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Aggregation techniques for frequency assignment in public transportation

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  • Benjamin Otto

    (Friedrich-Schiller-Universität Jena)

Abstract

In public transportation, frequency assignment is a sub-problem of line planning which is responsible for assigning each route of a line a certain frequency with which they are serviced by vehicles. Frequency assignment is among the most important decision problems for optimizing the waiting times in a transportation network and is often a very complex matter. This paper focuses on different aggregation techniques for reducing the computational effort to obtain (near-)optimal line frequencies. In detail, the influence of different model formulations and strategies for customer input data aggregation are investigated. For this purpose, six models are provided, their computational complexity is investigated and suitable mixed-integer mathematical programs are developed. These models vary in the levels of line utilization detail and predict the resulting travel times. Both aggregation techniques are evaluated according to their influence on the solution quality, which is determined by the transport suppliers’ point of view as forecast accuracy of the weighted number of customers using the transport. This comprehensive computational study reveals that some model formulations reduce the computational effort considerably by only small losses in line frequency quality. Furthermore, dramatically compressed customer data lead to (near-)optimal line frequencies.

Suggested Citation

  • Benjamin Otto, 2019. "Aggregation techniques for frequency assignment in public transportation," Public Transport, Springer, vol. 11(1), pages 51-87, June.
    • Handle: RePEc:spr:pubtra:v:11:y:2019:i:1:d:10.1007_s12469-018-0177-3
    DOI: 10.1007/s12469-018-0177-3
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    1. Dwi Groß & Horst Hamacher & Simone Horn & Anita Schöbel, 2009. "Stop location design in public transportation networks: covering and accessibility objectives," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(2), pages 335-346, December.
    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. Dennis Huisman & Leo G. Kroon & Ramon M. Lentink & Michiel J. C. M. Vromans, 2005. "Operations Research in passenger railway transportation," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(4), pages 467-497, November.
    4. 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.
    5. Bussieck, Michael R. & Kreuzer, Peter & Zimmermann, Uwe T., 1997. "Optimal lines for railway systems," European Journal of Operational Research, Elsevier, vol. 96(1), pages 54-63, January.
    6. LeBlanc, Larry J., 1988. "Transit system network design," Transportation Research Part B: Methodological, Elsevier, vol. 22(5), pages 383-390, October.
    7. Lawrence Frank & Mark Bradley & Sarah Kavage & James Chapman & T. Lawton, 2008. "Urban form, travel time, and cost relationships with tour complexity and mode choice," Transportation, Springer, vol. 35(1), pages 37-54, January.
    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. 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.
    10. 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.
    11. Ceder, Avishai & Wilson, Nigel H. M., 1986. "Bus network design," Transportation Research Part B: Methodological, Elsevier, vol. 20(4), pages 331-344, August.
    12. Jean-François Cordeau & Paolo Toth & Daniele Vigo, 1998. "A Survey of Optimization Models for Train Routing and Scheduling," Transportation Science, INFORMS, vol. 32(4), pages 380-404, November.
    13. David F. Rogers & Robert D. Plante & Richard T. Wong & James R. Evans, 1991. "Aggregation and Disaggregation Techniques and Methodology in Optimization," Operations Research, INFORMS, vol. 39(4), pages 553-582, August.
    14. Michael J. Klier & Knut Haase, 2008. "Line Optimization in Public Transport Systems," Operations Research Proceedings, in: Jörg Kalcsics & Stefan Nickel (ed.), Operations Research Proceedings 2007, pages 473-478, Springer.
    15. Jan-Willem Goossens & Stan van Hoesel & Leo Kroon, 2004. "A Branch-and-Cut Approach for Solving Railway Line-Planning Problems," Transportation Science, INFORMS, vol. 38(3), pages 379-393, August.
    16. Franz J. M. Salzborn, 1972. "Optimum Bus Scheduling," Transportation Science, INFORMS, vol. 6(2), pages 137-148, May.
    17. 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.
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