This paper investigates a location–routing problem with heterogeneous fleet and weight-based carbon emissions, aiming to minimize total operating costs, including depot and vehicle fixed costs and carbon emissions. The problem is formulated using an extended formulation, from which a relaxation is derived. The relaxation is further strengthened with additional cuts. For this problem, we devise an exact algorithm that combines a branch-price-and-cut algorithm with state-of-the-art technologies. The exact algorithm relies on a novel bidirectional labeling algorithm; it merges labels through cost compensation, leading to an effective solution. We conduct comprehensive computational experiments to validate the proposed algorithm, evaluating key factors related to carbon emissions. Our findings confirm the algorithm’s efficacy, highlighting its potential as a useful tool for addressing the location routing problem in heterogeneous fleet scenarios.

中文翻译：

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精确解决异构车队和基于重量的碳排放的位置路由问题


本文研究了异构车队和基于重量的碳排放的位置路由问题，旨在最大限度地降低总运营成本，包括车辆段和车辆的固定成本以及碳排放。该问题是使用扩展公式表述的，从中得出松弛。额外的削减进一步加强了松弛感。对于这个问题，我们设计了一个精确的算法，将 branch-price-and-cut 算法与最先进的技术相结合。确切的算法依赖于一种新的双向标记算法;它通过成本补偿合并标签，从而产生有效的解决方案。我们进行了全面的计算实验来验证所提出的算法，评估与碳排放相关的关键因素。我们的研究结果证实了该算法的有效性，突出了它作为解决异构队列场景中位置路由问题的有用工具的潜力。