Urban innovation capacity is increasingly critical to city development, and quantitative assessments of innovative cities’ innovation capability can be achieved via the composite index method, which fully integrates multidimensional indicators. This study develops a hierarchical data envelopment analysis (H-DEA) method to establish a composite index evaluation model for innovation capacity, which features flexible and objective two-level indicators—an advantage that avoids subjective weight assignment and adapts well to the hierarchical structure of innovation evaluation indicators. The proposed H-DEA model is applied to evaluate 67 innovative cities in China, yielding composite scores and rankings that are further compared with those from the traditional weighting method. Sensitivity analysis is conducted by adjusting different upper and lower bounds of the H-DEA model to verify its robustness. Additionally, these 67 cities are divided into four regions, with region-specific weights assigned to the evaluation indicators in the model. The results show that the eastern region has the highest average innovation capacity (0.3783), where technological innovation (weight 0.27) serves as a key driving force; the western region has the lowest average innovation capacity (0.3235), and its innovative cities should prioritize improving outcome transformation capacity (weight 0.1357). Overall, technological innovation receives the highest average weight (0.2422), while outcome transformation capacity gets the lowest (0.1647).

In recent years, China’s digital economy has become a key engine for high-quality development. Assessing the operational efficiency of leading digital enterprises is crucial for optimizing resource allocation and promoting sectoral growth. However, existing research largely remains at regional or industry levels and typically reports efficiency scores without diagnosing the root sources of inefficiency. To fill this gap, this study measures the operational efficiency of 99 firms selected from China’s Top 100 Digital Economy list (2017–2022) using the BCC-DEA model, and analyzes their dynamic evolution via kernel density estimation. The findings reveal a fluctuating upward trend in overall efficiency, and that the gap in overall technical efficiency primarily originates from scale efficiency rather than pure technical efficiency. The kernel density peak exhibits a “rise–decline–rise” pattern, indicating existing but narrowing efficiency differences among firms. By decomposing efficiency, this study further classifies firms into four types, revealing that inefficiency is heterogeneous. This paper makes three main contributions. First, it identifies scale efficiency as the main source of efficiency gaps. Second, it classifies firms into four types, revealing that inefficiency is heterogeneous. Third, it uses kernel density estimation to track the dynamic evolution of efficiency, showing a narrowing efficiency gap but a persistent superstar effect. Two policy implications follow: firms with low pure technical efficiency should focus on management training and technology adoption, while firms with low scale efficiency should pursue scale expansion through mergers or partnerships.

China’s economic development has achieved great success in recent years, but the problems of energy scarcity and environmental pollution have become increasingly serious. To enhance the reliability and efficiency between energy, the environment and the economy, sustainable development is an inevitable choice. In the context of measuring sustainability efficiency, a network data envelopment analysis model is proposed to formulate the two-stage process of energy use and operations management. A double frontier is derived to optimize the available energy for sustainable development. Due to nonlinearity, previous linear methods are not directly applicable to identify the double frontier and calculate stage efficiencies for inefficient decision-making units. To address this problem, this study develops the primal-dual relationship between multiplicative and envelopment network models based on the Lagrange duality principle of parametric linear programming. The newly developed approach is used to evaluate the sustainability efficiency of 30 administrative regions in China. The results show that insufficient sustainability efficiency is a systemic problem. Different regions should take different measures to conserve energy and reduce pollutant emissions for sustainable development. To increase sustainability efficiency, regions should support energy-saving and emission-reducing technologies in production processes and strengthen their capacity for technological innovation. Compared with energy use efficiency, operations management efficiency in China has a wider range of changes. During the operations management stage, there is not much difference between the capacity and quantity of each region. Based on benchmark regions at the efficiency frontier, there is an opportunity to improve operations management in the near future. Blockchain technology can effectively improve energy allocation efficiency.