An Optimized Grey–Markov Computational Framework for Accurate Energy Demand Forecasting and Industrial Decision Support

Authors

  • Ghazale Azimi Department of Industrial Engineering, NT.C., Islamic Azad University, Tehran, Iran.
  • Vahid Baradaran * Department of Industrial Engineering, NT.C., Islamic Azad University, Tehran, Iran. https://orcid.org/0000-0001-5385-629X

https://doi.org/10.22105/raise.v2i4.95

Abstract

Accurate long-term energy demand forecasting is essential for supporting strategic planning, infrastructure development, and resource allocation under increasing uncertainty. However, conventional forecasting methods often struggle to achieve reliable predictions when historical observations are limited, and energy consumption exhibits nonlinear and stochastic behavior. This study proposes a Simulated Annealing Markov Chain Grey Model (SA-MCGM) that integrates Grey System Theory, Markov Chain modelling, and Simulated Annealing (SA) optimization into a unified computational forecasting framework. The proposed approach combines deterministic trend modelling with probabilistic residual correction while simultaneously optimizing the grey model parameters and the number of Markov states to improve forecasting accuracy. The model is validated using annual energy consumption data for Asia from 2000 to 2022 and is compared with GM(1,1), the conventional Markov Chain Grey Model (MCGM), and ARIMA. Experimental results show that the proposed model achieves the best predictive performance during the testing period, reducing the Mean Squared Error (MSE) by 98.17% compared with the conventional MCGM and producing stable long-term forecasts through 2035. The findings demonstrate that simultaneous optimization of deterministic and stochastic model components significantly enhances forecasting robustness and generalization. The proposed SA-MCGM provides a computationally efficient forecasting framework that can support industrial engineering applications, including energy planning, infrastructure development, production planning, and strategic decision-making under uncertain conditions.

Keywords:

Grey system theory, Simulated annealing, Markov chain, Energy demand forecasting, Computational modelling

