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A branch-price-and-cut algorithm for sustainable milk-run vehicle scheduling problem with cross-dimensional integration
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DOI：10.1016/j.cor.2025.107361.png)
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Abstract
En 中文
In response to environmental deterioration and increasingly stringent regulations, this paper investigates a sustainable milk-run vehicle scheduling problem with cross-dimensional integration (SMVSPCI). The problem extends traditional milk-run models by integrating transportation tasks across bidirectional, temporal, and horizontal dimensions, while jointly considering returnable transport item (RTI) management and quantity decisions over multiple periods. To account for demand uncertainty, a scenario-based stochastic framework is adopted, allowing the model to capture multiple possible demand realizations and their associated probabilities. To effectively solve this complex problem, a tailored branch-price-and-cut (BPC) algorithm is proposed, incorporating innovative strategies such as pseudo-dominance, column combination, and column refinement to enhance computational efficiency. Extensive computational experiments on 270 instances demonstrate that the proposed algorithm efficiently handles medium-scale instances while achieving competitive results for larger cases. Comparative analyses further validate the effectiveness of the proposed strategies in improving solution quality and reducing computational time, providing valuable insights for sustainable logistics planning.
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