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Urbanization and the release of carbon emission are two significant features of contemporary economic and social progress in China. However, there are few studies that consider how urbanization policy goals affect carbon emission. This paper aims to study the nonlinear effects of urbanization policy goals on carbon emission in 13 cities of the Beijing-Tianjin-Hebei region. In this paper, a multi-dimensional spatial disturbance grey model is proposed. Based on matrix perturbation theory, this paper explores the spatial perturbation bounds of the novel model and verifies that the spatial property of the model is consistent with the viewpoint of the First Law of Geography. Then, the novel model is used to predict the urban carbon emission under different urbanization policy goal scenarios. The results showed that the novel model has spatial regional correlation in spatial region prediction. With the development of urbanization level, carbon emissions show a downward trend in more than 50% of cities from 2022 to 2025. In addition, the improvement of urbanization policy goals will promote the carbon peak time of most cities. The carbon emission intensity will exhibit an inverted U-shaped trend distribution in space. The research results are conducive to providing scientific guidance for the formulation of new-type urbanization policies and helping to achieve the dual carbon goals. • A multi-dimensional spatial disturbance grey model is proposed. • The novel grey model is consistent with the viewpoint of the First Law of Geography. • The spatial distribution of carbon intensity showed an inverted U-shaped pattern. [ABSTRACT FROM AUTHOR]

• A single-manufacturer multi-retailer cold chain is investigated. • Quality degradation of the product occurs at multiple stages of the cold chain. • Quality degradation is captured by several features and the global stability index. • An algorithm is presented to determine the optimal solution. • It is found that operating a cold chain as a regular supply chain leads to a higher cost. This paper develops a model for a cold chain operated among a single product manufacturer and multiple retailers to minimize the total cost of the chain. A distinguishing feature of the cold chain is that the quality of the product degrades with time. The storage temperature and time influence the degradation rate. In this context, quality can be measured using multiple distinct indices. A global stability index is used to quantify the overall quality. The non-Arrhenius model is exclusively applied to measure the quality degradation during the transportation and at retailers' storage as the product moves in the cold chain. Optimal replenishment times for the manufacturer and retailers are decision variables and the cold chain's total cost includes the cooling cost, carbon emission cost, and loss of value in addition to the traditional supply chain costs. It is found that for a given manufacturer's replenishment time, the total cost is convex on each retailer's replenishment time. Hence, an algorithm is developed based on this property to find the optimal replenishment times for the manufacturer and retailers. This paper also investigates how specific cold chain parameters influence optimal decisions and the total cost. The analyses show that the resulting costs will be significantly higher if quality degradation is ignored in a cold chain. [ABSTRACT FROM AUTHOR]

• An improved singular spectrum decomposition is proposed. • High complexity components are secondarily decomposed to reduce its complexity. • An improved prediction model of optimization algorithm is proposed. • Intelligent weighting strategy is introduced to overcome traditional weighting problem. • A combined prediction model for carbon emission is proposed. Accurate prediction of carbon emission is critical for the development of low-carbon economy. However, most carbon emission prediction studies use a single model with low prediction accuracy, and do not consider the instability of carbon emission. Therefore, this paper proposes a combined prediction model of carbon emission. Firstly, the original data is decomposed by singular spectrum decomposition to obtain a limited amount of singular spectrum components. Secondly, high complexity components are secondarily decomposed by variational mode decomposition. Then, chameleon swarm algorithm and carnivorous plant algorithm are used to train the regularization coefficients and kernel parameters of kernel extreme learning machine and least squares support vector machine respectively, and the trained model is used to predict the decomposition components. Finally, induced ordered weighted averaging operator is used to calculate the weight of single model, and error correction is introduced to further promote the prediction accuracy. The carbon emission data of China and the United States is used to make a prediction experiment. The results indicate that the proposed model is superior to other comparative models in different indexes, which provides a new idea for carbon emission prediction. [ABSTRACT FROM AUTHOR]

