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The flex-route transit planning problem with meeting points

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  • Li, Mingyang
  • Wu, Lingxiao
  • Wang, Yadong
  • Tang, Jinjun
  • Feng, Tao

Abstract

As an innovative alternative to ridesharing, flex-route transit (FRT) is widely acknowledged as a promising solution, especially in scenarios in which transportation demand is low or dispersed. This paper addresses the FRT planning problem with meeting points (FRTPP-MP), which conceptualizes each passenger’s pick-up/drop-off request as a set of points (i.e., a cluster) containing the designated pick-up/drop-off point and alternative points (i.e., meeting points), stipulating that only one point in each cluster needs to be visited to fulfill the request. The aim is to minimize both the travel cost of vehicles and the walking cost of passengers by simultaneously optimizing the routes of vehicles and the selection of nodes within their respective clusters. We formulate the FRTPP-MP as a mixed-integer programming (MIP) model and develop an exact branch-and-price (BAP) algorithm to solve it. To tackle the specific challenges of cluster visit restrictions in the pricing problem, we design a tailored bidirectional label correction algorithm (TBLCA), which is further enhanced by a novel acceleration strategy. Extensive computational experiments are conducted based on benchmark instances generated from a real-life FRT system. The numerical results highlight our solution algorithm’s satisfactory performance. Furthermore, managerial insights from a sensitivity analysis suggest that introducing meeting points can substantially reduce the costs associated with FRT.

