IDEAS home Printed from https://ideas.repec.org/p/jgu/wpaper/1616.html
   My bibliography  Save this paper

Branch-and-Price-and-Cut for the Vehicle Routing and Truck Driver Scheduling Problem

Author

Listed:
  • Christian Tilk

    (Johannes Gutenberg-University Mainz, Germany)

Abstract

Many governments worldwide have imposed hours of service regulations for truck drivers to ensure that break and rest periods are regularly taken. Transport companies have to take these into account and plan the routes and schedules of their truck drivers simultaneously. This problem is called vehicle routing and truck driver scheduling problem (VRTDSP). With their paper “An exact method for vehicle routing and truck driver scheduling problems” [Technical Report No. 33, Jacobs University, School of Engineering and Science, Bremen, Germany] Goel and Irnich presented the ?rst exact approach to the VRTDSP.They include hours of service regulations in a vehicle routing problem with time windows and use a branch-and-price algorithm to solve it. The main contribution of the paper at hand is to present a sophisticated branch-and-price-and-cut algorithm for the VRTDSP that is based on the parameter-free auxiliary network and the resource extension functions (REFs) de?ned in the work of Goel and Irnich. Their labeling algorithm is extended by means of de?ning backward REFs in order to build a bidirectional labeling. Feasible routes are constructed by a non-trivial merge procedure. Di?erent acceleration techniques are used to speed up the solution process of the pricing problem. In addition, several classes of known valid inequalities are used to further strengthen the LP-relaxation of the master program. We present a detailed computational study to analyze the impact of the di?erent techniques. The resulting algorithm is able to solve all VRTDSP benchmark instances with 25 customers and 44 out of 56 instances with 50 customers in two hours of computation time to proven optimality.

Suggested Citation

  • Christian Tilk, 2016. "Branch-and-Price-and-Cut for the Vehicle Routing and Truck Driver Scheduling Problem," Working Papers 1616, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    • Handle: RePEc:jgu:wpaper:1616
    as

    Download full text from publisher

    File URL: https://download.uni-mainz.de/RePEc/pdf/Discussion_Paper_1616.pdf
    File Function: First version, 2016
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Asvin Goel, 2009. "Vehicle Scheduling and Routing with Drivers' Working Hours," Transportation Science, INFORMS, vol. 43(1), pages 17-26, February.
    3. Alberto Ceselli & Giovanni Righini & Matteo Salani, 2009. "A Column Generation Algorithm for a Rich Vehicle-Routing Problem," Transportation Science, INFORMS, vol. 43(1), pages 56-69, February.
    4. Roberto Roberti & Aristide Mingozzi, 2014. "Dynamic ng-Path Relaxation for the Delivery Man Problem," Transportation Science, INFORMS, vol. 48(3), pages 413-424, August.
    5. Eric Prescott-Gagnon & Guy Desaulniers & Michael Drexl & Louis-Martin Rousseau, 2010. "European Driver Rules in Vehicle Routing with Time Windows," Transportation Science, INFORMS, vol. 44(4), pages 455-473, November.
    6. Mads Jepsen & Bjørn Petersen & Simon Spoorendonk & David Pisinger, 2008. "Subset-Row Inequalities Applied to the Vehicle-Routing Problem with Time Windows," Operations Research, INFORMS, vol. 56(2), pages 497-511, April.
    7. Christian Tilk & Ann-Kathrin Rothenbächer & Timo Gschwind & Stefan Irnich, 2016. "Asymmetry Helps: Dynamic Half-Way Points for Solving Shortest Path Problems with Resource Constraints Faster," Working Papers 1615, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    8. 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.
    9. 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.
    10. Marie-Eve Rancourt & Jean-François Cordeau & Gilbert Laporte, 2013. "Long-Haul Vehicle Routing and Scheduling with Working Hour Rules," Transportation Science, INFORMS, vol. 47(1), pages 81-107, February.
    11. Claudia Bode & Stefan Irnich, 2015. "In-Depth Analysis of Pricing Problem Relaxations for the Capacitated Arc-Routing Problem," Transportation Science, INFORMS, vol. 49(2), pages 369-383, May.
    12. Claudio Contardo & Jean-François Cordeau & Bernard Gendron, 2014. "An Exact Algorithm Based on Cut-and-Column Generation for the Capacitated Location-Routing Problem," INFORMS Journal on Computing, INFORMS, vol. 26(1), pages 88-102, February.
    13. Stefan Irnich & Guy Desaulniers, 2005. "Shortest Path Problems with Resource Constraints," Springer Books, in: Guy Desaulniers & Jacques Desrosiers & Marius M. Solomon (ed.), Column Generation, chapter 0, pages 33-65, Springer.
    14. Goel, Asvin, 2014. "Hours of service regulations in the United States and the 2013 rule change," Transport Policy, Elsevier, vol. 33(C), pages 48-55.
    15. Martin Savelsbergh & Marc Sol, 1998. "Drive: Dynamic Routing of Independent Vehicles," Operations Research, INFORMS, vol. 46(4), pages 474-490, August.
    16. 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.
    17. Moshe Dror, 1994. "Note on the Complexity of the Shortest Path Models for Column Generation in VRPTW," Operations Research, INFORMS, vol. 42(5), pages 977-978, October.
    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. Christian Tilk & Ann-Kathrin Rothenbächer & Timo Gschwind & Stefan Irnich, 2016. "Asymmetry Helps: Dynamic Half-Way Points for Solving Shortest Path Problems with Resource Constraints Faster," Working Papers 1615, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    2. Goel, Asvin, 2018. "Legal aspects in road transport optimization in Europe," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 114(C), pages 144-162.

