To scientifically predict the future energy demand of Shandong province, this study chose the past energy demand of Shandong province during 1995–2015 as the research object. Based on building model data sequences, the GM-ARIMA model, the GM (1,1) model, and the ARIMA model were used to predict the energy demand of Shandong province for the 2005–2015 data, the results of which were then compared to the actual result. By analyzing the relative average error, we found that the GM-ARIMA model had a higher accuracy for predicting the future energy demand data. The operation steps of the GM-ARIMA model were as follows: first, preprocessing the date and determining the dimensions of the GM (1,1) model. This was followed by the establishment of the metabolism GM (1,1) model and by calculation of the forecast data. Then, the ARIMA residual error was used to amend and test the model. Finally, the obtained prediction results and errors were analyzed. The prediction results show that the energy demand of Shandong province in 2016–2020 will grow at an average annual rate of 3.9%, and in 2020, the Shandong province energy demand will have increased to about 20% of that in 2015.

Better prediction of energy demand is of vital importance for developing countries to develop effective energy strategies to improve energy security, partly because those countries’ energy demands are increasing rapidly. In this work, metabolic grey model (MGM), autoregressive integrated moving average (ARIMA), MGM-ARIMA, and back propagation neural network (BP) are adopted to forecast energy demand in India, the third largest energy consumer in the world after China and the USA. The average relative errors between the actual and simulated value are 1.31% (MGM), 1.07%, 0.92% (MGM-ARIMA), and 0.39% (BP). The high prediction accuracy indicates that the prediction result is effective. The result shows that India’s energy consumption will increase by 4.75% a year in the next 14 years. Compared with the 5.1% per year on average in 1995–2016, India’s energy consumption will still continue its steady growth at about 5% growth from 2017 to 2030.

Renewable energy batteries play a crucial role in the stable storage of clean energy. However, the supply risks associated with critical mineral raw materials closely related to renewable energy batteries - namely lithium, manganese, cobalt, and nickel - significantly threaten the safety and stability of these batteries. Therefore, this study selects representative factors from four aspects: resources, market, international relations, and technology, and employs the SMAA-TRI method to assess the supply risks of critical minerals required for renewable energy storage batteries. The results indicate that: (1) From 2006 to 2022, the supply risk of lithium resources for renewable energy batteries in China evolved from medium-high to high, while the risks for manganese, nickel, and cobalt resources remain within the high-risk range; (2) Predictions from the BP neural network model suggest that lithium, manganese, nickel, and cobalt would continue to be in the high-risk range over the next three years; (3) Sensitivity analysis reveals that environmental safety, resource recovery rates, substitution rates, external dependencies, and production concentration would become significant factors constraining the supply risks of renewable energy storage batteries.

Exploration of the green flexible job-shop scheduling problem is essential for enterprises aiming for sustainable practices, including energy conservation, emissions reduction, and enhanced economic and social benefits. While existing research has predominantly focused on carbon emissions or energy consumption as green scheduling objectives, this paper addresses the broader scope by incorporating the impact of variable energy prices on energy cost. Through the introduction of an energy cost model based on time-of-use electricity pricing, the study formulates a multi-objective optimization model for green flexible job-shop scheduling. The objectives include minimizing cost, reducing carbon emissions, and maximizing customer satisfaction. To prevent premature convergence and maintain population diversity, an enhanced genetic algorithm is employed for solving. The validation of the algorithm’s effectiveness is demonstrated through specific examples, providing decision results for optimal scheduling under various weight combinations. The research outcomes hold substantial practical value as they can significantly reduce energy expenses, lower carbon emissions, and elevate customer satisfaction while safeguarding production efficiency. This contributes to enhancing the market competitiveness and green brand image of businesses.

Most existing studies on energy sustainability have focused on qualitative research. Few studies have applied quantitative methods, and there has not been a systematic review of energy sustainability. To fill this gap, this study first developed a sustainable energy evaluation index system consisting of 20 indicators across the three dimensions of economy, energy, and environment based on the pressure-state-response (PSR) model. The weights of these indicators were then determined in conjunction with the weighting method. Finally, the matter-element extension method was improved to quantify energy sustainability. The proposed method was applied to evaluate China’s energy sustainability status from 2000 to 2015. The results show that China’s status continued to improve; however, it remained at a low level. To improve China’s energy sustainability, more efforts are needed in the economic, energy, and environmental dimensions.

India’s coal consumption is closely related to greenhouse gas emissions and the balance of supply and demand in energy trading markets. Most existing research on India focuses on total energy, renewable energy and energy intensity. To fill this gap, this study used two single forecasting models: the metabolic grey model (MGM) and the Back-Pro-Pagation Network (BP) to make predictions. In addition, based on these two single models, this study also developed the ARIMA correction principle and derived two combined models: the metabolic grey model, the Autoregressive Integrated Moving Average model (MGM-ARIMA) and Back-Pro-Pagation Network; and the Autoregressive Integrated Moving Average model (BP-ARIMA). After fitting India’s coal consumption during 1995–2017, the average relative errors of the four models were 2.28%, 1.53%, 1.50% and 1.42% respectively. The forecast results show that coal consumption in India will continue to increase at an average annual rate of 2.5% during the period from 2018–2030.