• Inventory games and carbon emissions in multi-echelon supply chains are studied. • Cost and emissions reduction are achieved by synchronizing the ordering cycles. • An algebraic method is used to find solutions for vertical cooperation. • The models are developed under the carbon tax policy. • The effect of the carbon tax on cost, emissions, and cooperation savings are examined. This paper studies carbon tax policy in inventory games of multi-echelon supply chains. Four structures are considered with regard to the decision-making of supply chain members (decentralized, vertical downward cooperation, vertical upward cooperation, and horizontal cooperation). The purposes are to find the solutions of inventory games at each cooperation scheme, to compare strategies, and to examine the impact of the carbon tax on costs, emissions, and cooperation savings. A coordination mechanism with synchronized cycles is proposed, using cooperative game theory concepts in SC centralization. Closed-form equilibrium values were calculated for the optimal replenishment cycles, costs, and carbon emissions functions. For this intent, an algebraic method was deployed for vertical cooperation games. Though, other games were solved by an exact solution method. The numerical examples examined the impacts of the carbon tax on each structure and compared optimal solutions. Moreover, the impact of inventory and carbon emissions parameters on the cost and carbon emissions savings from cooperation settings were evaluated, indicating that SCs can reduce both costs and carbon emissions through cooperation. Additionally, it was found that the carbon tax can reduce the level of carbon emissions, while simultaneously decreasing coalition costs and emissions savings. [ABSTRACT FROM AUTHOR]

• A retailer-dominated supply chain with corporate social responsibility is modeled. • Impacts of emission reduction on supply chain's sustainability are analyzed. • Motivations of investing in emission reduction technology are proposed. • Supply chains sustainability is proved to be improved by coordination mechanism. • Performance of the coordination contract is tested analytically and numerically. This paper studies a retailer-dominated supply chain including a single upstream manufacturer that produces two substitutable products and a single downstream retailer that undertakes corporate social responsibility activities. The manufacturer is also regulated by a cap-and-trade policy. We first compare two optimization models for a decentralized system, one that does and one that does not incorporate emission reduction technology, to show that the profit of each system member in the former is higher than that in the latter, while the opposite is true for carbon emissions when the technology level invested by the manufacturer is higher than a threshold. To test the performance of the decentralized model that incorporates emission reduction technology, we model a centralized system and reveal that the system profit in the decentralized model is increased and the corresponding carbon emissions generated during production can be reduced. These findings motivate us to propose a revenue and cost-sharing contract to coordinate the decentralized system. The result shows that the economic and environmental sustainability of the decentralized system can be improved. Finally, several managerial implications are derived by conducting a numerical study. [ABSTRACT FROM AUTHOR]

• Four time-delay weights structural types are designed by the grey incidence model. • The novel multivariable grey prediction model considering the time-delay periods and time-delay weights is proposed. • The accumulating impact of influencing factors on CO 2 emissions of China's transport sector is measured. CO 2 emissions from the transportation sector occupy an increasingly important proportion in China's carbon dioxide emissions. Measuring the accumulative impact of factors on carbon emissions over time is of great significance for formulating corresponding policies. This paper aims to propose a novel time-delay multivariate grey model to measure the CO 2 emissions' accumulating impact of China's transportation sector. Firstly, the grey incidence model is used to identify time lags between the input and output variables, and also analyze the structure type of time-delay weights. Then, an accumulative time-delay multivariate grey prediction model is developed. In this model, a Gaussian formula is used to discretize the convolution integral of the time response function, and the particle swarm optimization algorithm is employed to determine the optimal weight coefficients. Finally, a case for CO 2 emissions prediction is adopted to test the effectiveness and practicality of this model compared with the alternative models. The results show that the proposed model outperforms other six competing models in accordance with two measuring indices, and suggestions on emissions mitigation are proposed based on the prediction results. [ABSTRACT FROM AUTHOR]

This paper develops a new inventory model with carbon tax policy and imperfect quality items in which the buyer exerts power over its supplier. It employs an order overlapping scheme to avoid shortages, overcomes some flaws in the literature, and develops two efficient solution algorithms. It also investigates different carbon tax systems on the performance of the model. Numerical results are discussed to bring some managerial insights. [ABSTRACT FROM AUTHOR]