How to cite this paper
Fatemi, Z., Sadjadi, S & Makui, A. (2025). A review of mathematical methods in energy management optimization.Current Chemistry Letters, 14(1), 1-10.
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1. Dominguez, R., Cannella, S., & Framinan, J. M. (2021). Remanufacturing configuration in complex supply chains. Omega, 101, 102268, https://doi.org/10.1016/j.omega.2020.102268.
2. Huang, W., & Zhu, H. (2021). Performance evaluation and improvement for ZEV credit regulation in a competitive environment. Omega, 102, 102294, https://doi.org/10.1016/j.omega.2020.102294.
3. Napp, T. A., Gambhir, A., Hills, T. P., Florin, N., & Fennell, P. S. (2014). A review of the technologies, economics, and policy instruments for decarbonising energy-intensive manufacturing industries. Renew. Sustain. Energ. Rev, 30, 616-640.
4. Zhang, Q., Tang, W., & Zhang, J. (2018). Who should determine energy efficiency level in a green cost-sharing supply chain with learning effect?. Comput. Ind. Eng., 115, 226-239.
5. Safarzadeh, S., & Rasti-Barzoki, M. (2020). A duopolistic game for designing a comprehensive energy-efficiency scheme regarding consumer features: Which energy policy is the best? J. Clean. Prod., 255, 120195, https://doi.org/10.1016/j.jclepro.2020.120195.
6. Safarzadeh, S., Rasti-Barzoki, M., & Hejazi, S. R. (2020). A review of optimal energy policy instruments on industrial energy efficiency programs, rebound effects, and government policies. Energ. Pol., 139, 111342, https://doi.org/10.1016/j.enpol.2020.111342.
7. Safarzadeh, S., Rasti-Barzoki, M., Hejazi, S. R., & Piran, M. J. (2020). A game-theoretic approach for the duopoly pricing of energy-efficient appliances regarding innovation protection and social welfare. Energy, 200, 117517, https://doi.org/10.1016/j.energy.2020.117517.
8. Liu, K., Li, W., Jia, F., & Lan, Y. (2022). Optimal strategies of green product supply chains based on behavior-based pricing. J. Clean. Prod., 130288, https://doi.org/10.1016/j.jclepro.2021.130288.
9. Nielsen, I. E., Majumder, S., Sana, S. S., & Saha, S. (2019). Comparative analysis of government incentives and game structures on single and two-period green supply chain. J. Clean. Prod., 235, 1371-1398.
10. Mahmoudi, R., & Rasti-Barzoki, M. (2018). Sustainable supply chains under government intervention with a real-world case study: An evolutionary game-theoretic approach. Comput. Ind. Eng., 116, 130-143.
11. Huang, W., Zhou, W., Chen, J., & Chen, X. (2019). The government’s optimal subsidy scheme under Manufacturers’ competition of price and product energy efficiency. Omega, 84, 70-101.
12. Bilgen, S., Keleş, S., Kaygusuz, A., Sarı, A., & Kaygusuz, K. (2008). Global warming and renewable energy sources for sustainable development: a case study in Turkey. Renew. Sustain. Energy Rev., 12(2), 372-396.
13. Zhang, X., Pei, W., Deng, W., Du, Y., Qi, Z., & Dong, Z. (2015). Emerging smart grid technology for mitigating global warming. Int. J. Energy Res., 39(13), 1742-1756.
14. Kirchhoff, H., Kebir, N., Neumann, K., Heller, P. W., & Strunz, K. (2016). Developing mutual success factors and their application to swarm electrification: microgrids with 100% renewable energies in the Global South and Germany. J. Clean. Prod., 128, 190-200.
15. Papageorgiou, A., Ashok, A., Farzad, T. H., & Sundberg, C. (2020). Climate change impact of integrating a solar microgrid system into the Swedish electricity grid. Appl. Energy, 268, 114981, https://doi.org/10.1016/j.apenergy.2020.114981.
16. Yoldaş, Y., Önen, A., Muyeen, S. M., Vasilakos, A. V., & Alan, I. (2017). Enhancing smart grid with microgrids: Challenges and opportunities. Renew. Sustain. Energy Rev., 72, 205-214.
