IDEAS home Printed from https://ideas.repec.org/a/inm/ortrsc/v53y2019i4p986-1000.html
   My bibliography  Save this article

An Exact Algorithm for a Rich Vehicle Routing Problem with Private Fleet and Common Carrier

Author

Listed:
  • Said Dabia

    (School of Business and Economics, VU University Amsterdam, 1081 HV Amsterdam, Netherlands; Eyefreight B.V., 3981 AJ Bunnik, Netherlands)

  • David Lai

    (School of Business and Economics, VU University Amsterdam, 1081 HV Amsterdam, Netherlands)

  • Daniele Vigo

    (School of Business and Economics, VU University Amsterdam, 1081 HV Amsterdam, Netherlands; Department of Electrical, Electronic and Information Engineering, University of Bologna, 40126 Bologna BO, Italy)

Abstract

The vehicle routing problem with private fleet and common carrier (VRPPC) is a generalization of the classical vehicle routing problem in which the owner of a private fleet can either visit a customer with one of the owner’s vehicles or assign the customer to a common carrier. The latter case occurs if the demand exceeds the total capacity of the private fleet or if it is more economically convenient to do so. The owner’s objective is to minimize the variable and fixed costs for operating the owner’s fleet plus the total cost charged by the common carrier. This family of problems has many practical applications, particularly in the design of last-mile distribution services and has received some attention in the literature, in which some heuristics were proposed. We extend here the VRPPC by considering more realistic cost structures that account for quantity discounts on outsourcing costs and by considering time windows resulting in a rich VRPPC (RVRPPC). We present an exact approach based on a branch-and-cut-and-price algorithm for the RVRPPC and test the algorithm on instances from the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ortrsc:v:53:y:2019:i:4:p:986-1000
    DOI: 10.1287/trsc.2018.0852
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/trsc.2018.0852
    Download Restriction: no
    File URL: https://libkey.io/10.1287/trsc.2018.0852?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
    ---><---

    References listed on IDEAS

    as
    1. G. Clarke & J. W. Wright, 1964. "Scheduling of Vehicles from a Central Depot to a Number of Delivery Points," Operations Research, INFORMS, vol. 12(4), pages 568-581, August.
    2. F-H Liu & S-Y Shen, 1999. "The fleet size and mix vehicle routing problem with time windows," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(7), pages 721-732, July.
    3. 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.
    4. 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.
    5. 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.
    6. Martin Desrochers & Jacques Desrosiers & Marius Solomon, 1992. "A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows," Operations Research, INFORMS, vol. 40(2), pages 342-354, April.
    7. Stefan Irnich & Daniel Villeneuve, 2006. "The Shortest-Path Problem with Resource Constraints and k -Cycle Elimination for k (ge) 3," INFORMS Journal on Computing, INFORMS, vol. 18(3), pages 391-406, August.
    8. Thibaut Vidal & Nelson Maculan & Luiz Satoru Ochi & Puca Huachi Vaz Penna, 2016. "Large Neighborhoods with Implicit Customer Selection for Vehicle Routing Problems with Profits," Transportation Science, INFORMS, vol. 50(2), pages 720-734, May.
    9. Irnich, S. & Schneider, M. & Vigo, D., 2014. "Four Variants of the Vehicle Routing Problem," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 63514, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    10. Zonghao Gu & George L. Nemhauser & Martin W. P. Savelsbergh, 1998. "Lifted Cover Inequalities for 0-1 Integer Programs: Computation," INFORMS Journal on Computing, INFORMS, vol. 10(4), pages 427-437, November.
    11. 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.
    12. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    13. Côté, Jean-François & Potvin, Jean-Yves, 2009. "A tabu search heuristic for the vehicle routing problem with private fleet and common carrier," European Journal of Operational Research, Elsevier, vol. 198(2), pages 464-469, October.
    14. Gilbert Laporte, 2007. "What you should know about the vehicle routing problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(8), pages 811-819, December.
    15. Kaparis, Konstantinos & Letchford, Adam N., 2008. "Local and global lifted cover inequalities for the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 186(1), pages 91-103, April.
    16. David Pisinger, 1997. "A Minimal Algorithm for the 0-1 Knapsack Problem," Operations Research, INFORMS, vol. 45(5), pages 758-767, October.
    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. M-C Bolduc & J Renaud & F Boctor & G Laporte, 2008. "A perturbation metaheuristic for the vehicle routing problem with private fleet and common carriers," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(6), pages 776-787, June.
    19. Stenger, A. & Schneider, M. & Goeke, D., 2013. "The Prize-Collecting Vehicle Routing Problem with Single and Multiple Depots and Non-Linear Cost," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 62372, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    20. Laporte, Gilbert, 1992. "The vehicle routing problem: An overview of exact and approximate algorithms," European Journal of Operational Research, Elsevier, vol. 59(3), pages 345-358, June.
    21. Chu, Ching-Wu, 2005. "A heuristic algorithm for the truckload and less-than-truckload problem," European Journal of Operational Research, Elsevier, vol. 165(3), pages 657-667, September.
    22. 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.
    23. J-Y Potvin & M-A Naud, 2011. "Tabu search with ejection chains for the vehicle routing problem with private fleet and common carrier," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(2), pages 326-336, 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. Vidal, Thibaut & Laporte, Gilbert & Matl, Piotr, 2020. "A concise guide to existing and emerging vehicle routing problem variants," European Journal of Operational Research, Elsevier, vol. 286(2), pages 401-416.
    2. Yang, Fei & Dai, Ying & Ma, Zu-Jun, 2020. "A cooperative rich vehicle routing problem in the last-mile logistics industry in rural areas," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 141(C).
    3. Lin, Na & Akkerman, Renzo & Kanellopoulos, Argyris & Hu, Xiangpei & Wang, Xuping & Ruan, Junhu, 2023. "Vehicle routing with heterogeneous service types: Optimizing post-harvest preprocessing operations for fruits and vegetables in short food supply chains," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 172(C).
    4. Jan Pelikán & Petr Štourač & Ondřej Sokol, 2022. "Vehicle routing problem with uniform private fleet and common carrier: a node subset heuristic," 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. 30(2), pages 683-697, June.
    5. Wang, Congke & Liu, Yankui & Yang, Guoqing, 2023. "Adaptive distributionally robust hub location and routing problem with a third-party logistics strategy," Socio-Economic Planning Sciences, Elsevier, vol. 87(PA).
    6. Annelieke C. Baller & Said Dabia & Wout E. H. Dullaert & Daniele Vigo, 2020. "The Vehicle Routing Problem with Partial Outsourcing," Transportation Science, INFORMS, vol. 54(4), pages 1034-1052, July.

