IDEAS home Printed from https://ideas.repec.org/a/inm/ortrsc/v51y2017i2p607-628.html
   My bibliography  Save this article

An Exact Approach for a Variant of the Pollution-Routing Problem

Author

Listed:
  • Said Dabia

    (Department of Economics and Business Administration, VU University Amsterdam, 1081 HV Amsterdam, Netherlands; and Eyefreight BV, 3981 AJ Bunnik, Netherlands)

  • Emrah Demir

    (School of Industrial Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands)

  • Tom Van Woensel

    (School of Industrial Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands)

Abstract

The pollution-routing problem (PRP) is a recently introduced green vehicle routing problem in the field of green logistics. It concerns routing a number of vehicles to serve a set of geographically dispersed customers within their time windows, jointly with determining their speed on each arc so as to minimize fuel and driving costs. Because of its complexity, all known solution methods are based on (meta-)heuristics. This paper presents an exact solution based on a branch-and-price algorithm for a variant of the PRP. The master problem is a set-partitioning problem, and the pricing problem is a speed- and start-time elementary shortest path problem with resource constraints, in which the speed and start time at the depot needs to be decided on for each individual route. The master problem is solved by means of column generation, and a tailored labeling algorithm is used to solve the pricing problem. New dominance criteria are developed to discard unpromising labels by exploiting the structure of the ready time and the fuel consumption functions. Extensive computational experiments show the value of the proposed algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ortrsc:v:51:y:2017:i:2:p:607-628
    DOI: 10.1287/trsc.2015.0651
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/trsc.2015.0651
    Download Restriction: no
    File URL: https://libkey.io/10.1287/trsc.2015.0651?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. 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.
    2. 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.
    3. Franceschetti, Anna & Honhon, Dorothée & Van Woensel, Tom & Bektaş, Tolga & Laporte, Gilbert, 2013. "The time-dependent pollution-routing problem," Transportation Research Part B: Methodological, Elsevier, vol. 56(C), pages 265-293.
    4. 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.
    5. Barth, Matthew & Younglove, Theodore & Scora, George, 2005. "Development of a Heavy-Duty Diesel Modal Emissions and Fuel Consumption Model," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt67f0v3zf, Institute of Transportation Studies, UC Berkeley.
    6. 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.
    7. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    8. Koç, Çağrı & Bektaş, Tolga & Jabali, Ola & Laporte, Gilbert, 2014. "The fleet size and mix pollution-routing problem," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 239-254.
    9. Barth, Matthew & Boriboonsomsin, Kanok, 2008. "Real-World CO2 Impacts of Traffic Congestion," University of California Transportation Center, Working Papers qt4fx9g4gn, University of California Transportation Center.
    10. 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.
    11. 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.
    12. Demir, Emrah & Huang, Yuan & Scholts, Sebastiaan & Van Woensel, Tom, 2015. "A selected review on the negative externalities of the freight transportation: Modeling and pricing," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 77(C), pages 95-114.
    13. 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.
    14. 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.
    15. 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.
    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. Chen, Jie & Hu, Maobin & Shi, Congling, 2023. "Development of eco-routing guidance for connected electric vehicles in urban traffic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
    2. Zhang, Li & Liu, Zhongshan & Yu, Lan & Fang, Ke & Yao, Baozhen & Yu, Bin, 2022. "Routing optimization of shared autonomous electric vehicles under uncertain travel time and uncertain service time," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 157(C).
    3. Ángel Corberán & Güneş Erdoğan & Gilbert Laporte & Isaac Plana & José M. Sanchis, 2018. "The Chinese Postman Problem with Load-Dependent Costs," Transportation Science, INFORMS, vol. 52(2), pages 370-385, March.
    4. Thomas Kirschstein & Arne Heinold & Martin Behnke & Frank Meisel & Christian Bierwirth, 2022. "Eco‐labeling of freight transport services: Design, evaluation, and research directions," Journal of Industrial Ecology, Yale University, vol. 26(3), pages 801-814, June.
    5. Yiming Liu & Yang Yu & Yu Zhang & Roberto Baldacci & Jiafu Tang & Xinggang Luo & Wei Sun, 2023. "Branch-Cut-and-Price for the Time-Dependent Green Vehicle Routing Problem with Time Windows," INFORMS Journal on Computing, INFORMS, vol. 35(1), pages 14-30, January.
    6. 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.
    7. Nasreddine Ouertani & Hajer Ben-Romdhane & Saoussen Krichen & Issam Nouaouri, 2022. "A vector evaluated evolutionary algorithm with exploitation reinforcement for the dynamic pollution routing problem," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1011-1038, September.
    8. Martin Wölck & Stephan Meisel, 2022. "Branch-and-Price Approaches for Real-Time Vehicle Routing with Picking, Loading, and Soft Time Windows," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2192-2211, July.
    9. Darvish, Maryam & Archetti, Claudia & Coelho, Leandro C., 2019. "Trade-offs between environmental and economic performance in production and inventory-routing problems," International Journal of Production Economics, Elsevier, vol. 217(C), pages 269-280.
    10. 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.
    11. Xiao, Yiyong & Zuo, Xiaorong & Huang, Jiaoying & Konak, Abdullah & Xu, Yuchun, 2020. "The continuous pollution routing problem," Applied Mathematics and Computation, Elsevier, vol. 387(C).
    12. Çağrı Koç, 2019. "Analysis of vehicle emissions in location-routing problem," Flexible Services and Manufacturing Journal, Springer, vol. 31(1), pages 1-33, March.
    13. 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.

    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. 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.
    2. Emna Marrekchi & Walid Besbes & Diala Dhouib & Emrah Demir, 2021. "A review of recent advances in the operations research literature on the green routing problem and its variants," Annals of Operations Research, Springer, vol. 304(1), pages 529-574, September.
    3. 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.
    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. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Asghari, Mohammad & Mirzapour Al-e-hashem, S. Mohammad J., 2021. "Green vehicle routing problem: A state-of-the-art review," International Journal of Production Economics, Elsevier, vol. 231(C).
    10. 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.
    11. 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.
    12. Xiao, Yiyong & Konak, Abdullah, 2016. "The heterogeneous green vehicle routing and scheduling problem with time-varying traffic congestion," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 88(C), pages 146-166.
    13. Koç, Çağrı & Bektaş, Tolga & Jabali, Ola & Laporte, Gilbert, 2016. "The impact of depot location, fleet composition and routing on emissions in city logistics," Transportation Research Part B: Methodological, Elsevier, vol. 84(C), pages 81-102.
    14. 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.
    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. 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.
    17. 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.
    18. Stefan Irnich & Guy Desaulniers & Jacques Desrosiers & Ahmed Hadjar, 2010. "Path-Reduced Costs for Eliminating Arcs in Routing and Scheduling," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 297-313, May.
    19. 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.
    20. Mohammad Asghari & Seyed Mohammad Javad Mirzapour Al-E-Hashem, 2021. "Green vehicle routing problem: A state-of-the-art review," Post-Print hal-03182944, HAL.

    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:51:y:2017:i:2:p:607-628. 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.