References

  1. [1] BP's Website. (2022). Annual report and form 20-F 2022. https://www.bp.com/api/files/6cqieuqhq4no/master/10C5j6Wi2CkktKj1WH3OuG/7635c09e4bf89081483a3ff319c70ed9/bp-annual-report-and-form-20f-2022.pdf
  2. [2] Nations, U. (2021). Policy Brief 9: SDG 7 in Asia and the Pacific. https://sdgs.un.org/sites/default/files/2021-05/POLICY BRIEF 9 - SDG 7 IN ASIA AND THE PACIFIC.pdf
  3. [3] International Energy Agency. (2021). Energy Transition in Southeast Asia. https://www.iea.org/reports/energy-transition-in-southeast-asia/
  4. [4] Chen, S. Y., Qu, G. F., Wang, X. H., & Zhang, H. Z. (2003). Traffic flow forecasting based on grey neural network model. Proceedings of the 2003 international conference on machine learning and cybernetics (Vol. 2, pp. 1275-1278). IEEE. https://doi.org/10.1109/ICMLC.2003.1259684
  5. [5] Sharma, G., Dhore, M. L., Jansirani, D., Bala Jeshurun, S., Sathi, G., Sherje, N., & Vivek, V. (2024). AI and machine learning applications in predicting energy market prices and trends. E3S web of conferences (Vol. 591, p. 01002). EDP Sciences. https://doi.org/10.1051/e3sconf/202459101002
  6. [6] Khezeli, M., Seidi, M., & Najafi, S. E. (2025). Performance evaluation using the hybrid resilience threshold based on reliability, efficiency and specific energy consumption. Journal of applied research on industrial engineering, 12(2), 334–361. https://doi.org/10.22105/jarie.2025.464447.1624
  7. [7] Ejegwa, P. A., Anum, M. T., Kausar, N., Nwokoro, C. O., & Cagin, T. A. (2025). A novel Q-rung Orthopair fuzzy distance metric for energy source selection. Journal of applied research on industrial engineering, 12(3), 429–464. https://doi.org/10.22105/jarie.2025.530199.1821
  8. [8] Ju-Long, D. (1982). Control problems of grey systems. Systems & control letters, 1(5), 288–294. https://doi.org/10.1016/S0167-6911(82)80025-X
  9. [9] Kayacan, E., Ulutas, B., & Kaynak, O. (2010). Grey system theory-based models in time series prediction. Expert systems with applications, 37(2), 1784–1789. https://doi.org/10.1016/j.eswa.2009.07.064
  10. [10] Huang, L., Liao, Q., Zhang, H., Jiang, M., Yan, J., & Liang, Y. (2021). Forecasting power consumption with an activation function combined grey model: A case study of China. International journal of electrical power & energy systems, 130, 106977. https://doi.org/10.1016/j.ijepes.2021.106977
  11. [11] Ma, X., Qi, C., Ye, L., Yang, D., & Hong, J. (2017). Life cycle assessment of tungsten carbide powder production: A case study in China. Journal of cleaner production, 149, 936–944. https://doi.org/10.1016/j.jclepro.2017.06.167
  12. [12] Liu, D., Li, G., Chanda, E. K., Hu, N., & Ma, Z. (2019). An improved GM (1.1) model with background value optimization and Fourier-series residual error correction and its application in cost forecasting of coal mine. Gospodarka surowcami mineralnymi, 35(3), 75–98. https://doi: 10.24425/gsm.2019.128528
  13. [13] Xiao, L., Chen, X., & Wang, H. (2021). Calculation and realization of new method grey residual error correction model. Plos one, 16(7), e0254154. https://doi.org/10.1371/journal.pone.0254154
  14. [14] Kazemi, A., Modarres, M., Mehregan, M., & others. (2013). Energy demand forecast of Iran’s industrial sector using Markov chain Grey model. The international journal of humanities, 20(1), 1–12. https://dor.isc.ac/dor/20.1001.1.25382640.2013.20.1.6.3
  15. [15] Zhou, W., Jiang, H., & Chang, J. (2023). Forecasting renewable energy generation based on a novel dynamic accumulation grey seasonal model. Sustainability, 15(16), 12188. https://doi.org/10.3390/su151612188
  16. [16] Sun, X., Sun, W., Wang, J., Zhang, Y., & Gao, Y. (2016). Using a Grey--Markov model optimized by Cuckoo search algorithm to forecast the annual foreign tourist arrivals to China. Tourism management, 52, 369–379. https://doi.org/10.1016/j.tourman.2015.07.005
  17. [17] Ren, Y., Xia, L., & Wang, Y. (2023). Forecasting China's hydropower generation using a novel seasonal optimized multivariate grey model. Technological forecasting and social change, 194, 122677. https://doi.org/10.1016/j.techfore.2023.122677
  18. [18] Wang, Y., Chi, P., Nie, R., Ma, X., Wu, W., & Guo, B. (2022). Self-adaptive discrete grey model based on a novel fractional order reverse accumulation sequence and its application in forecasting clean energy power generation in China. Energy, 253, 124093. https://doi.org/10.1016/j.energy.2022.124093
  19. [19] Li, X., Li, J., Zhao, Y., & Zhou, S. (2025). A novel discrete multivariable grey model with seasonal time-lag effect for clean energy generation forecasting. Energy, 137678. https://doi.org/10.1016/j.energy.2025.137678
  20. [20] Zhang, G. P. (2003). Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing, 50, 159–175. https://doi.org/10.1016/S0925-2312(01)00702-0
  21. [21] Lee, G.-C. (2024). A regression-based method for monthly electric load forecasting in South Korea. Energies, 17(23), 5860. https://doi.org/10.3390/en17235860
  22. [22] Azadeh, A., Ghaderi, S. F., & Sohrabkhani, S. (2008). Annual electricity consumption forecasting by neural network in high energy consuming industrial sectors. Energy conversion and management, 49(8), 2272–2278. https://doi.org/10.1016/j.enconman.2008.01.035
  23. [23] Kirkpatrick, S., Gelatt, C. D., & Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220(4598), 671–680. https://doi.org/10.1126/science.220.4598.671
  24. [24] Li, X., Dang, Y., & Zhao, J. (2010). An optimization method of estimating parameters in GM (1, 1) Model. In Advances in grey systems research (pp. 341–347). Springer. https://doi.org/10.1007/978-3-642-13938-3_29
  25. [25] Saxena, A. (2021). Grey forecasting models based on internal optimization for Novel Corona virus (COVID-19). Applied soft computing, 111, 107735. https://doi.org/10.1016/j.asoc.2021.107735
  26. [26] Aarts, E., & Korst, J. (1989). Simulated annealing and Boltzmann machines: A stochastic approach to combinatorial optimization and neural computing. John Wiley & Sons, Inc.. https://dl.acm.org/doi/abs/10.5555/61990

Downloads

Published

2025-12-10

Issue

Vol. 2 No. 4 (2025): Research Annals of Industrial and Systems Engineering

Section

Articles

How to Cite

Azimi, G. ., & Baradaran, V. . (2025). An Optimized Grey–Markov Computational Framework for Accurate Energy Demand Forecasting and Industrial Decision Support. Research Annals of Industrial and Systems Engineering, 2(4), 272-289. https://doi.org/10.22105/raise.v2i4.95

Similar Articles

11-20 of 32

You may also start an advanced similarity search for this article.