IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v81y2015ip1p267-288.html
   My bibliography  Save this article

A branch-and-cut algorithm for a realistic dial-a-ride problem

Author

Listed:
  • Liu, Mengyang
  • Luo, Zhixing
  • Lim, Andrew

Abstract

In this paper we study a realistic dial-a-ride problem which simultaneously considers multiple trips, heterogeneous vehicles, multiple request types, configurable vehicle capacity and manpower planning. All of these features originate from practical applications in recent years. To formulate the problem, we propose two mathematical models that use different methods to deal with requests associated with the depot. To further strengthen the models, we propose eight families of valid inequalities, and based on them, we propose a branch-and-cut algorithm to solve the problem. The branch-and-cut algorithm was extensively tested on a set of instances generated according to the data of a real world application. The computational results showed that seven families of inequalities can improve the lower bounds substantially and the branch-and-cut algorithm can solve instances with up to 22 requests within 4h.

Suggested Citation

  • Liu, Mengyang & Luo, Zhixing & Lim, Andrew, 2015. "A branch-and-cut algorithm for a realistic dial-a-ride problem," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 267-288.
    • Handle: RePEc:eee:transb:v:81:y:2015:i:p1:p:267-288
    DOI: 10.1016/j.trb.2015.05.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191261515001113
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.trb.2015.05.009?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dumas, Yvan & Desrosiers, Jacques & Soumis, Francois, 1991. "The pickup and delivery problem with time windows," European Journal of Operational Research, Elsevier, vol. 54(1), pages 7-22, September.
    2. Lysgaard, Jens, 2006. "Reachability cuts for the vehicle routing problem with time windows," European Journal of Operational Research, Elsevier, vol. 175(1), pages 210-223, November.
    3. Xiang, Zhihai & Chu, Chengbin & Chen, Haoxun, 2006. "A fast heuristic for solving a large-scale static dial-a-ride problem under complex constraints," European Journal of Operational Research, Elsevier, vol. 174(2), pages 1117-1139, October.
    4. Luo, Ying & Schonfeld, Paul, 2007. "A rejected-reinsertion heuristic for the static Dial-A-Ride Problem," Transportation Research Part B: Methodological, Elsevier, vol. 41(7), pages 736-755, August.
    5. Kirchler, Dominik & Wolfler Calvo, Roberto, 2013. "A Granular Tabu Search algorithm for the Dial-a-Ride Problem," Transportation Research Part B: Methodological, Elsevier, vol. 56(C), pages 120-135.
    6. Zhang, Zhenzhen & Liu, Mengyang & Lim, Andrew, 2015. "A memetic algorithm for the patient transportation problem," Omega, Elsevier, vol. 54(C), pages 60-71.
    7. Diana, Marco & Dessouky, Maged M., 2004. "A new regret insertion heuristic for solving large-scale dial-a-ride problems with time windows," Transportation Research Part B: Methodological, Elsevier, vol. 38(6), pages 539-557, July.
    8. Augerat, P. & Belenguer, J. M. & Benavent, E. & Corberan, A. & Naddef, D., 1998. "Separating capacity constraints in the CVRP using tabu search," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 546-557, April.
    9. M. W. P. Savelsbergh & M. Sol, 1995. "The General Pickup and Delivery Problem," Transportation Science, INFORMS, vol. 29(1), pages 17-29, February.
    10. Harilaos N. Psaraftis, 1980. "A Dynamic Programming Solution to the Single Vehicle Many-to-Many Immediate Request Dial-a-Ride Problem," Transportation Science, INFORMS, vol. 14(2), pages 130-154, May.
    11. Stefan Ropke & David Pisinger, 2006. "An Adaptive Large Neighborhood Search Heuristic for the Pickup and Delivery Problem with Time Windows," Transportation Science, INFORMS, vol. 40(4), pages 455-472, November.