Suggested Citation

  • Li, Mingyang & Wu, Lingxiao & Wang, Yadong & Tang, Jinjun & Feng, Tao, 2025. "The flex-route transit planning problem with meeting points," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 195(C).
    • Handle: RePEc:eee:transe:v:195:y:2025:i:c:s1366554525000225
    DOI: 10.1016/j.tre.2025.103981
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    as
    1. Mourad, Abood & Puchinger, Jakob & Chu, Chengbin, 2019. "A survey of models and algorithms for optimizing shared mobility," Transportation Research Part B: Methodological, Elsevier, vol. 123(C), pages 323-346.
    2. Quadrifoglio, Luca & Dessouky, Maged M. & Ordonez, Fernando, 2008. "Mobility allowance shuttle transit (MAST) services: MIP formulation and strengthening with logic constraints," European Journal of Operational Research, Elsevier, vol. 185(2), pages 481-494, March.
    3. Li, Mingyang & Tang, Jinjun, 2023. "Simulation-based optimization considering energy consumption for assisted station locations to enhance flex-route transit," Energy, Elsevier, vol. 277(C).
    4. Ozbaygin, Gizem & Ekin Karasan, Oya & Savelsbergh, Martin & Yaman, Hande, 2017. "A branch-and-price algorithm for the vehicle routing problem with roaming delivery locations," Transportation Research Part B: Methodological, Elsevier, vol. 100(C), pages 115-137.
    5. Yang, Weibo & Ke, Liangjun & Wang, David Z.W. & Lam, Jasmine Siu Lee, 2021. "A branch-price-and-cut algorithm for the vehicle routing problem with release and due dates," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 145(C).
    6. Ho, Sin C. & Szeto, W.Y. & Kuo, Yong-Hong & Leung, Janny M.Y. & Petering, Matthew & Tou, Terence W.H., 2018. "A survey of dial-a-ride problems: Literature review and recent developments," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 395-421.
    7. Li, Jiliu & Qin, Hu & Baldacci, Roberto & Zhu, Wenbin, 2020. "Branch-and-price-and-cut for the synchronized vehicle routing problem with split delivery, proportional service time and multiple time windows," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 140(C).
    8. Wenyi Chen & Martijn Mes & Marco Schutten & Job Quint, 2019. "A Ride-Sharing Problem with Meeting Points and Return Restrictions," Transportation Science, INFORMS, vol. 53(2), pages 401-426, March.
    9. Sangveraphunsiri, Tawit & Cassidy, Michael J. & Daganzo, Carlos F., 2022. "Jitney-lite: a flexible-route feeder service for developing countries," Transportation Research Part B: Methodological, Elsevier, vol. 156(C), pages 1-13.
    10. Stiglic, Mitja & Agatz, Niels & Savelsbergh, Martin & Gradisar, Mirko, 2015. "The benefits of meeting points in ride-sharing systems," Transportation Research Part B: Methodological, Elsevier, vol. 82(C), pages 36-53.
    11. Tiniç, Gizem Ozbaygin & Karasan, Oya E. & Kara, Bahar Y. & Campbell, James F. & Ozel, Aysu, 2023. "Exact solution approaches for the minimum total cost traveling salesman problem with multiple drones," Transportation Research Part B: Methodological, Elsevier, vol. 168(C), pages 81-123.
    12. Guy Desaulniers & François Lessard & Ahmed Hadjar, 2008. "Tabu Search, Partial Elementarity, and Generalized k -Path Inequalities for the Vehicle Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 42(3), pages 387-404, August.
    13. Furuhata, Masabumi & Dessouky, Maged & Ordóñez, Fernando & Brunet, Marc-Etienne & Wang, Xiaoqing & Koenig, Sven, 2013. "Ridesharing: The state-of-the-art and future directions," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 28-46.
    14. Mohammad Reihaneh & Ahmed Ghoniem, 2018. "A branch-cut-and-price algorithm for the generalized vehicle routing problem," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 69(2), pages 307-318, February.
    15. Jean-François Cordeau, 2006. "A Branch-and-Cut Algorithm for the Dial-a-Ride Problem," Operations Research, INFORMS, vol. 54(3), pages 573-586, June.
    16. Feng, Tao & Lusby, Richard M. & Zhang, Yongxiang & Peng, Qiyuan, 2024. "Integrating train service route design with passenger flow allocation for an urban rail transit line," European Journal of Operational Research, Elsevier, vol. 313(1), pages 146-170.
    17. Feng, Tao & Lusby, Richard M. & Zhang, Yongxiang & Tao, Siyu & Zhang, Bojian & Peng, Qiyuan, 2024. "A branch-and-price algorithm for integrating urban rail crew scheduling and rostering problems," Transportation Research Part B: Methodological, Elsevier, vol. 183(C).
    18. Faheng Deng & Hu Qin & Jiliu Li & Chun Cheng, 2023. "The Pickup and Delivery Problem with Time Windows and Incompatibility Constraints in Cold Chain Transportation," Transportation Science, INFORMS, vol. 57(2), pages 444-462, March.
    19. Agatz, Niels & Erera, Alan & Savelsbergh, Martin & Wang, Xing, 2012. "Optimization for dynamic ride-sharing: A review," European Journal of Operational Research, Elsevier, vol. 223(2), pages 295-303.
    20. GALARZA MONTENEGRO, Bryan David & SÖRENSEN, Kenneth & VANSTEENWEGEN, Pieter, 2023. "A demand-responsive feeder service with a maximum headway at mandatory stops," Working Papers 2023001, University of Antwerp, Faculty of Business and Economics.
    21. Liu, Xiaohan & Qu, Xiaobo & Ma, Xiaolei, 2021. "Improving flex-route transit services with modular autonomous vehicles," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 149(C).
    22. Stiglic, M. & Agatz, N.A.H. & Savelsbergh, M.W.P. & Gradisar, M., 2015. "The Benefits of Meeting Points in Ride-sharing Systems," ERIM Report Series Research in Management ERS-2015-003-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    23. Stefan Ropke & Jean-François Cordeau, 2009. "Branch and Cut and Price for the Pickup and Delivery Problem with Time Windows," Transportation Science, INFORMS, vol. 43(3), pages 267-286, August.
    24. Xin Li & Wanying Liu & Jingyuan Qiao & Yanhao Li & Jia Hu, 2023. "An Enhanced Semi-Flexible Transit Service with Introducing Meeting Points," Networks and Spatial Economics, Springer, vol. 23(3), pages 487-527, September.
    25. Lera-Romero, Gonzalo & Miranda Bront, Juan José & Soulignac, Francisco J., 2024. "A branch-cut-and-price algorithm for the time-dependent electric vehicle routing problem with time windows," European Journal of Operational Research, Elsevier, vol. 312(3), pages 978-995.
    26. Yue Zheng & Liangpeng Gao & Wenquan Li & Tingsong Wang, 2021. "Vehicle Routing and Scheduling of Flex-Route Transit under a Dynamic Operating Environment," Discrete Dynamics in Nature and Society, Hindawi, vol. 2021, pages 1-10, January.
    27. Yuan, Yuan & Cattaruzza, Diego & Ogier, Maxime & Semet, Frédéric, 2020. "A branch-and-cut algorithm for the generalized traveling salesman problem with time windows," European Journal of Operational Research, Elsevier, vol. 286(3), pages 849-866.
    28. Agatz, Niels A.H. & Erera, Alan L. & Savelsbergh, Martin W.P. & Wang, Xing, 2011. "Dynamic ride-sharing: A simulation study in metro Atlanta," Transportation Research Part B: Methodological, Elsevier, vol. 45(9), pages 1450-1464.
    29. Bettinelli, Andrea & Cacchiani, Valentina & Crainic, Teodor Gabriel & Vigo, Daniele, 2019. "A Branch-and-Cut-and-Price algorithm for the Multi-trip Separate Pickup and Delivery Problem with Time Windows at Customers and Facilities," European Journal of Operational Research, Elsevier, vol. 279(3), pages 824-839.
    30. Adamo, Tommaso & Gendreau, Michel & Ghiani, Gianpaolo & Guerriero, Emanuela, 2024. "A review of recent advances in time-dependent vehicle routing," European Journal of Operational Research, Elsevier, vol. 319(1), pages 1-15.
    31. Sophie N. Parragh & Jorge Pinho de Sousa & Bernardo Almada-Lobo, 2015. "The Dial-a-Ride Problem with Split Requests and Profits," Transportation Science, INFORMS, vol. 49(2), pages 311-334, May.
    32. Roberto Roberti & Mario Ruthmair, 2021. "Exact Methods for the Traveling Salesman Problem with Drone," Transportation Science, INFORMS, vol. 55(2), pages 315-335, March.
    33. Wang, Mengtong & Miao, Lixin & Zhang, Canrong, 2021. "A branch-and-price algorithm for a green location routing problem with multi-type charging infrastructure," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 156(C).
    34. Hua, Shijia & Zeng, Wenjia & Liu, Xinglu & Qi, Mingyao, 2022. "Optimality-guaranteed algorithms on the dynamic shared-taxi problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 164(C).
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