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Augmented Lagrangian relaxation approach for logistics vehicle routing problem with mixed backhauls and time windows

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  • Yang, Senyan
  • Ning, Lianju
  • Shang, Pan
  • (Carol) Tong, Lu

Abstract

This paper studies the vehicle routing problem with mixed backhauls and time windows (VRPMBTW) for city logistics. A time-discretized multi-commodity network flow optimization model is proposed in an extended state-space-time network representation, where the time-dependent pickups and deliveries can be depicted by extending the state dimensions. By implementing an augmented Lagrangian relaxation technique, the VRPMBTW is reformulated as a quadratic 0–1 programming model, which is further decomposed into the standard least-cost-path sub-problems, and iteratively solved by dynamic programming in a block nonlinear Gauss-Seidel framework. The proposed approach is tested on the simple 9-node network and the real-world Chicago sketch network.

Suggested Citation

  • Yang, Senyan & Ning, Lianju & Shang, Pan & (Carol) Tong, Lu, 2020. "Augmented Lagrangian relaxation approach for logistics vehicle routing problem with mixed backhauls and time windows," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 135(C).
    • Handle: RePEc:eee:transe:v:135:y:2020:i:c:s1366554519314814
    DOI: 10.1016/j.tre.2020.101891
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