17. Zhang, M., Jiao, Z., Ran, L., & Zhang, Y. (2023). Optimal energy and reserve scheduling in a renewable-dominant power system. Omega, 118, 102848, https://doi.org/10.1016/j.omega.2023.102848.
18. Wang, G., Zhang, Q., Li, H., McLellan, B. C., Chen, S., Li, Y., & Tian, Y. (2017). Study on the promotion impact of demand response on distributed PV penetration by using non-cooperative game theoretical analysis. Appl. Energy, 185, 1869-1878.
19. Tushar, M. H. K., Zeineddine, A. W., & Assi, C. (2017). Demand-side management by regulating charging and discharging of the EV, ESS, and utilizing renewable energy. IEEE Trans. Ind. Inform., 14(1), 117-126.
20. Van Ackooij, W., De Boeck, J., Detienne, B., Pan, S., & Poss, M. (2018). Optimizing power generation in the presence of micro-grids. Eur. J. Oper. Res., 271(2), 450-461.
21. Fang, Y., Wei, W., Liu, F., Mei, S., Chen, L., & Li, J. (2019). Improving solar power usage with electric vehicles: Analyzing a public-private partnership cooperation scheme based on evolutionary game theory. J. Clean. Prod., 233, 1284-1297.
22. Akbari-Dibavar, A., Nojavan, S., Mohammadi-Ivatloo, B., & Zare, K. (2020). Smart home energy management using hybrid robust-stochastic optimization. Comput. Ind. Eng., 143, 106425, https://doi.org/10.1016/j.cie.2020.106425.
23. Dai, Y., Qi, Y., Li, L., Wang, B., & Gao, H. (2021). A dynamic pricing scheme for electric vehicle in photovoltaic charging station based on Stackelberg game considering user satisfaction. Comput. Ind. Eng., 154, 107117, https://doi.org/10.1016/j.cie.2021.107117.
24. Lin, Q., Liu, L. J., Yuan, M., Ge, L. J., Wang, Y. H., & Zhang, M. (2021). Choice of the distributed photovoltaic power generation operating mode for a manufacturing enterprise: Surrounding users vs a power grid. J. Clean. Prod., 293, 126199, https://doi.org/10.1016/j.jclepro.2021.126199.
25. Erol, Ö., & Filik, Ü. B. (2022). A Stackelberg game approach for energy sharing management of a microgrid providing flexibility to entities. Appl. Energy, 316, 118944, https://doi.org/10.1016/j.apenergy.2022.118944.
26. Luo, X., Shi, W., Jiang, Y., Liu, Y., & Xia, J. (2022). Distributed peer-to-peer energy trading based on game theory in a community microgrid considering ownership complexity of distributed energy resources. J. Clean. Prod., 351, 131573, https://doi.org/10.1016/j.jclepro.2022.131573.
27. Zhou, W., & Huang, W. (2016). Contract designs for energy-saving product development in a monopoly. Eur. J. Oper. Res., 250(3), 902-913.
28. Zhou, W., Huang, W., & Zhou, S. X. (2017). Energy performance contracting in a competitive environment. Decis. Sci. J., 48(4), 723-765.
29. Safarzadeh, S., & Rasti-Barzoki, M. (2019). A game-theoretic approach for pricing policies in a duopolistic supply chain considering energy productivity, industrial rebound effect, and government policies. Energy, 167, 92-105.
30. Safarzadeh, S., & Rasti-Barzoki, M. (2019). A game-theoretic approach for assessing residential energy-efficiency program considering rebound, consumer behavior, and government policies. Appl. Energ., 233, 44-61.
31. uit het Broek, M. A., Van der Heide, G., & Van Foreest, N. D. (2020). Energy-saving policies for temperature-controlled production systems with state-dependent setup times and costs. Eur. J. Oper. Res., 287(3), 916-928.
32. Rasti-Barzoki, M., & Moon, I. (2020). A game-theoretic approach for car pricing and its energy efficiency level versus governmental sustainability goals by considering rebound effect: A case study of South Korea. Appl. Energ., 271, 115196.
