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On the Distance Constrained Vehicle Routing Problem

Author

Listed:
  • Chung-Lun Li

    (Washington University, St. Louis, Missouri)

  • David Simchi-Levi

    (Columbia University, New York, New York)

  • Martin Desrochers

    (GERAD and Ecole Polytechnique, Montreal, Canada)

Abstract

We analyze the vehicle routing problem with constraints on the total distance traveled by each vehicle. Two objective functions are considered: minimize the total distance traveled by vehicles and minimize the number of vehicles used. We demonstrate a close relationship between the optimal solutions for the two objective functions and perform a worst case analysis for a class of heuristics. We present a heuristic that provides a good worst case result when the number of vehicles used is relatively small.

Suggested Citation

  • Chung-Lun Li & David Simchi-Levi & Martin Desrochers, 1992. "On the Distance Constrained Vehicle Routing Problem," Operations Research, INFORMS, vol. 40(4), pages 790-799, August.
    • Handle: RePEc:inm:oropre:v:40:y:1992:i:4:p:790-799
    DOI: 10.1287/opre.40.4.790
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    Citations

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    Cited by:

    1. Lai, David S.W. & Caliskan Demirag, Ozgun & Leung, Janny M.Y., 2016. "A tabu search heuristic for the heterogeneous vehicle routing problem on a multigraph," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 86(C), pages 32-52.
    2. Liu, Ran & Jiang, Zhibin, 2012. "The close–open mixed vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 220(2), pages 349-360.
    3. Nussbaum, M. & Sepulveda, M. & Cobian, A. & Gaete, J. & Parra, E. & Cruz, J., 1997. "A fuel distribution knowledge-based decision support system," Omega, Elsevier, vol. 25(2), pages 225-234, April.
    4. Michael Schneider & Andreas Stenger & Dominik Goeke, 2014. "The Electric Vehicle-Routing Problem with Time Windows and Recharging Stations," Transportation Science, INFORMS, vol. 48(4), pages 500-520, November.
    5. Chebbi, Olfa & Chaouachi, Jouhaina, 2016. "Reducing the wasted transportation capacity of Personal Rapid Transit systems: An integrated model and multi-objective optimization approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 89(C), pages 236-258.
    6. Young Kim, Ki & Hwan Kim, Kap, 1999. "A routing algorithm for a single straddle carrier to load export containers onto a containership," International Journal of Production Economics, Elsevier, vol. 59(1-3), pages 425-433, March.
    7. Roberto Aringhieri & Maurizio Bruglieri & Federico Malucelli & Maddalena Nonato, 2018. "A Special Vehicle Routing Problem Arising in the Optimization of Waste Disposal: A Real Case," Transportation Science, INFORMS, vol. 52(2), pages 277-299, March.
    8. Jian Liang & Xiaohui Huang & Zhao Zhang, 2019. "Approximation algorithms for distance constraint sweep coverage with base stations," Journal of Combinatorial Optimization, Springer, vol. 37(4), pages 1111-1125, May.
    9. Luo, Zhixing & Qin, Hu & Lim, Andrew, 2014. "Branch-and-price-and-cut for the multiple traveling repairman problem with distance constraints," European Journal of Operational Research, Elsevier, vol. 234(1), pages 49-60.
    10. Koyuncu, Işıl & Yavuz, Mesut, 2019. "Duplicating nodes or arcs in green vehicle routing: A computational comparison of two formulations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 122(C), pages 605-623.
    11. Cheang, Brenda & Gao, Xiang & Lim, Andrew & Qin, Hu & Zhu, Wenbin, 2012. "Multiple pickup and delivery traveling salesman problem with last-in-first-out loading and distance constraints," European Journal of Operational Research, Elsevier, vol. 223(1), pages 60-75.
    12. Malmborg, Charles J., 1996. "A genetic algorithm for service level based vehicle scheduling," European Journal of Operational Research, Elsevier, vol. 93(1), pages 121-134, August.
    13. Andrea Lodi & Enrico Malaguti & Nicolás E. Stier-Moses & Tommaso Bonino, 2016. "Design and Control of Public-Service Contracts and an Application to Public Transportation Systems," Management Science, INFORMS, vol. 62(4), pages 1165-1187, April.
    14. Wei Yu & Zhaohui Liu & Xiaoguang Bao, 2022. "Distance constrained vehicle routing problem to minimize the total cost: algorithms and complexity," Journal of Combinatorial Optimization, Springer, vol. 43(5), pages 1405-1422, July.

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