IDEAS home Printed from https://ideas.repec.org/a/spr/flsman/v31y2019i2d10.1007_s10696-018-9323-0.html
   My bibliography  Save this article

A constraint relaxation-based algorithm for the load-dependent vehicle routing problem with time windows

Author

Listed:
  • Ran Liu

    (Shanghai Jiao Tong University)

  • Zhibin Jiang

    (Shanghai Jiao Tong University)

Abstract

We introduce the load-dependent vehicle routing problem with time windows (LDVRPTW) in this paper. Transportation costs in this new problem, unlike those in the classical vehicle routing problem with time windows (VRPTW), are calculated based on not only the travel distances but also the vehicular loads on travel arcs. To solve this challenging NP-hard problem, we design a new constraint relaxation-based algorithm. In the proposed algorithm, a new constraint relaxation is introduced, i.e., some clients are not visited by a real vehicle and instead are entrusted to an additional virtual vehicle. Based on this relaxation, we present an effective execution scheme of local search procedures. The proposed algorithm is tested on benchmark instances of several special cases of the LDVRPTW, including the VRPTW. Numerical results for different variant problems demonstrate that the algorithm consistently yields impressive results: in particular, for one special variant, namely the fuel consumption rate considered vehicle routing problem (FCR-VRP), the algorithm improves the best-known solutions found by existing state-of-the-art methods.

Suggested Citation

  • Ran Liu & Zhibin Jiang, 2019. "A constraint relaxation-based algorithm for the load-dependent vehicle routing problem with time windows," Flexible Services and Manufacturing Journal, Springer, vol. 31(2), pages 331-353, June.
    • Handle: RePEc:spr:flsman:v:31:y:2019:i:2:d:10.1007_s10696-018-9323-0
    DOI: 10.1007/s10696-018-9323-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10696-018-9323-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10696-018-9323-0?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. Michel Gendreau & Alain Hertz & Gilbert Laporte, 1994. "A Tabu Search Heuristic for the Vehicle Routing Problem," Management Science, INFORMS, vol. 40(10), pages 1276-1290, October.
    2. 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.
    3. 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.
    4. 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.
    5. Thibaut Vidal & Teodor Gabriel Crainic & Michel Gendreau & Nadia Lahrichi & Walter Rei, 2012. "A Hybrid Genetic Algorithm for Multidepot and Periodic Vehicle Routing Problems," Operations Research, INFORMS, vol. 60(3), pages 611-624, June.
    6. Andreas Stenger & Daniele Vigo & Steffen Enz & Michael Schwind, 2013. "An Adaptive Variable Neighborhood Search Algorithm for a Vehicle Routing Problem Arising in Small Package Shipping," Transportation Science, INFORMS, vol. 47(1), pages 64-80, February.
    7. Hemmelmayr, Vera C. & Doerner, Karl F. & Hartl, Richard F., 2009. "A variable neighborhood search heuristic for periodic routing problems," European Journal of Operational Research, Elsevier, vol. 195(3), pages 791-802, June.
    8. Liu, Ran & Xie, Xiaolan & Garaix, Thierry, 2014. "Hybridization of tabu search with feasible and infeasible local searches for periodic home health care logistics," Omega, Elsevier, vol. 47(C), pages 17-32.
    9. Demir, Emrah & Bektaş, Tolga & Laporte, Gilbert, 2012. "An adaptive large neighborhood search heuristic for the Pollution-Routing Problem," European Journal of Operational Research, Elsevier, vol. 223(2), pages 346-359.
    10. Gilbert Laporte, 2009. "Fifty Years of Vehicle Routing," Transportation Science, INFORMS, vol. 43(4), pages 408-416, November.
    11. Zachariadis, Emmanouil E. & Tarantilis, Christos D. & Kiranoudis, Chris T., 2015. "The load-dependent vehicle routing problem and its pick-up and delivery extension," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 158-181.
    12. İbrahim Muter & Ş. İlker Birbil & Güvenç Şahin, 2010. "Combination of Metaheuristic and Exact Algorithms for Solving Set Covering-Type Optimization Problems," INFORMS Journal on Computing, INFORMS, vol. 22(4), pages 603-619, November.
    13. Kramer, Raphael & Subramanian, Anand & Vidal, Thibaut & Cabral, Lucídio dos Anjos F., 2015. "A matheuristic approach for the Pollution-Routing Problem," European Journal of Operational Research, Elsevier, vol. 243(2), pages 523-539.
    14. Emilie Danna & Claude Pape, 2005. "Branch-and-Price Heuristics: A Case Study on the Vehicle Routing Problem with Time Windows," Springer Books, in: Guy Desaulniers & Jacques Desrosiers & Marius M. Solomon (ed.), Column Generation, chapter 0, pages 99-129, Springer.
    15. 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.
    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. Rui Song & Wanen Qin & Wen Shi & Xingjian Xue, 2023. "Optimizing Freight Vehicle Routing in Dynamic Time-Varying Networks with Carbon Dioxide Emission Trajectory Analysis," Sustainability, MDPI, vol. 15(21), pages 1-24, October.
    2. Sina Rastani & Bülent Çatay, 2023. "A large neighborhood search-based matheuristic for the load-dependent electric vehicle routing problem with time windows," Annals of Operations Research, Springer, vol. 324(1), pages 761-793, May.