    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. Asvin Goel & Stefan Irnich, 2017. "An Exact Method for Vehicle Routing and Truck Driver Scheduling Problems," Transportation Science, INFORMS, vol. 51(2), pages 737-754, May.
    2. Christian Tilk & Asvin Goel, 2019. "Bidirectional labeling for solving vehicle routing and truck driver scheduling problems," Working Papers 1914, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    3. Tilk, Christian & Goel, Asvin, 2020. "Bidirectional labeling for solving vehicle routing and truck driver scheduling problems," European Journal of Operational Research, Elsevier, vol. 283(1), pages 108-124.
    4. Luciano Costa & Claudio Contardo & Guy Desaulniers, 2019. "Exact Branch-Price-and-Cut Algorithms for Vehicle Routing," Transportation Science, INFORMS, vol. 53(4), pages 946-985, July.
    5. Asvin Goel & Thibaut Vidal & Adrianus Leendert Kok, 2021. "To team up or not: single versus team driving in European road freight transport," Flexible Services and Manufacturing Journal, Springer, vol. 33(4), pages 879-913, December.
    6. Goel, Asvin, 2018. "Legal aspects in road transport optimization in Europe," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 114(C), pages 144-162.
    7. Christian Tilk & Stefan Irnich, 2017. "Dynamic Programming for the Minimum Tour Duration Problem," Transportation Science, INFORMS, vol. 51(2), pages 549-565, May.
    8. 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.
    9. Diego Pecin & Claudio Contardo & Guy Desaulniers & Eduardo Uchoa, 2017. "New Enhancements for the Exact Solution of the Vehicle Routing Problem with Time Windows," INFORMS Journal on Computing, INFORMS, vol. 29(3), pages 489-502, August.
    10. 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.
    11. 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.
    12. Christian Tilk & Ann-Kathrin Rothenbächer & Timo Gschwind & Stefan Irnich, 2016. "Asymmetry Helps: Dynamic Half-Way Points for Solving Shortest Path Problems with Resource Constraints Faster," Working Papers 1615, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    13. Tilk, Christian & Rothenbächer, Ann-Kathrin & Gschwind, Timo & Irnich, Stefan, 2017. "Asymmetry matters: Dynamic half-way points in bidirectional labeling for solving shortest path problems with resource constraints faster," European Journal of Operational Research, Elsevier, vol. 261(2), pages 530-539.
    14. Maximilian Schiffer & Michael Schneider & Grit Walther & Gilbert Laporte, 2019. "Vehicle Routing and Location Routing with Intermediate Stops: A Review," Transportation Science, INFORMS, vol. 53(2), pages 319-343, March.
    15. Qie He & Stefan Irnich & Yongjia Song, 2018. "Branch-Cut-and-Price for the Vehicle Routing Problem with Time Windows and Convex Node Costs," Working Papers 1804, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    16. Qie He & Stefan Irnich & Yongjia Song, 2019. "Branch-and-Cut-and-Price for the Vehicle Routing Problem with Time Windows and Convex Node Costs," Transportation Science, INFORMS, vol. 53(5), pages 1409-1426, September.
    17. Daiane Maria Genaro Chiroli & Sérgio Fernando Mayerle & João Neiva Figueiredo, 2022. "Using state-space shortest-path heuristics to solve the long-haul point-to-point vehicle routing and driver scheduling problem subject to hours-of-service regulatory constraints," Journal of Heuristics, Springer, vol. 28(1), pages 23-59, February.
    18. Guy Desaulniers & Fausto Errico & Stefan Irnich & Michael Schneider, 2016. "Exact Algorithms for Electric Vehicle-Routing Problems with Time Windows," Operations Research, INFORMS, vol. 64(6), pages 1388-1405, December.
    19. Pottel, Steffen & Goel, Asvin, 2022. "Scheduling activities with time-dependent durations and resource consumptions," European Journal of Operational Research, Elsevier, vol. 301(2), pages 445-457.
    20. Eskandarzadeh, Saman & Fahimnia, Behnam, 2022. "Rest break policy comparison for heavy vehicle drivers in Australia," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 159(C).

    More about this item

    Keywords

    truck driver; routing and scheduling; branch-and-price-and-cut;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:jgu:wpaper:1616. 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: Research Unit IPP (email available below). General contact details of provider: https://edirc.repec.org/data/vlmaide.html .

    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.