This paper addresses the sustainable design of hub networks under uncertainty in the context of less-than-truckload transportation, taking into account factors related to carbon pricing. The problem is modeled to maximize profits in a stochastic demand environment, where a portion of the demand may remain unserved depending on the trade-off between profits, costs, and carbon emissions. The model explicitly incorporates a carbon tax into the objective function, along with transportation and hub operation costs. To ensure compliance with the carbon cap, a constraint is incorporated to limit the emissions across the entire transportation network. The carbon emission on each arc of the network is modeled using a generic convex function that depends on the total demand routed on the arc which is then approximated by a piecewise linear function to derive a mixed-integer stochastic formulation. A Benders-decomposition-based algorithm coupled with a sample average approximation scheme is developed to solve the stochastic model. The algorithm is enhanced with acceleration techniques to solve large-scale instances. Extensive computational experiments are conducted to evaluate the efficiency of the proposed algorithm and also to analyze the impact of incorporating carbon pricing factors on optimal hub networks. Computational results provide insights into sustainable hub network designs.

中文翻译：

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不确定性下可持续的枢纽选址


本文讨论了零担运输背景下不确定性下枢纽网络的可持续设计，并考虑了与碳定价相关的因素。该问题的模型是为了在随机需求环境中实现利润最大化，在这种环境中，根据利润、成本和碳排放之间的权衡，部分需求可能仍未得到满足。该模型明确将碳税以及运输和枢纽运营成本纳入目标函数。为了确保遵守碳排放上限，纳入了限制整个运输网络的排放量的约束。网络每个弧上的碳排放量使用通用凸函数进行建模，该凸函数取决于弧上路由的总需求，然后通过分段线性函数进行近似，以得出混合整数随机公式。开发了基于 Benders 分解的算法与样本平均近似方案相结合来求解随机模型。该算法通过加速技术得到增强，可以解决大规模实例。进行了大量的计算实验来评估所提出算法的效率，并分析纳入碳定价因素对最佳枢纽网络的影响。计算结果为可持续枢纽网络设计提供了见解。