Inspired by real-world applications of cross-docking and the presence of uncertainties in travel time and loading efficiency in manufacturing and retailing logistics, this study investigates a practical two-dimensional loading-constrained vehicle routing problem with cross-docking and stochastic travel time (2L-VRPCDSTT). A stochastic programming model is developed for the 2L-VRPCDSTT using sample average approximation with Monte Carlo-generated travel-time scenarios. Furthermore, a hybrid solution approach combining an adaptive large neighbourhood search (ALNS) algorithm and a multi-order bottom-fill-skyline (MOBFS) packing heuristic is proposed to efficiently solve the problem. Numerical experiments demonstrate that the proposed algorithm can effectively solve the 2L-VRPCDSTT, and the effectiveness of the stochastic programming model is verified. In addition, extensive computational experiments under various loading configurations are conducted to further validate the efficiency of the proposed model and solution approach. Comparisons between the ALNS-MOBFS algorithm and existing heuristics further demonstrate its effectiveness and adaptability for solving variants of the 2L-VRPCDSTT.
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Ji et al. (2026) studied this question.
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