IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v289y2021i3p879-896.html
   My bibliography  Save this article

A branch and cut algorithm for the time-dependent profitable tour problem with resource constraints

Author

Listed:
  • Lera-Romero, Gonzalo
  • Miranda-Bront, Juan José

Abstract

In this paper we study the time-dependent profitable tour problem with resource constraints (TDPTPRC), a generalization of the profitable tour problem (PTP) which includes variable travel times to account for road congestion. In this problem, the set of customers to be served is not given and must be determined based on the profit collected when visited, keeping a balance with the total travel time. We propose a mixed integer linear programming (MILP) formulation that exploits the travel time function to reduce the size of a standard formulation from the literature. We derive four new families of valid inequalities and study the connections among them, as well as their associated separation problems. We develop a tailored Branch and Cut (BC) algorithm including these new families in addition to some well known valid inequalities from related problems. Computational results on four different problems, with alternative resources and objectives, show that the approach is flexible and effective. The algorithm achieves significant reductions in the computing times on benchmark instances from the related literature, and outperforms a recent method proposed for the time-dependent traveling salesman problem with time windows.

Suggested Citation

  • Lera-Romero, Gonzalo & Miranda-Bront, Juan José, 2021. "A branch and cut algorithm for the time-dependent profitable tour problem with resource constraints," European Journal of Operational Research, Elsevier, vol. 289(3), pages 879-896.
    • Handle: RePEc:eee:ejores:v:289:y:2021:i:3:p:879-896
    DOI: 10.1016/j.ejor.2019.07.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221719305788
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2019.07.014?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. Sun, Peng & Veelenturf, Lucas P. & Hewitt, Mike & Van Woensel, Tom, 2018. "The time-dependent pickup and delivery problem with time windows," Transportation Research Part B: Methodological, Elsevier, vol. 116(C), pages 1-24.
    2. Taccari, Leonardo, 2016. "Integer programming formulations for the elementary shortest path problem," European Journal of Operational Research, Elsevier, vol. 252(1), pages 122-130.
    3. Said Dabia & Stefan Ropke & Tom van Woensel & Ton De Kok, 2013. "Branch and Price for the Time-Dependent Vehicle Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 47(3), pages 380-396, August.
    4. Jean-Claude Picard & Maurice Queyranne, 1978. "The Time-Dependent Traveling Salesman Problem and Its Application to the Tardiness Problem in One-Machine Scheduling," Operations Research, INFORMS, vol. 26(1), pages 86-110, February.
    5. Ichoua, Soumia & Gendreau, Michel & Potvin, Jean-Yves, 2003. "Vehicle dispatching with time-dependent travel times," European Journal of Operational Research, Elsevier, vol. 144(2), pages 379-396, January.
    6. Miranda-Bront, Juan José & Méndez-Díaz, Isabel & Zabala, Paula, 2014. "Facets and valid inequalities for the time-dependent travelling salesman problem," European Journal of Operational Research, Elsevier, vol. 236(3), pages 891-902.
    7. Verbeeck, C. & Sörensen, K. & Aghezzaf, E.-H. & Vansteenwegen, P., 2014. "A fast solution method for the time-dependent orienteering problem," European Journal of Operational Research, Elsevier, vol. 236(2), pages 419-432.
    8. Huang, Yixiao & Zhao, Lei & Van Woensel, Tom & Gross, Jean-Philippe, 2017. "Time-dependent vehicle routing problem with path flexibility," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 169-195.
    9. Drexl, Michael, 2013. "A note on the separation of subtour elimination constraints in elementary shortest path problems," European Journal of Operational Research, Elsevier, vol. 229(3), pages 595-598.
    10. Cédric Verbeeck & Pieter Vansteenwegen & El-Houssaine Aghezzaf, 2017. "The time-dependent orienteering problem with time windows: a fast ant colony system," Annals of Operations Research, Springer, vol. 254(1), pages 481-505, July.
    11. Remy Spliet & Said Dabia & Tom Van Woensel, 2018. "The Time Window Assignment Vehicle Routing Problem with Time-Dependent Travel Times," Transportation Science, INFORMS, vol. 52(2), pages 261-276, March.
    12. Sun, Peng & Veelenturf, Lucas P. & Dabia, Said & Van Woensel, Tom, 2018. "The time-dependent capacitated profitable tour problem with time windows and precedence constraints," European Journal of Operational Research, Elsevier, vol. 264(3), pages 1058-1073.
    13. Roberto Baldacci & Aristide Mingozzi & Roberto Roberti, 2011. "New Route Relaxation and Pricing Strategies for the Vehicle Routing Problem," Operations Research, INFORMS, vol. 59(5), pages 1269-1283, October.
    14. Jean-François Cordeau & Gianpaolo Ghiani & Emanuela Guerriero, 2014. "Analysis and Branch-and-Cut Algorithm for the Time-Dependent Travelling Salesman Problem," Transportation Science, INFORMS, vol. 48(1), pages 46-58, February.
    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. Gonzalo Lera-Romero & Juan José Miranda Bront & Francisco J. Soulignac, 2022. "Dynamic Programming for the Time-Dependent Traveling Salesman Problem with Time Windows," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3292-3308, November.

