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The single vehicle routing problem with toll-by-weight scheme: A branch-and-bound approach

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  • Zhang, Zizhen
  • Qin, Hu
  • Zhu, Wenbin
  • Lim, Andrew

Abstract

Expressways in China make use of the toll-by-weight scheme, in which expressway tolls are collected based on the weight and traveling distance of the vehicle. Most vehicle routing models assume that the cost of traversing each edge is equivalent to edge length or some constant; as a result, such models cannot be practically applied to the Chinese expressway transportation system. This study addresses a new single vehicle routing problem that takes the vehicle’s (laden and unladen) weight into account. To solve this problem exactly, we provide a branch-and-bound algorithm with a provably valid lower bound measure, along with five dominance checkers for additional pruning. We analyze our algorithm using instances generated from standard TSP test cases, as well as two new sets of test cases based on real expressway information from the Gansu and Jiangxi provinces in China. The algorithm can be applied to any toll scheme in which the toll per unit distance monotonically increases with weight, even if the toll function is non-linear.

Suggested Citation

  • Zhang, Zizhen & Qin, Hu & Zhu, Wenbin & Lim, Andrew, 2012. "The single vehicle routing problem with toll-by-weight scheme: A branch-and-bound approach," European Journal of Operational Research, Elsevier, vol. 220(2), pages 295-304.
    • Handle: RePEc:eee:ejores:v:220:y:2012:i:2:p:295-304
    DOI: 10.1016/j.ejor.2012.01.035
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    References listed on IDEAS

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    Cited by:

    1. Luo, Zhixing & Qin, Hu & Zhang, Dezhi & Lim, Andrew, 2016. "Adaptive large neighborhood search heuristics for the vehicle routing problem with stochastic demands and weight-related cost," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 85(C), pages 69-89.
    2. Xue, Li & Luo, Zhixing & Lim, Andrew, 2016. "Exact approaches for the pickup and delivery problem with loading cost," Omega, Elsevier, vol. 59(PB), pages 131-145.
    3. Qin, Hu & Zhang, Zizhen & Lim, Andrew & Liang, Xiaocong, 2016. "An enhanced branch-and-bound algorithm for the talent scheduling problem," European Journal of Operational Research, Elsevier, vol. 250(2), pages 412-426.
    4. 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.
    5. Li, Jiliu & Qin, Hu & Shen, Huaxiao & Tsui, Kwok Leung, 2019. "The unilateral transportation problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 132(C), pages 1-29.

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