    12. Jonathan F. Bard & George Kontoravdis & Gang Yu, 2002. "A Branch-and-Cut Procedure for the Vehicle Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 36(2), pages 250-269, May.
    13. Guy Desaulniers, 2010. "Branch-and-Price-and-Cut for the Split-Delivery Vehicle Routing Problem with Time Windows," Operations Research, INFORMS, vol. 58(1), pages 179-192, February.
    14. Cordeau, Jean-François & Laporte, Gilbert, 2003. "A tabu search heuristic for the static multi-vehicle dial-a-ride problem," Transportation Research Part B: Methodological, Elsevier, vol. 37(6), pages 579-594, July.
    15. Roberto Baldacci & Enrico Bartolini & Aristide Mingozzi, 2011. "An Exact Algorithm for the Pickup and Delivery Problem with Time Windows," Operations Research, INFORMS, vol. 59(2), pages 414-426, April.
    16. Jaw, Jang-Jei & Odoni, Amedeo R. & Psaraftis, Harilaos N. & Wilson, Nigel H. M., 1986. "A heuristic algorithm for the multi-vehicle advance request dial-a-ride problem with time windows," Transportation Research Part B: Methodological, Elsevier, vol. 20(3), pages 243-257, June.
    17. 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.
    18. Jean-François Cordeau & Gilbert Laporte, 2007. "The dial-a-ride problem: models and algorithms," Annals of Operations Research, Springer, vol. 153(1), pages 29-46, September.
    19. 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.
    20. Nanry, William P. & Wesley Barnes, J., 2000. "Solving the pickup and delivery problem with time windows using reactive tabu search," Transportation Research Part B: Methodological, Elsevier, vol. 34(2), pages 107-121, February.
    21. Martin Savelsbergh & Marc Sol, 1998. "Drive: Dynamic Routing of Independent Vehicles," Operations Research, INFORMS, vol. 46(4), pages 474-490, August.
    22. Harilaos N. Psaraftis, 1983. "An Exact Algorithm for the Single Vehicle Many-to-Many Dial-A-Ride Problem with Time Windows," Transportation Science, INFORMS, vol. 17(3), pages 351-357, August.
    23. Niklas Kohl & Jacques Desrosiers & Oli B. G. Madsen & Marius M. Solomon & François Soumis, 1999. "2-Path Cuts for the Vehicle Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 33(1), pages 101-116, February.
    24. Coslovich, Luca & Pesenti, Raffaele & Ukovich, Walter, 2006. "A two-phase insertion technique of unexpected customers for a dynamic dial-a-ride problem," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1605-1615, December.
    25. Paolo Toth & Daniele Vigo, 1997. "Heuristic Algorithms for the Handicapped Persons Transportation Problem," Transportation Science, INFORMS, vol. 31(1), pages 60-71, February.
    26. Braekers, Kris & Caris, An & Janssens, Gerrit K., 2014. "Exact and meta-heuristic approach for a general heterogeneous dial-a-ride problem with multiple depots," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 166-186.
    27. Paquette, Julie & Cordeau, Jean-François & Laporte, Gilbert & Pascoal, Marta M.B., 2013. "Combining multicriteria analysis and tabu search for dial-a-ride problems," Transportation Research Part B: Methodological, Elsevier, vol. 52(C), pages 1-16.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Braekers, Kris & Kovacs, Attila A., 2016. "A multi-period dial-a-ride problem with driver consistency," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 355-377.
    2. Schulz, Arne & Pfeiffer, Christian, 2024. "Using fixed paths to improve branch-and-cut algorithms for precedence-constrained routing problems," European Journal of Operational Research, Elsevier, vol. 312(2), pages 456-472.
    3. Baïou, Mourad & Colares, Rafael & Kerivin, Hervé, 2023. "Complexity, algorithmic, and computational aspects of a dial-a-ride type problem," European Journal of Operational Research, Elsevier, vol. 310(2), pages 552-565.
    4. Li, Chongshou & Gong, Lijun & Luo, Zhixing & Lim, Andrew, 2019. "A branch-and-price-and-cut algorithm for a pickup and delivery problem in retailing," Omega, Elsevier, vol. 89(C), pages 71-91.
