Cold chain logistics has become one of the main sources of carbon emissions. Meanwhile, the implementation of low-carbon economy has become an inevitable way to promote sustainable development. However, previous studies on the cold chain inventory routing problem (IRP) paid less attention to the cost of carbon emissions. In this paper, a linear programming (LP) model is established, which takes the costs of vehicle transportation, time window and carbon emission into consideration. Although the simple LP model is easy to be solved, it cannot handle the problems with uncertainty. Therefore, in order to overcome the influence of uncertainty, the proposed LP model is developed into three low-carbon robust optimization (RO) models. In addition, this paper takes a cold chain logistics enterprise in Yangtze River Delta as an example for empirical analysis. The results of the case study prove that the RO models can quickly solve the problems with uncertainty and still maintain robustness, while the LP model has failed. Specifically, the R-ellipsoid model produces the best result among the three RO models. It is suggested that when the carbon emission tax increases, the decision makers tend to choose a better path planning scheme, which will not only reduce the total cost, but also obtain environmental benefits. Finally, the findings of this paper generate some implications for the low-carbon transformation of cold chain logistics enterprises.

中文翻译：

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考虑碳排放和随机需求的两梯队农业冷链物流鲁棒优化方法

冷链物流已成为碳排放的主要来源之一。同时，推行低碳经济已成为促进可持续发展的必然途径。然而，之前关于冷链库存路径问题（IRP）的研究较少关注碳排放成本。本文建立了一个线性规划（LP）模型，该模型考虑了车辆运输成本、时间窗口和碳排放。简单的LP模型虽然容易求解，但无法处理不确定性问题。因此，为了克服不确定性的影响，将所提出的LP模型发展为三个低碳鲁棒优化（RO）模型。此外，本文以长三角某冷链物流企业为例进行实证分析。案例研究结果证明，RO模型可以快速解决具有不确定性的问题并仍然保持鲁棒性，而LP模型则失败了。具体来说，R-椭球模型在三个 RO 模型中产生了最好的结果。建议当碳排放税增加时，决策者倾向于选择更好的路径规划方案，这样既能降低总成本，又能获得环境效益。最后，本文的研究结果对冷链物流企业的低碳转型产生了一定的启示。而 LP 模型失败了。具体来说，R-椭球模型在三个 RO 模型中产生了最好的结果。建议当碳排放税增加时，决策者倾向于选择更好的路径规划方案，这样既能降低总成本，又能获得环境效益。最后，本文的研究结果对冷链物流企业的低碳转型产生了一定的启示。而 LP 模型失败了。具体来说，R-椭球模型在三个 RO 模型中产生了最好的结果。建议当碳排放税增加时，决策者倾向于选择更好的路径规划方案，这样既能降低总成本，又能获得环境效益。最后，本文的研究结果对冷链物流企业的低碳转型产生了一定的启示。