    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. Lu, Jiawei & Nie, Qinghui & Mahmoudi, Monirehalsadat & Ou, Jishun & Li, Chongnan & Zhou, Xuesong Simon, 2022. "Rich arc routing problem in city logistics: Models and solution algorithms using a fluid queue-based time-dependent travel time representation," Transportation Research Part B: Methodological, Elsevier, vol. 166(C), pages 143-182.
    2. Vu, Duc Minh & Hewitt, Mike & Vu, Duc D., 2022. "Solving the time dependent minimum tour duration and delivery man problems with dynamic discretization discovery," European Journal of Operational Research, Elsevier, vol. 302(3), pages 831-846.
    3. 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.
    4. Sun, Peng & Veelenturf, Lucas P. & Hewitt, Mike & Van Woensel, Tom, 2020. "Adaptive large neighborhood search for the time-dependent profitable pickup and delivery problem with time windows," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 138(C).
    5. Pan, Binbin & Zhang, Zhenzhen & Lim, Andrew, 2021. "Multi-trip time-dependent vehicle routing problem with time windows," European Journal of Operational Research, Elsevier, vol. 291(1), pages 218-231.
    6. Sun, Peng & Veelenturf, Lucas P. & Hewitt, Mike & Van Woensel, Tom, 2018. "The time-dependent pickup and delivery problem with time windows," Transportation Research Part B: Methodological, Elsevier, vol. 116(C), pages 1-24.
    7. Avraham, Edison & Raviv, Tal, 2020. "The data-driven time-dependent traveling salesperson problem," Transportation Research Part B: Methodological, Elsevier, vol. 134(C), pages 25-40.
    8. 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.
    9. Cacchiani, Valentina & Contreras-Bolton, Carlos & Toth, Paolo, 2020. "Models and algorithms for the Traveling Salesman Problem with Time-dependent Service times," European Journal of Operational Research, Elsevier, vol. 283(3), pages 825-843.
    10. Thomas R. Visser & Remy Spliet, 2020. "Efficient Move Evaluations for Time-Dependent Vehicle Routing Problems," Transportation Science, INFORMS, vol. 54(4), pages 1091-1112, July.
    11. Remy Spliet & Said Dabia & Tom Van Woensel, 2018. "The Time Window Assignment Vehicle Routing Problem with Time-Dependent Travel Times," Transportation Science, INFORMS, vol. 52(2), pages 261-276, March.
    12. Thibaut Vidal & Rafael Martinelli & Tuan Anh Pham & Minh Hoàng Hà, 2021. "Arc Routing with Time-Dependent Travel Times and Paths," Transportation Science, INFORMS, vol. 55(3), pages 706-724, May.
    13. Liu, Yiming & Roberto, Baldacci & Zhou, Jianwen & Yu, Yang & Zhang, Yu & Sun, Wei, 2023. "Efficient feasibility checks and an adaptive large neighborhood search algorithm for the time-dependent green vehicle routing problem with time windows," European Journal of Operational Research, Elsevier, vol. 310(1), pages 133-155.
    14. Sun, Peng & Veelenturf, Lucas P. & Dabia, Said & Van Woensel, Tom, 2018. "The time-dependent capacitated profitable tour problem with time windows and precedence constraints," European Journal of Operational Research, Elsevier, vol. 264(3), pages 1058-1073.
    15. Guo, Feng & Wei, Qu & Wang, Miao & Guo, Zhaoxia & Wallace, Stein W., 2023. "Deep attention models with dimension-reduction and gate mechanisms for solving practical time-dependent vehicle routing problems," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 173(C).
    16. Tom Woensel, 2019. "Comments on: Perspectives on integer programming for time-dependent models," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 180-183, July.
    17. Hamza Ben Ticha & Nabil Absi & Dominique Feillet & Alain Quilliot & Tom Woensel, 2021. "The Time-Dependent Vehicle Routing Problem with Time Windows and Road-Network Information," SN Operations Research Forum, Springer, vol. 2(1), pages 1-25, March.
    18. Jianbin Xin & Benyang Yu & Andrea D’Ariano & Heshan Wang & Meng Wang, 2022. "Time-dependent rural postman problem: time-space network formulation and genetic algorithm," Operational Research, Springer, vol. 22(3), pages 2943-2972, July.
    19. Merve Kayacı Çodur & Mustafa Yılmaz, 2020. "A time-dependent hierarchical Chinese postman problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(1), pages 337-366, March.
    20. Nicolas Rincon-Garcia & Ben J. Waterson & Tom J. Cherrett, 2018. "Requirements from vehicle routing software: perspectives from literature, developers and the freight industry," Transport Reviews, Taylor & Francis Journals, vol. 38(1), pages 117-138, January.

    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:ejores:v:289:y:2021:i:3:p:879-896. 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/locate/eor .

    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.