Climate change has become a global concern, and the development of a green economy has attracted wide attention. Understanding the driving factors and growth potential of provincial-level carbon productivity is crucial for China’s green economic development in the new normal phase. In this study, the logarithmic mean Divisia index (LMDI) is adopted to systematically investigate the driving factors of provincial carbon productivity and explore the growth potential of provinces’ carbon productivity based on the clustering analysis. The results show that: (1) China’s provincial carbon productivity presents an increasing trend in 2001–2017, but the differences in carbon productivity among provinces are widening. (2) Economic activity and industrial structure are key to push up regional carbon productivity in China, while energy intensity is the main factor pulling it down. (3) The potential for carbon productivity improvement varies greatly among provinces in the four groups. Specifically, in groups 1 and 2, the developed provinces have little potential for improving carbon productivity, while the developing provinces in group 4 are just the opposite. These findings can enlighten policymakers that the development of a green economy should focus on optimizing and upgrading industrial structure and reducing energy intensity, and provincial heterogeneity must be considered when formulating green economic development policies.

In this paper, we propose a time-bound optimal planning model to reconcile the dilemma between the cutting efficiency and the cutting security. Unlike the traditional planning method, we consider the bound of the kinematic constraints to be flexible in the form of a fuzzy set. It is reasonable to use such an expression considering that the safety of the computer numerical control (CNC) machine is susceptible to the potential disturbance in the cutting process. A fuzzy optimization method is used to obtain a compromise bound aiming to balance the cutting efficiency and the cutting security. The original problem can be reduced into a convex problem in some weak conditions, for which some interesting results are proved and the numerical method is also used to solve it. The proposed algorithm is experimented on our self-designed CNC machine. We verify the effectiveness of our proposed method through air-cutting and milling process with two respect experiment, and verify the efficiency of our algorithm by comparing traditional open-loop strategies. Note to Practitioners —The starting point of this article is to improve the safety performance under the premise of ensuring the efficiency of CNC machining, but this method is also applicable to other robot arm path planning and design. The boundary of the existing speed planning problem cannot guarantee the safety of the machining process, and blindly reducing the kinematic boundary will greatly sacrifice the processing efficiency. This paper proposes a new method based on fuzzy programming to determine the optimal kinematic boundary, and this process can be completely realized in an open-loop manner, avoiding the method of avoiding risks through machine reorganization. In this paper, we mathematically describe the conditions for forming flexible kinematic boundaries, and then we resolve this problem into a fast-solvable optimization problem through a series of transformations. We perform air-cutting on the formed machining paths, incorporate them into the CAD system or carry out pocket milling tests in production. Preliminary physical experiments show that this method is feasible and has unique advantages over existing open-loop methods. In future research, we will give a more accurate estimate of the security membership function and extend the method to higher-order kinematically constrained problems.