen, R. & Muñoz, J.C., 2015. "Planning, operation, and control of bus transport systems: A literature review," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 38-75.
    9. Wang, Zhenjie & Zhang, Dezhi & Tavasszy, Lóránt & Fazi, Stefano, 2023. "Integrated multimodal freight service network design and pricing with a competing service integrator and heterogeneous shipper classes," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 179(C).
    10. Dakic, Igor & Yang, Kaidi & Menendez, Monica & Chow, Joseph Y.J., 2021. "On the design of an optimal flexible bus dispatching system with modular bus units: Using the three-dimensional macroscopic fundamental diagram," Transportation Research Part B: Methodological, Elsevier, vol. 148(C), pages 38-59.
    11. Sánchez-Martínez, Gabriel E. & Koutsopoulos, Haris N. & Wilson, Nigel H.M., 2016. "Optimal allocation of vehicles to bus routes using automatically collected data and simulation modelling," Research in Transportation Economics, Elsevier, vol. 59(C), pages 268-276.

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