Modelling and heuristically solving three-dimensional loading constrained vehicle routing problem with cross-docking

Cross-docking is a logistics strategy widely applied in numerous enterprises, where vehicle scheduling is one of the most important factor in operational level for cost reduction. In sight of the widespread applications of the three-dimensional loading on the vehicle scheduling, this study addresses a vehicle routing problem with cross-docking and three-dimensional loading constraints (3L-VRPCD). A relaxation mixed integer linear programming (MILP) model is proposed for solving the 3L-VRPCD. In order to effectively solve large-scale 3LVRPCD instances, a hybrid heuristic algorithm is then proposed, which combines adaptive large neighbourhood search (ALNS) and multi-order local search packing (LSP) algorithm. In addition, a storage-pool-based strategy is integrated into the proposed algorithm for efficiency enhancement. A large number of 3L-VRPCD instances with wide-ranging properties are generated to test the feasibility and effectiveness of the proposed MILP model and heuristic method. Experimental results demonstrate remarkable advantages of the proposed heuristic over the MILP-based method with respect to solution quality and computational efficiency, especially for medium to large-scale instances. Meanwhile, the results verify that the proposed storage-pool-based strategy is capable of accelerating the search process and reducing the computational burden of the heuristic. Furthermore, the impacts of different properties (e.g., loading conditions) on the solution of 3L-VRPCD have been analysed and discussed.