    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. Vidal, Thibaut & Crainic, Teodor Gabriel & Gendreau, Michel & Prins, Christian, 2013. "Heuristics for multi-attribute vehicle routing problems: A survey and synthesis," European Journal of Operational Research, Elsevier, vol. 231(1), pages 1-21.
    2. Michael Schneider & Andreas Stenger & Dominik Goeke, 2014. "The Electric Vehicle-Routing Problem with Time Windows and Recharging Stations," Transportation Science, INFORMS, vol. 48(4), pages 500-520, November.
    3. 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.
    4. Dayarian, Iman & Crainic, Teodor Gabriel & Gendreau, Michel & Rei, Walter, 2016. "An adaptive large-neighborhood search heuristic for a multi-period vehicle routing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 95(C), pages 95-123.
    5. Paraskevopoulos, Dimitris C. & Laporte, Gilbert & Repoussis, Panagiotis P. & Tarantilis, Christos D., 2017. "Resource constrained routing and scheduling: Review and research prospects," European Journal of Operational Research, Elsevier, vol. 263(3), pages 737-754.
    6. Henriette Koch & Andreas Bortfeldt & Gerhard Wäscher, 2018. "A hybrid algorithm for the vehicle routing problem with backhauls, time windows and three-dimensional loading constraints," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(4), pages 1029-1075, October.
    7. Goeke, Dominik & Schneider, Michael, 2015. "Routing a mixed fleet of electric and conventional vehicles," European Journal of Operational Research, Elsevier, vol. 245(1), pages 81-99.
    8. Schneider, Michael & Schwahn, Fabian & Vigo, Daniele, 2017. "Designing granular solution methods for routing problems with time windows," European Journal of Operational Research, Elsevier, vol. 263(2), pages 493-509.
    9. Ricardo Fukasawa & Qie He & Yongjia Song, 2016. "A Branch-Cut-and-Price Algorithm for the Energy Minimization Vehicle Routing Problem," Transportation Science, INFORMS, vol. 50(1), pages 23-34, February.
    10. Asvin Goel & Thibaut Vidal, 2014. "Hours of Service Regulations in Road Freight Transport: An Optimization-Based International Assessment," Transportation Science, INFORMS, vol. 48(3), pages 391-412, August.
    11. Behnke, Martin & Kirschstein, Thomas & Bierwirth, Christian, 2021. "A column generation approach for an emission-oriented vehicle routing problem on a multigraph," European Journal of Operational Research, Elsevier, vol. 288(3), pages 794-809.
    12. Said Dabia & Emrah Demir & Tom Van Woensel, 2017. "An Exact Approach for a Variant of the Pollution-Routing Problem," Transportation Science, INFORMS, vol. 51(2), pages 607-628, May.
    13. Ehmke, Jan Fabian & Campbell, Ann Melissa & Thomas, Barrett W., 2016. "Vehicle routing to minimize time-dependent emissions in urban areas," European Journal of Operational Research, Elsevier, vol. 251(2), pages 478-494.
    14. Goeke, D. & Schneider, M., 2015. "Routing a Mixed Fleet of Electric and Conventional Vehicles," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 65939, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    15. Franceschetti, Anna & Demir, Emrah & Honhon, Dorothée & Van Woensel, Tom & Laporte, Gilbert & Stobbe, Mark, 2017. "A metaheuristic for the time-dependent pollution-routing problem," European Journal of Operational Research, Elsevier, vol. 259(3), pages 972-991.
    16. Ostermeier, Manuel, 2024. "The supply of convenience stores: Challenges of short-distance routing within the constraints of working time regulations," European Journal of Operational Research, Elsevier, vol. 314(3), pages 997-1012.
    17. Yu Zhang & Zhenzhen Zhang & Andrew Lim & Melvyn Sim, 2021. "Robust Data-Driven Vehicle Routing with Time Windows," Operations Research, INFORMS, vol. 69(2), pages 469-485, March.
    18. Vidal, Thibaut & Crainic, Teodor Gabriel & Gendreau, Michel & Prins, Christian, 2014. "A unified solution framework for multi-attribute vehicle routing problems," European Journal of Operational Research, Elsevier, vol. 234(3), pages 658-673.
    19. Said Dabia & David Lai & Daniele Vigo, 2019. "An Exact Algorithm for a Rich Vehicle Routing Problem with Private Fleet and Common Carrier," Transportation Science, INFORMS, vol. 53(4), pages 986-1000, July.
    20. Chen, Cheng & Demir, Emrah & Huang, Yuan, 2021. "An adaptive large neighborhood search heuristic for the vehicle routing problem with time windows and delivery robots," European Journal of Operational Research, Elsevier, vol. 294(3), pages 1164-1180.

    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:spr:flsman:v:31:y:2019:i:2:d:10.1007_s10696-018-9323-0. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.