    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. Said Dabia & Stefan Ropke & Tom van Woensel, 2019. "Cover Inequalities for a Vehicle Routing Problem with Time Windows and Shifts," Transportation Science, INFORMS, vol. 53(5), pages 1354-1371, September.
    2. Zhenzhen Zhang & Zhixing Luo & Hu Qin & Andrew Lim, 2019. "Exact Algorithms for the Vehicle Routing Problem with Time Windows and Combinatorial Auction," Transportation Science, INFORMS, vol. 53(2), pages 427-441, March.
    3. Annelieke C. Baller & Said Dabia & Wout E. H. Dullaert & Daniele Vigo, 2020. "The Vehicle Routing Problem with Partial Outsourcing," Transportation Science, INFORMS, vol. 54(4), pages 1034-1052, July.
    4. 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.
    5. Bulhões, Teobaldo & Hà, Minh Hoàng & Martinelli, Rafael & Vidal, Thibaut, 2018. "The vehicle routing problem with service level constraints," European Journal of Operational Research, Elsevier, vol. 265(2), pages 544-558.
    6. Bhusiri, Narath & Qureshi, Ali Gul & Taniguchi, Eiichi, 2014. "The trade-off between fixed vehicle costs and time-dependent arrival penalties in a routing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 62(C), pages 1-22.
    7. 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.
    8. Miao Yu & Viswanath Nagarajan & Siqian Shen, 2022. "Improving Column Generation for Vehicle Routing Problems via Random Coloring and Parallelization," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 953-973, March.
    9. 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.
    10. Koç, Çağrı & Bektaş, Tolga & Jabali, Ola & Laporte, Gilbert, 2016. "Thirty years of heterogeneous vehicle routing," European Journal of Operational Research, Elsevier, vol. 249(1), pages 1-21.
    11. 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.
    12. Bertazzi, Luca & Bosco, Adamo & Laganà, Demetrio, 2015. "Managing stochastic demand in an Inventory Routing Problem with transportation procurement," Omega, Elsevier, vol. 56(C), pages 112-121.
    13. Guy Desaulniers & Diego Pecin & Claudio Contardo, 2019. "Selective pricing in branch-price-and-cut algorithms for vehicle routing," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 8(2), pages 147-168, June.
    14. 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.
    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. Dayarian, Iman & Crainic, Teodor Gabriel & Gendreau, Michel & Rei, Walter, 2015. "A column generation approach for a multi-attribute vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 241(3), pages 888-906.
    17. 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.
    18. 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.
    19. 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.
    20. Paul, J. & Agatz, N.A.H. & Spliet, R. & de Koster, M.B.M., 2017. "Shared Capacity Routing Problem – An Omni-channel Retail Study," ERIM Report Series Research in Management ERS-2017-012-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.

    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:inm:ortrsc:v:53:y:2019:i:4:p:986-1000. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.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.