    5. Farshad Majzoubi & Lihui Bai & Sunderesh S. Heragu, 2021. "The EMS vehicle patient transportation problem during a demand surge," Journal of Global Optimization, Springer, vol. 79(4), pages 989-1006, April.
    6. Ahamed, Tanvir & Zou, Bo & Farazi, Nahid Parvez & Tulabandhula, Theja, 2021. "Deep Reinforcement Learning for Crowdsourced Urban Delivery," Transportation Research Part B: Methodological, Elsevier, vol. 152(C), pages 227-257.
    7. Masmoudi, Mohamed Amine & Hosny, Manar & Demir, Emrah & Genikomsakis, Konstantinos N. & Cheikhrouhou, Naoufel, 2018. "The dial-a-ride problem with electric vehicles and battery swapping stations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 118(C), pages 392-420.
    8. Johnsen, Lennart C. & Meisel, Frank, 2022. "Interrelated trips in the rural dial-a-ride problem with autonomous vehicles," European Journal of Operational Research, Elsevier, vol. 303(1), pages 201-219.
    9. Wei, Xiaoyang & Jia, Shuai & Meng, Qiang & Tan, Kok Choon, 2020. "Tugboat scheduling for container ports," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 142(C).
    10. 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.
    11. Sun, Yanshuo & Chen, Zhi-Long & Zhang, Lei, 2020. "Nonprofit peer-to-peer ridesharing optimization," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 142(C).
    12. Masmoudi, Mohamed Amine & Hosny, Manar & Braekers, Kris & Dammak, Abdelaziz, 2016. "Three effective metaheuristics to solve the multi-depot multi-trip heterogeneous dial-a-ride problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 96(C), pages 60-80.
    13. Mohamed Amine Masmoudi & Manar Hosny & Emrah Demir & Erwin Pesch, 2020. "Hybrid adaptive large neighborhood search algorithm for the mixed fleet heterogeneous dial-a-ride problem," Journal of Heuristics, Springer, vol. 26(1), pages 83-118, February.
    14. Wu, Weitiao & Liu, Ronghui & Jin, Wenzhou, 2016. "Designing robust schedule coordination scheme for transit networks with safety control margins," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 495-519.
    15. Tamke, Felix & Buscher, Udo, 2021. "A branch-and-cut algorithm for the vehicle routing problem with drones," Transportation Research Part B: Methodological, Elsevier, vol. 144(C), pages 174-203.
    16. Gaul, Daniela & Klamroth, Kathrin & Stiglmayr, Michael, 2022. "Event-based MILP models for ridepooling applications," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1048-1063.
    17. 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).
    18. Yves Molenbruch & Kris Braekers & An Caris, 2017. "Typology and literature review for dial-a-ride problems," Annals of Operations Research, Springer, vol. 259(1), pages 295-325, December.
    19. Molenbruch, Yves & Braekers, Kris & Hirsch, Patrick & Oberscheider, Marco, 2021. "Analyzing the benefits of an integrated mobility system using a matheuristic routing algorithm," European Journal of Operational Research, Elsevier, vol. 290(1), pages 81-98.
    20. Sharif Azadeh, Sh. & Atasoy, Bilge & Ben-Akiva, Moshe E. & Bierlaire, M. & Maknoon, M.Y., 2022. "Choice-driven dial-a-ride problem for demand responsive mobility service," Transportation Research Part B: Methodological, Elsevier, vol. 161(C), pages 128-149.
    21. Shang, Huayan & Chang, Yi & Huang, Haijun & Zhao, Fangxia, 2022. "Integration of conventional and customized bus services: An empirical study in Beijing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yves Molenbruch & Kris Braekers & An Caris, 2017. "Typology and literature review for dial-a-ride problems," Annals of Operations Research, Springer, vol. 259(1), pages 295-325, December.
    2. 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.
    3. Hou, Liwen & Li, Dong & Zhang, Dali, 2018. "Ride-matching and routing optimisation: Models and a large neighbourhood search heuristic," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 118(C), pages 143-162.
    4. 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).
