IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v202y2010i3p756-763.html
   My bibliography  Save this article

An exact algorithm for a vehicle routing problem with time windows and multiple use of vehicles

Author

Listed:
  • Azi, Nabila
  • Gendreau, Michel
  • Potvin, Jean-Yves

Abstract

The vehicle routing problem with multiple use of vehicles is a variant of the classical vehicle routing problem. It arises when each vehicle performs several routes during the workday due to strict time limits on route duration (e.g., when perishable goods are transported). The routes are defined over customers with a revenue, a demand and a time window. Given a fixed-size fleet of vehicles, it might not be possible to serve all customers. Thus, the customers must be chosen based on their associated revenue minus the traveling cost to reach them. We introduce a branch-and-price approach to address this problem where lower bounds are computed by solving the linear programming relaxation of a set packing formulation, using column generation. The pricing subproblems are elementary shortest path problems with resource constraints. Computational results are reported on euclidean problems derived from well-known benchmark instances for the vehicle routing problem with time windows.

Suggested Citation

  • Azi, Nabila & Gendreau, Michel & Potvin, Jean-Yves, 2010. "An exact algorithm for a vehicle routing problem with time windows and multiple use of vehicles," European Journal of Operational Research, Elsevier, vol. 202(3), pages 756-763, May.
    • Handle: RePEc:eee:ejores:v:202:y:2010:i:3:p:756-763
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(09)00495-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Ann Melissa Campbell & Martin W. P. Savelsbergh, 2005. "Decision Support for Consumer Direct Grocery Initiatives," Transportation Science, INFORMS, vol. 39(3), pages 313-327, August.
    2. Chao, I-Ming & Golden, Bruce L. & Wasil, Edward A., 1996. "A fast and effective heuristic for the orienteering problem," European Journal of Operational Research, Elsevier, vol. 88(3), pages 475-489, February.
    3. Azi, Nabila & Gendreau, Michel & Potvin, Jean-Yves, 2007. "An exact algorithm for a single-vehicle routing problem with time windows and multiple routes," European Journal of Operational Research, Elsevier, vol. 178(3), pages 755-766, May.
    4. Cynthia Barnhart & Ellis L. Johnson & George L. Nemhauser & Martin W. P. Savelsbergh & Pamela H. Vance, 1998. "Branch-and-Price: Column Generation for Solving Huge Integer Programs," Operations Research, INFORMS, vol. 46(3), pages 316-329, June.
    5. Marius M. Solomon, 1987. "Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints," Operations Research, INFORMS, vol. 35(2), pages 254-265, April.
    6. J C S Brandão & A Mercer, 1998. "The multi-trip vehicle routing problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 49(8), pages 799-805, August.
    7. Ann Melissa Campbell & Martin Savelsbergh, 2004. "Efficient Insertion Heuristics for Vehicle Routing and Scheduling Problems," Transportation Science, INFORMS, vol. 38(3), pages 369-378, August.
    8. Brandao, Jose & Mercer, Alan, 1997. "A tabu search algorithm for the multi-trip vehicle routing and scheduling problem," European Journal of Operational Research, Elsevier, vol. 100(1), pages 180-191, July.
    9. Dominique Feillet & Pierre Dejax & Michel Gendreau, 2005. "Traveling Salesman Problems with Profits," Transportation Science, INFORMS, vol. 39(2), pages 188-205, May.
    Full references (including those not matched with items on IDEAS)

