IDEAS home Printed from https://ideas.repec.org/a/gam/jsusta/v9y2017i5p776-d97945.html
   My bibliography  Save this article

A Lagrangian Relaxation-Based Solution Method for a Green Vehicle Routing Problem to Minimize Greenhouse Gas Emissions

Author

Listed:
  • Yanjie Zhou

    (Department of Industrial Engineering, Pusan National University, Busan 46241, Korea)

  • Gyu M. Lee

    (Department of Industrial Engineering, Pusan National University, Busan 46241, Korea)

Abstract

The effects of greenhouse gas (GHG) on the weather has caused ever-increasing disasters around the world. Many countries are making significant efforts to reduce GHG emissions in all industrial sectors. In this study, a green vehicle routing problem (GVRP) has been formulated as a nonlinear integer programming problem to minimize GHG emissions, considering various realistic factors that include three-dimensional customer locations, gravity, vehicle speed, vehicle operating time, vehicle capacity, rolling resistance, air density, road grade and inertia. Lagrangian relaxation has been introduced to propose a simple solution method. In contrast to traditional vehicle routing problems, the vehicle speed, vehicle weight, and road grade between two customer locations are also determined along with vehicle routes. The computational results demonstrate the effectiveness and efficiency of the proposed solution method.

Suggested Citation

  • Yanjie Zhou & Gyu M. Lee, 2017. "A Lagrangian Relaxation-Based Solution Method for a Green Vehicle Routing Problem to Minimize Greenhouse Gas Emissions," Sustainability, MDPI, vol. 9(5), pages 1-17, May.
    • Handle: RePEc:gam:jsusta:v:9:y:2017:i:5:p:776-:d:97945
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2071-1050/9/5/776/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2071-1050/9/5/776/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Marshall L. Fisher, 2004. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 50(12_supple), pages 1861-1871, December.
    2. Ye Li & Lei Bao & Wenxiang Li & Haopeng Deng, 2016. "Inventory and Policy Reduction Potential of Greenhouse Gas and Pollutant Emissions of Road Transportation Industry in China," Sustainability, MDPI, vol. 8(12), pages 1-19, November.
    3. Kirschstein, Thomas & Meisel, Frank, 2015. "GHG-emission models for assessing the eco-friendliness of road and rail freight transports," Transportation Research Part B: Methodological, Elsevier, vol. 73(C), pages 13-33.
    4. Bektas, Tolga & Laporte, Gilbert, 2011. "The Pollution-Routing Problem," Transportation Research Part B: Methodological, Elsevier, vol. 45(8), pages 1232-1250, September.
    5. Demir, Emrah & Bektaş, Tolga & Laporte, Gilbert, 2014. "The bi-objective Pollution-Routing Problem," European Journal of Operational Research, Elsevier, vol. 232(3), pages 464-478.
    6. Ilkyeong Moon & Yoon Jea Jeong & Subrata Saha, 2016. "Fuzzy Bi-Objective Production-Distribution Planning Problem under the Carbon Emission Constraint," Sustainability, MDPI, vol. 8(8), pages 1-17, August.
    7. Akcelik, R. & Biggs, D. C., 1985. "A discussion on the paper on fuel consumption modeling by Post et al," Transportation Research Part B: Methodological, Elsevier, vol. 19(6), pages 529-533, December.
    8. Demir, Emrah & Bektaş, Tolga & Laporte, Gilbert, 2014. "A review of recent research on green road freight transportation," European Journal of Operational Research, Elsevier, vol. 237(3), pages 775-793.
    9. Marshall L. Fisher, 2004. "Comments on ÜThe Lagrangian Relaxation Method for Solving Integer Programming ProblemsÝ," Management Science, INFORMS, vol. 50(12_supple), pages 1872-1874, December.
    10. Helsgaun, Keld, 2000. "An effective implementation of the Lin-Kernighan traveling salesman heuristic," European Journal of Operational Research, Elsevier, vol. 126(1), pages 106-130, October.
    11. Billy E. Gillett & Leland R. Miller, 1974. "A Heuristic Algorithm for the Vehicle-Dispatch Problem," Operations Research, INFORMS, vol. 22(2), pages 340-349, 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. Bo Peng & Lifan Wu & Yuxin Yi & Xiding Chen, 2020. "Solving the Multi-Depot Green Vehicle Routing Problem by a Hybrid Evolutionary Algorithm," Sustainability, MDPI, vol. 12(5), pages 1-19, March.
    2. Joonyup Eun & Byung Duk Song & Sangbok Lee & Dae-Eun Lim, 2019. "Mathematical Investigation on the Sustainability of UAV Logistics," Sustainability, MDPI, vol. 11(21), pages 1-15, October.
    3. Yong Wang & Qin Li & Xiangyang Guan & Jianxin Fan & Yong Liu & Haizhong Wang, 2020. "Collaboration and Resource Sharing in the Multidepot Multiperiod Vehicle Routing Problem with Pickups and Deliveries," Sustainability, MDPI, vol. 12(15), pages 1-33, July.
    4. Brunner, Carlos & Giesen, Ricardo & Klapp, Mathias A. & Flórez-Calderón, Luz, 2021. "Vehicle routing problem with steep roads," Transportation Research Part A: Policy and Practice, Elsevier, vol. 151(C), pages 1-17.
    5. 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.
    6. Yong Wang & Shouguo Peng & Kevin Assogba & Yong Liu & Haizhong Wang & Maozeng Xu & Yinhai Wang, 2018. "Implementation of Cooperation for Recycling Vehicle Routing Optimization in Two-Echelon Reverse Logistics Networks," Sustainability, MDPI, vol. 10(5), pages 1-27, April.
    7. Mariusz Brzeziński & Dariusz Pyza, 2023. "A Refined Model for Carbon Footprint Estimation in Electric Railway Transport," Energies, MDPI, vol. 16(18), pages 1-18, September.
    8. Liyang Xiao & Mahjoub Dridi & Amir Hajjam El Hassani & Hongying Fei & Wanlong Lin, 2018. "An Improved Cuckoo Search for a Patient Transportation Problem with Consideration of Reducing Transport Emissions," Sustainability, MDPI, vol. 10(3), pages 1-19, March.
    9. 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.
    10. Zoltan Lakner & Anna Kiss & Bela Vizvari & Jozsef Popp, 2021. "Trade Liberalisation and Sustainability: A Case Study of Agro-Food Transport Optimisation," European Research Studies Journal, European Research Studies Journal, vol. 0(1), pages 822-839.
    11. Chiang, Wen-Chyuan & Li, Yuyu & Shang, Jennifer & Urban, Timothy L., 2019. "Impact of drone delivery on sustainability and cost: Realizing the UAV potential through vehicle routing optimization," Applied Energy, Elsevier, vol. 242(C), pages 1164-1175.

