IDEAS home Printed from https://ideas.repec.org/p/jgu/wpaper/1801.html
   My bibliography  Save this paper

Nested Branch-and-Price-and-Cut for Vehicle Routing Problems with Multiple Resource Interdependencies

Author

Listed:
  • Christian Tilk

    (Johannes Gutenberg-University Mainz, Germany)

  • Michael Drexl

    (Faculty of Applied Natural Sciences and Industrial Engineering, Deggendorf, Germany)

  • Stefan Irnich

    (Johannes Gutenberg-University Mainz, Germany)

Abstract

This paper considers vehicle routing problems (VRPs) with multiple resource interdependencies and addresses the development and computational evaluation of an exact branch-and-price-and-cut algorithm for their solution. An interdependency between two resources means that the two resource consumptions influence one another in such a way that a tradeoff exists between them. This impacts the feasibility and/or the cost of a solution. The subproblem in branch-and-price-and-cut procedures for VRPs is very often a variant of the shortestpath problem with resource constraints (SPPRC). For the exact solution of many SPPRC variants, dynamicprogramming based labeling algorithms are predominant. The tradeoffs in problems with multiple resource interdependencies, however, render the application of labeling algorithms unpromising. This is because complex data structures for managing the tradeoff curves are necessary and only weak dominance criteria are possible, so that the labeling algorithm becomes almost a pure enumeration. Therefore, we propose to solve also the SPPRC subproblem with branch-and-price-and-cut. This results in a two-level, nested branch-and-price-and-cut algorithm. We analyze different variants of the algorithm to enable the exchange of columns and also rows between the different levels. To demonstrate the computational viability of our approach, we perform computational experiments on a prototypical VRP with time windows, minimal and maximal delivery quantities for each customer, a customer-dependent profit paid for each demand unit delivered, and temporal synchronization constraints between some pairs of customers. In this problem, tradeoffs exist between cost and load and between cost and time.

Suggested Citation

  • Christian Tilk & Michael Drexl & Stefan Irnich, 2018. "Nested Branch-and-Price-and-Cut for Vehicle Routing Problems with Multiple Resource Interdependencies," Working Papers 1801, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
  • Handle: RePEc:jgu:wpaper:1801
    as

