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

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.

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