    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. Tang, Jiafu & Yu, Yang & Li, Jia, 2015. "An exact algorithm for the multi-trip vehicle routing and scheduling problem of pickup and delivery of customers to the airport," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 73(C), pages 114-132.
    2. Fleckenstein, David & Klein, Robert & Steinhardt, Claudius, 2023. "Recent advances in integrating demand management and vehicle routing: A methodological review," European Journal of Operational Research, Elsevier, vol. 306(2), pages 499-518.
    3. Diego Cattaruzza & Nabil Absi & Dominique Feillet, 2018. "Vehicle routing problems with multiple trips," Annals of Operations Research, Springer, vol. 271(1), pages 127-159, December.
    4. Diego Cattaruzza & Nabil Absi & Dominique Feillet, 2016. "Vehicle routing problems with multiple trips," 4OR, Springer, vol. 14(3), pages 223-259, September.
    5. 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.
    6. J. Arturo Castillo-Salazar & Dario Landa-Silva & Rong Qu, 2016. "Workforce scheduling and routing problems: literature survey and computational study," Annals of Operations Research, Springer, vol. 239(1), pages 39-67, April.
    7. Koch, Sebastian & Klein, Robert, 2020. "Route-based approximate dynamic programming for dynamic pricing in attended home delivery," European Journal of Operational Research, Elsevier, vol. 287(2), pages 633-652.
    8. Balcik, Burcu, 2017. "Site selection and vehicle routing for post-disaster rapid needs assessment," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 101(C), pages 30-58.
    9. Gunawan, Aldy & Lau, Hoong Chuin & Vansteenwegen, Pieter, 2016. "Orienteering Problem: A survey of recent variants, solution approaches and applications," European Journal of Operational Research, Elsevier, vol. 255(2), pages 315-332.
    10. Rahma Lahyani & Mahdi Khemakhem & Frédéric Semet, 2017. "A unified matheuristic for solving multi-constrained traveling salesman problems with profits," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(3), pages 393-422, September.
    11. Cattaruzza, Diego & Absi, Nabil & Feillet, Dominique & Vidal, Thibaut, 2014. "A memetic algorithm for the Multi Trip Vehicle Routing Problem," European Journal of Operational Research, Elsevier, vol. 236(3), pages 833-848.
    12. Azi, Nabila & Gendreau, Michel & Potvin, Jean-Yves, 2007. "An exact algorithm for a single-vehicle routing problem with time windows and multiple routes," European Journal of Operational Research, Elsevier, vol. 178(3), pages 755-766, May.
    13. Niels Agatz & Yingjie Fan & Daan Stam, 2021. "The Impact of Green Labels on Time Slot Choice and Operational Sustainability," Production and Operations Management, Production and Operations Management Society, vol. 30(7), pages 2285-2303, July.
    14. Huang, Nan & Li, Jiliu & Zhu, Wenbin & Qin, Hu, 2021. "The multi-trip vehicle routing problem with time windows and unloading queue at depot," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).
    15. Wouter Souffriau & Pieter Vansteenwegen & Greet Vanden Berghe & Dirk Van Oudheusden, 2013. "The Multiconstraint Team Orienteering Problem with Multiple Time Windows," Transportation Science, INFORMS, vol. 47(1), pages 53-63, February.
    16. Agatz, N.A.H. & Fan, Y. & Stam, D.A., 2020. "Going green: the effect of green labels on delivery time slot choices," ERIM Report Series Research in Management ERS-2020-009-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.
    17. Macedo, Rita & Alves, Cláudio & Valério de Carvalho, J.M. & Clautiaux, François & Hanafi, Saïd, 2011. "Solving the vehicle routing problem with time windows and multiple routes exactly using a pseudo-polynomial model," European Journal of Operational Research, Elsevier, vol. 214(3), pages 536-545, November.
    18. Robert Klein & Jochen Mackert & Michael Neugebauer & Claudius Steinhardt, 2018. "A model-based approximation of opportunity cost for dynamic pricing in attended home delivery," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(4), pages 969-996, October.
    19. Lu, Quan & Dessouky, Maged M., 2006. "A new insertion-based construction heuristic for solving the pickup and delivery problem with time windows," European Journal of Operational Research, Elsevier, vol. 175(2), pages 672-687, December.
    20. Gutiérrez-Jarpa, Gabriel & Desaulniers, Guy & Laporte, Gilbert & Marianov, Vladimir, 2010. "A branch-and-price algorithm for the Vehicle Routing Problem with Deliveries, Selective Pickups and Time Windows," European Journal of Operational Research, Elsevier, vol. 206(2), pages 341-349, 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:ejores:v:202:y:2010:i:3:p:756-763. 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.