    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. 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.
    2. Ehmke, Jan Fabian & Campbell, Ann M. & Thomas, Barrett W., 2018. "Optimizing for total costs in vehicle routing in urban areas," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 116(C), pages 242-265.
    3. Yu, Yang & Wu, Yuting & Wang, Junwei, 2019. "Bi-objective green ride-sharing problem: Model and exact method," International Journal of Production Economics, Elsevier, vol. 208(C), pages 472-482.
    4. Li, Wenjie & Yang, Lixing & Wang, Li & Zhou, Xuesong & Liu, Ronghui & Gao, Ziyou, 2017. "Eco-reliable path finding in time-variant and stochastic networks," Energy, Elsevier, vol. 121(C), pages 372-387.
    5. Dukkanci, Okan & Karsu, Özlem & Kara, Bahar Y., 2022. "Planning sustainable routes: Economic, environmental and welfare concerns," European Journal of Operational Research, Elsevier, vol. 301(1), pages 110-123.
    6. Behnke, Martin & Kirschstein, Thomas, 2017. "The impact of path selection on GHG emissions in city logistics," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 106(C), pages 320-336.
    7. 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).
    8. 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.
    9. Brunner, Carlos & Giesen, Ricardo & Klapp, Mathias A. & Flórez-Calderón, Luz, 2021. "Vehicle routing problem with steep roads," Transportation Research Part A: Policy and Practice, Elsevier, vol. 151(C), pages 1-17.
    10. 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.
    11. Suzuki, Yoshinori & Lan, Bo, 2018. "Cutting fuel consumption of truckload carriers by using new enhanced refueling policies," International Journal of Production Economics, Elsevier, vol. 202(C), pages 69-80.
    12. Xia, Jun & Wang, Kai & Wang, Shuaian, 2019. "Drone scheduling to monitor vessels in emission control areas," Transportation Research Part B: Methodological, Elsevier, vol. 119(C), pages 174-196.
    13. 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.
    14. 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.
    15. Shih-Che Lo & Yi-Cheng Shih, 2021. "A Genetic Algorithm with Quantum Random Number Generator for Solving the Pollution-Routing Problem in Sustainable Logistics Management," Sustainability, MDPI, vol. 13(15), pages 1-18, July.
    16. Zhou, Yizi & Mandania, Rupal & Liu, Jiyin, 2022. "Green vehicle routing and dynamic pricing for scheduling on-site services," International Journal of Production Economics, Elsevier, vol. 254(C).
    17. 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).
    18. Pelletier, Samuel & Jabali, Ola & Laporte, Gilbert & Veneroni, Marco, 2017. "Battery degradation and behaviour for electric vehicles: Review and numerical analyses of several models," Transportation Research Part B: Methodological, Elsevier, vol. 103(C), pages 158-187.
    19. Micheli, Guido J.L. & Mantella, Fabio, 2018. "Modelling an environmentally-extended inventory routing problem with demand uncertainty and a heterogeneous fleet under carbon control policies," International Journal of Production Economics, Elsevier, vol. 204(C), pages 316-327.
    20. 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.

    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:gam:jsusta:v:9:y:2017:i:5:p:776-:d:97945. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.