Amid the ever growing interest in operational supply chain models that incorporate environmental aspects as an integral part of the decision making process, this paper addresses the dynamic lot sizing problem of a cold product while accounting for carbon emissions generated during temperature-controlled storage and transportation activities. We present two mixed integer programming models to tackle the two cases where the carbon cap is imposed over the whole planning horizon versus the more stringent version of a cap per period. For the first model, a Lagrangian relaxation approach is proposed which provides a mean for comparing the operational cost and carbon footprint performance of the carbon tax and the carbon cap policies. Subsequently, a Bisection based algorithm is developed to solve the relaxed model and generate the optimal ordering policy. The second model, however, is solved via a dynamic programming based algorithm while respecting two established lower and upper bounds on the periodic carbon cap. The results of the computational experiments for the first model display a stepwise increase (decrease) in the total carbon emissions (operational cost) as the preset cap value is increased. A similar behavior is also observed for the second model with the exception that paradoxical increases in the total emissions are sometimes realized with slightly tighter values of the periodic cap.

中文翻译：

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碳限额政策下冷产品的可持续动态批量调整模型

随着对将环境因素作为决策过程的一个组成部分的运营供应链模型的兴趣日益增长，本文解决了冷产品的动态批量调整问题，同时考虑了温控存储和运输活动期间产生的碳排放. 我们提出了两个混合整数规划模型，以解决在整个规划范围内强加碳上限与每个时期的更严格版本的碳上限的两种情况。对于第一个模型，提出了拉格朗日松弛方法，该方法为比较碳税和碳上限政策的运营成本和碳足迹性能提供了一种手段。随后，开发了基于二分的算法来解决松弛模型并生成最佳排序策略。然而，第二个模型是通过基于动态规划的算法求解的，同时尊重周期性碳上限的两个既定下限和上限。第一个模型的计算实验结果显示，随着预设上限值的增加，总碳排放量（运营成本）逐步增加（减少）。对于第二个模型也观察到类似的行为，不同之处在于总排放量的矛盾增加有时是通过稍微收紧周期性上限的值来实现的。第一个模型的计算实验结果显示，随着预设上限值的增加，总碳排放量（运营成本）逐步增加（减少）。对于第二个模型也观察到类似的行为，不同之处在于总排放量的矛盾增加有时是通过稍微收紧周期性上限的值来实现的。第一个模型的计算实验结果显示，随着预设上限值的增加，总碳排放量（运营成本）逐步增加（减少）。对于第二个模型也观察到类似的行为，不同之处在于总排放量的矛盾增加有时是通过稍微收紧周期性上限的值来实现的。