    Download full text from publisher

    File URL: https://download.uni-mainz.de/RePEc/pdf/Discussion_Paper_1801.pdf
    File Function: First version, 2018
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Marielle Christiansen & Bjorn Nygreen, 1998. "A method for solving ship routing problemswith inventory constraints," Annals of Operations Research, Springer, vol. 81(0), pages 357-378, June.
    2. François Vanderbeck, 2001. "A Nested Decomposition Approach to a Three-Stage, Two-Dimensional Cutting-Stock Problem," Management Science, INFORMS, vol. 47(6), pages 864-879, June.
    3. Jans, Raf, 2010. "Classification of Dantzig-Wolfe reformulations for binary mixed integer programming problems," European Journal of Operational Research, Elsevier, vol. 204(2), pages 251-254, July.
    4. Lahyani, Rahma & Khemakhem, Mahdi & Semet, Frédéric, 2015. "Rich vehicle routing problems: From a taxonomy to a definition," European Journal of Operational Research, Elsevier, vol. 241(1), pages 1-14.
    5. C. Archetti & M. Bouchard & G. Desaulniers, 2011. "Enhanced Branch and Price and Cut for Vehicle Routing with Split Deliveries and Time Windows," Transportation Science, INFORMS, vol. 45(3), pages 285-298, August.
    6. 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.
    7. 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.
    8. Guy Desaulniers & Jacques Desrosiers & Marius M. Solomon (ed.), 2005. "Column Generation," Springer Books, Springer, number 978-0-387-25486-9, September.
    9. Michel Gamache & François Soumis & Gérald Marquis & Jacques Desrosiers, 1999. "A Column Generation Approach for Large-Scale Aircrew Rostering Problems," Operations Research, INFORMS, vol. 47(2), pages 247-263, April.
    10. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    11. Samir Elhedhli & Jean-Louis Goffin, 2005. "Efficient Production-Distribution System Design," Management Science, INFORMS, vol. 51(7), pages 1151-1164, July.
    12. Jean-François Cordeau & Goran Stojković & François Soumis & Jacques Desrosiers, 2001. "Benders Decomposition for Simultaneous Aircraft Routing and Crew Scheduling," Transportation Science, INFORMS, vol. 35(4), pages 375-388, November.
    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. Yvan Dumas & François Soumis & Jacques Desrosiers, 1990. "Technical Note—Optimizing the Schedule for a Fixed Vehicle Path with Convex Inconvenience Costs," Transportation Science, INFORMS, vol. 24(2), pages 145-152, May.
    15. Ioachim, Irina & Desrosiers, Jacques & Soumis, Francois & Belanger, Nicolas, 1999. "Fleet assignment and routing with schedule synchronization constraints," European Journal of Operational Research, Elsevier, vol. 119(1), pages 75-90, November.
    16. Tagmouti, Mariam & Gendreau, Michel & Potvin, Jean-Yves, 2007. "Arc routing problems with time-dependent service costs," European Journal of Operational Research, Elsevier, vol. 181(1), pages 30-39, August.
    17. 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.
    18. Michael Drexl, 2012. "Synchronization in Vehicle Routing---A Survey of VRPs with Multiple Synchronization Constraints," Transportation Science, INFORMS, vol. 46(3), pages 297-316, August.
    19. 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.
    20. Dominique Feillet & Pierre Dejax & Michel Gendreau, 2005. "Traveling Salesman Problems with Profits," Transportation Science, INFORMS, vol. 39(2), pages 188-205, May.
    21. 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.
    22. Dorota Mankowska & Frank Meisel & Christian Bierwirth, 2014. "The home health care routing and scheduling problem with interdependent services," Health Care Management Science, Springer, vol. 17(1), pages 15-30, March.
    23. Dohn, Anders & Mason, Andrew, 2013. "Branch-and-price for staff rostering: An efficient implementation using generic programming and nested column generation," European Journal of Operational Research, Elsevier, vol. 230(1), pages 157-169.
    24. Francesco Maffioli & Anna Sciomachen, 1997. "A mixed-integer model for solving ordering problems with side constraints," Annals of Operations Research, Springer, vol. 69(0), pages 277-297, January.
    25. Karabuk, Suleyman, 2009. "A nested decomposition approach for solving the paratransit vehicle scheduling problem," Transportation Research Part B: Methodological, Elsevier, vol. 43(4), pages 448-465, May.
    26. Ibrahim Muter & Jean-François Cordeau & Gilbert Laporte, 2014. "A Branch-and-Price Algorithm for the Multidepot Vehicle Routing Problem with Interdepot Routes," Transportation Science, INFORMS, vol. 48(3), pages 425-441, August.
    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. Tilk, Christian & Drexl, Michael & Irnich, Stefan, 2019. "Nested branch-and-price-and-cut for vehicle routing problems with multiple resource interdependencies," European Journal of Operational Research, Elsevier, vol. 276(2), pages 549-565.
    2. 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.
    3. 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.
    4. Timo Gschwind & Stefan Irnich, 2012. "Effective Handling of Dynamic Time Windows and Synchronization with Precedences for Exact Vehicle Routing," Working Papers 1211, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    5. Christian Tilk & Nicola Bianchessi & Michael Drexl & Stefan Irnich & Frank Meisel, 2018. "Branch-and-Price-and-Cut for the Active-Passive Vehicle-Routing Problem," Transportation Science, INFORMS, vol. 52(2), pages 300-319, March.
    6. Christian Tilk & Katharina Olkis & Stefan Irnich, 2020. "The Last-mile Vehicle Routing Problem with Delivery Options," Working Papers 2017, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    7. 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.
    8. Nicola Bianchessi & Stefan Irnich & Christian Tilk, 2020. "A Branch-Price-and-Cut Algorithm for the Capacitated Multiple Vehicle Traveling Purchaser Problem with Unitary Demand," Working Papers 2003, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    9. 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.
    10. Ann-Kathrin Rothenbächer & Michael Drexl & Stefan Irnich, 2018. "Branch-and-Price-and-Cut for the Truck-and-Trailer Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 52(5), pages 1174-1190, October.
    11. Ann-Kathrin Rothenbächer, 2017. "Branch-and-Price-and-Cut for the Periodic Vehicle Routing Problem with Flexible Schedule Structures," Working Papers 1714, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    12. Timo Gschwind & Stefan Irnich, 2015. "Effective Handling of Dynamic Time Windows and Its Application to Solving the Dial-a-Ride Problem," Transportation Science, INFORMS, vol. 49(2), pages 335-354, May.
    13. Timo Gschwind & Stefan Irnich & Simon Emde & Christian Tilk, 2018. "Branch-Cut-and-Price for the Scheduling Deliveries with Time Windows in a Direct Shipping Network," Working Papers 1805, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    14. Nicola Bianchessi & Stefan Irnich, 2016. "Branch-and-Cut for the Split Delivery Vehicle Routing Problem with Time Windows," Working Papers 1620, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    15. Bakker, Steffen J. & Wang, Akang & Gounaris, Chrysanthos E., 2021. "Vehicle routing with endogenous learning: Application to offshore plug and abandonment campaign planning," European Journal of Operational Research, Elsevier, vol. 289(1), pages 93-106.
    16. Ann-Kathrin Rothenbächer, 2019. "Branch-and-Price-and-Cut for the Periodic Vehicle Routing Problem with Flexible Schedule Structures," Transportation Science, INFORMS, vol. 53(3), pages 850-866, May.
    17. Guy Desaulniers & Jørgen G. Rakke & Leandro C. Coelho, 2016. "A Branch-Price-and-Cut Algorithm for the Inventory-Routing Problem," Transportation Science, INFORMS, vol. 50(3), pages 1060-1076, August.
    18. Juho Andelmin & Enrico Bartolini, 2017. "An Exact Algorithm for the Green Vehicle Routing Problem," Transportation Science, INFORMS, vol. 51(4), pages 1288-1303, November.
    19. 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.
    20. Nicola Bianchessi & Stefan Irnich, 2019. "Branch-and-Cut for the Split Delivery Vehicle Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 53(2), pages 442-462, March.

    More about this item

    Keywords

    Routing; Vehicle routing; Synchronization; Nested decomposition; 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:1801. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/vlmaide.html .

    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 hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.