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Optimization models for the single delay management problem in public transportation

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  • Heilporn, Géraldine
  • De Giovanni, Luigi
  • Labbé, Martine

Abstract

Passengers travelling in public transportation networks often have to use different lines to cover the trip from their origin to the desired destination. As a consequence, the reliability of connections between vehicles is a key issue for the attractiveness of the intermodal transportation network and it is strongly affected by some unpredictable events like breakdowns or vehicle delays. In such cases, a decision is required to determine if the connected vehicles should wait for the delayed ones or keep their schedule. The delay management problem (DMP) consists in defining the wait/depart policy which minimizes the total delay on the network. In this work, we present two equivalent mixed integer linear programming models for the DMP with a single initial delay, able to reduce the number of variables with respect to the formulations proposed by the literature. The two models are solved by a branch and cut procedure and by a constraint generation approach respectively, and preliminary computational results are presented.

Suggested Citation

  • Heilporn, Géraldine & De Giovanni, Luigi & Labbé, Martine, 2008. "Optimization models for the single delay management problem in public transportation," European Journal of Operational Research, Elsevier, vol. 189(3), pages 762-774, September.
    • Handle: RePEc:eee:ejores:v:189:y:2008:i:3:p:762-774
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    1. Robert Fourer & David M. Gay & Brian W. Kernighan, 1990. "A Modeling Language for Mathematical Programming," Management Science, INFORMS, vol. 36(5), pages 519-554, May.
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    1. Twan Dollevoet & Dennis Huisman & Marie Schmidt & Anita Schöbel, 2012. "Delay Management with Rerouting of Passengers," Transportation Science, INFORMS, vol. 46(1), pages 74-89, February.
    2. Julius Pätzold, 2021. "Finding robust periodic timetables by integrating delay management," Public Transport, Springer, vol. 13(2), pages 349-374, June.
    3. Yiting Xing & Ling Li & Zhuming Bi & Marzena Wilamowska‐Korsak & Li Zhang, 2013. "Operations Research (OR) in Service Industries: A Comprehensive Review," Systems Research and Behavioral Science, Wiley Blackwell, vol. 30(3), pages 300-353, May.
    4. Sato, Keisuke & Fukumura, Naoto, 2012. "Real-time freight locomotive rescheduling and uncovered train detection during disruption," European Journal of Operational Research, Elsevier, vol. 221(3), pages 636-648.
    5. Cristina ALPOPI & Sofia Elena COLESCA, 2010. "Management Of Public Passenger Transport Services During Economic Crisis," Proceedings of Administration and Public Management International Conference, Research Centre in Public Administration and Public Services, Bucharest, Romania, vol. 6(1), pages 104-121, June.
    6. Dollevoet, T.A.B. & Huisman, D. & Schöbel, A. & Schmidt, M.E., 2012. "Delay Management including Capacities of Stations," Econometric Institute Research Papers EI 2012-22, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    7. Anita Schöbel & Silvia Schwarze, 2013. "Finding delay-resistant line concepts using a game-theoretic approach," Netnomics, Springer, vol. 14(3), pages 95-117, November.
    8. Dollevoet, T.A.B. & Huisman, D. & Schmidt, M.E. & Schöbel, A., 2010. "Delay Management with Re-Routing of Passengers," Econometric Institute Research Papers EI 2010-31, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    9. Twan Dollevoet & Dennis Huisman & Leo Kroon & Marie Schmidt & Anita Schöbel, 2015. "Delay Management Including Capacities of Stations," Transportation Science, INFORMS, vol. 49(2), pages 185-203, May.
    10. Schön, Cornelia & König, Eva, 2018. "A stochastic dynamic programming approach for delay management of a single train line," European Journal of Operational Research, Elsevier, vol. 271(2), pages 501-518.
    11. Veronica Dal Sasso & Luigi De Giovanni & Martine Labbé, 2019. "Strengthened Formulations and Valid Inequalities for Single Delay Management in Public Transportation," Transportation Science, INFORMS, vol. 53(5), pages 1271-1286, September.
    12. Mizuyo Takamatsu & Azuma Taguchi, 2020. "Bus Timetable Design to Ensure Smooth Transfers in Areas with Low-Frequency Public Transportation Services," Transportation Science, INFORMS, vol. 54(5), pages 1238-1250, September.
    13. Michael Schachtebeck & Anita Schöbel, 2010. "To Wait or Not to Wait---And Who Goes First? Delay Management with Priority Decisions," Transportation Science, INFORMS, vol. 44(3), pages 307-321, August.
    14. repec:rom:campco:v:6:y:2010:i:1:p:104-121 is not listed on IDEAS
    15. Li, Wenxin & Peng, Qiyuan & Wen, Chao & Wang, Pengling & Lessan, Javad & Xu, Xinyue, 2020. "Joint optimization of delay-recovery and energy-saving in a metro system: A case study from China," Energy, Elsevier, vol. 202(C).
    16. König, Eva & Schön, Cornelia, 2021. "Railway delay management with passenger rerouting considering train capacity constraints," European Journal of Operational Research, Elsevier, vol. 288(2), pages 450-465.
    17. Eva König, 2020. "A review on railway delay management," Public Transport, Springer, vol. 12(2), pages 335-361, June.
    18. Dollevoet, T.A.B. & Corman, F. & D'Ariano, A. & Huisman, D., 2012. "An Iterative Optimization Framework for Delay Management and Train Scheduling," Econometric Institute Research Papers EI 2012-10, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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