    5. Häme, Lauri, 2011. "An adaptive insertion algorithm for the single-vehicle dial-a-ride problem with narrow time windows," European Journal of Operational Research, Elsevier, vol. 209(1), pages 11-22, February.
    6. Mahmoudi, Monirehalsadat & Chen, Junhua & Shi, Tie & Zhang, Yongxiang & Zhou, Xuesong, 2019. "A cumulative service state representation for the pickup and delivery problem with transfers," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 351-380.
    7. Mahmoudi, Monirehalsadat & Zhou, Xuesong, 2016. "Finding optimal solutions for vehicle routing problem with pickup and delivery services with time windows: A dynamic programming approach based on state–space–time network representations," Transportation Research Part B: Methodological, Elsevier, vol. 89(C), pages 19-42.
    8. Liu, Ran & Xie, Xiaolan & Augusto, Vincent & Rodriguez, Carlos, 2013. "Heuristic algorithms for a vehicle routing problem with simultaneous delivery and pickup and time windows in home health care," European Journal of Operational Research, Elsevier, vol. 230(3), pages 475-486.
    9. Schaumann, Sarah K. & Bergmann, Felix M. & Wagner, Stephan M. & Winkenbach, Matthias, 2023. "Route efficiency implications of time windows and vehicle capacities in first- and last-mile logistics," European Journal of Operational Research, Elsevier, vol. 311(1), pages 88-111.
    10. Andrew Lim & Zhenzhen Zhang & Hu Qin, 2017. "Pickup and Delivery Service with Manpower Planning in Hong Kong Public Hospitals," Transportation Science, INFORMS, vol. 51(2), pages 688-705, May.
    11. Kirchler, Dominik & Wolfler Calvo, Roberto, 2013. "A Granular Tabu Search algorithm for the Dial-a-Ride Problem," Transportation Research Part B: Methodological, Elsevier, vol. 56(C), pages 120-135.
    12. Cortés, Cristián E. & Matamala, Martín & Contardo, Claudio, 2010. "The pickup and delivery problem with transfers: Formulation and a branch-and-cut solution method," European Journal of Operational Research, Elsevier, vol. 200(3), pages 711-724, February.
    13. Jean-François Cordeau & Gilbert Laporte, 2007. "The dial-a-ride problem: models and algorithms," Annals of Operations Research, Springer, vol. 153(1), pages 29-46, September.
    14. Xue, Li & Luo, Zhixing & Lim, Andrew, 2016. "Exact approaches for the pickup and delivery problem with loading cost," Omega, Elsevier, vol. 59(PB), pages 131-145.
    15. Ertan Yakıcı & Robert F. Dell & Travis Hartman & Connor McLemore, 2018. "Daily aircraft routing for amphibious ready groups," Annals of Operations Research, Springer, vol. 264(1), pages 477-498, May.
    16. Yuan Qu & Jonathan F. Bard, 2015. "A Branch-and-Price-and-Cut Algorithm for Heterogeneous Pickup and Delivery Problems with Configurable Vehicle Capacity," Transportation Science, INFORMS, vol. 49(2), pages 254-270, May.
    17. Garaix, Thierry & Artigues, Christian & Feillet, Dominique & Josselin, Didier, 2010. "Vehicle routing problems with alternative paths: An application to on-demand transportation," European Journal of Operational Research, Elsevier, vol. 204(1), pages 62-75, July.
    18. Braekers, Kris & Caris, An & Janssens, Gerrit K., 2014. "Exact and meta-heuristic approach for a general heterogeneous dial-a-ride problem with multiple depots," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 166-186.
    19. Detti, Paolo & Papalini, Francesco & Lara, Garazi Zabalo Manrique de, 2017. "A multi-depot dial-a-ride problem with heterogeneous vehicles and compatibility constraints in healthcare," Omega, Elsevier, vol. 70(C), pages 1-14.
    20. Xiang, Zhihai & Chu, Chengbin & Chen, Haoxun, 2006. "A fast heuristic for solving a large-scale static dial-a-ride problem under complex constraints," European Journal of Operational Research, Elsevier, vol. 174(2), pages 1117-1139, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:transb:v:81:y:2015:i:p1:p:267-288. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/548/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.