As'ad Rami, Hariga Moncer, Shamayleh Abdulrahim
Department of Industrial Engineering, College of Engineering, American University of Sharjah, P.O. Box 26666, Sharjah, United Arab Emirates.
Comput Ind Eng. 2020 Nov;149:106800. doi: 10.1016/j.cie.2020.106800. Epub 2020 Sep 4.
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.
在对将环境因素作为决策过程不可或缺部分的运营供应链模型的兴趣日益浓厚之际，本文探讨了冷藏产品的动态批量问题，同时考虑了温控存储和运输活动中产生的碳排放。我们提出了两个混合整数规划模型，以处理两种情况：一种是在整个规划期内设定碳排放上限，另一种是更严格的每期设定碳排放上限。对于第一个模型，我们提出了一种拉格朗日松弛方法，该方法提供了一种比较碳税和碳排放上限政策的运营成本和碳足迹表现的手段。随后，开发了一种基于二分法的算法来求解松弛模型并生成最优订购策略。然而，第二个模型是通过基于动态规划的算法求解的，同时考虑了每期碳排放上限的两个既定下限和上限。第一个模型的计算实验结果表明，随着预设上限值的增加，总碳排放量（运营成本）呈逐步增加（减少）趋势。第二个模型也观察到了类似的行为，不同的是，有时在每期上限值稍紧的情况下会出现总排放量的反常增加。
