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

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  • 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
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    References listed on IDEAS

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    2. Çağrı Koç, 2019. "Analysis of vehicle emissions in location-routing problem," Flexible Services and Manufacturing Journal, Springer, vol. 31(1), pages 1-33, March.
    3. 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.
    4. 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).
    5. 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.
    6. 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.
    7. 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.
    8. 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).
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Xiao, Yiyong & Zuo, Xiaorong & Huang, Jiaoying & Konak, Abdullah & Xu, Yuchun, 2020. "The continuous pollution routing problem," Applied Mathematics and Computation, Elsevier, vol. 387(C).

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