33. Yan, J., Deng, D., Lu, F., & Zhang, Z. (2020). A new efficient energy-preserving finite volume element scheme for the improved Boussinesq equation. Appl. Math. Model., 87, 20-41.
34. Wang, W., Du, W., Cheng, C., Lu, X., & Zou, W. (2022). Output feedback control for energy-saving asymmetric hydraulic servo system based on desired compensation approach. Appl. Math. Model., 101, 360-379.
35. Chargui, K., Zouadi, T., Sreedharan, V. R., El Fallahi, A., & Reghioui, M. (2023). A novel robust exact decomposition algorithm for berth and quay crane allocation and scheduling problems considering uncertainty and energy efficiency. Omega, 118, 102868, https://doi.org/10.1016/j.omega.2023.102868.
36. Bai, Q., Chen, J., & Xu, J. (2023). Energy conservation investment and supply chain structure under cap-and-trade regulation for a green product. Omega, 119, 102886, https://doi.org/10.1016/j.omega.2023.102886.
37. Fatemi, Z., Sadjadi, S. J., Jabbarzadeh, A., & Makui, A. (2023). Investments in energy efficiency with government environmental sensitiveness: An application of geometric programming and game theory. Sci. Iran., 10.24200/sci.2023.60289.6706.
38. Diaby, M., Cruz, J. M., & Nsakanda, A. L. (2013). Shortening cycle times in multi-product, capacitated production environments through quality level improvements and setup reduction. Eur. J. Oper. Res., 228(3), 526-535.
39. Duffin, R. J., & Peterson, E. L. (1973). Geometric programming with signomials. J. Optim. Theor. Appl., 11(1), 3-35.
40. Shen, P., Zhu, Z., & Chen, X. (2019). A practicable contraction approach for the sum of the generalized polynomial ratios problem. Eur. J. Oper. Res., 278(1), 36-48.
41. Sadjadi, S. J., Oroujee, M., & Aryanezhad, M. B. (2005). Optimal production and marketing planning. Comput. Optim. Appl ., 30, 195-203.
42. Sadjadi, S. J., Ghazanfari, M., & Yousefli, A. (2010). Fuzzy pricing and marketing planning model: A possibilistic geometric programming approach. Expert Syst. Appl., 37(4), 3392-3397.
43. Sadjadi, S. J., Yazdian, S. A., & Shahanaghi, K. (2012). Optimal pricing, lot-sizing and marketing planning in a capacitated and imperfect production system. Comput. Ind. Eng., 62(1), 349-358.
44. Lim, S. (2013). A joint optimal pricing and order quantity model under parameter uncertainty and its practical implementation. Omega, 41(6), 998-1007.
45. Ruby, R., Zhong, S., Ng, D. W. K., Wu, K., & Leung, V. C. (2019). Enhanced energy-efficient downlink resource allocation in green non-orthogonal multiple access systems. Comput. Commun., 139, 78-90.
46. Yaghin, R. G. (2020). Enhancing supply chain production-marketing planning with geometric multivariate demand function (a case study of textile industry). Comput. Ind. Eng., 140, 106220.
47. Hayhoe, M., Barreras, F., & Preciado, V. M. (2021). Multitask learning and nonlinear optimal control of the COVID-19 outbreak: A geometric programming approach. Annu. Rev. Control., 52, 495-507.
48. Liu, Z., Zhu, H., Yuan, Y., Chan, K. Y., Yang, Y., & Guan, X. (2022). Maximizing lower bound of energy efficiency in multi-tier heterogeneous cellular network via stochastic geometry. Comput. Commun., 184, 64-72.
49. Boyd, S., Kim, S. J., Vandenberghe, L., & Hassibi, A. (2007). A tutorial on geometric programming. Optim. Eng., 8(1), 67-127.
50. Islam, S. (2008). Multi-objective marketing planning inventory model: a geometric programming approach. Appl. Math. Comput., 205(1), 238-246.
51. Liu, S. T. (2009). Using geometric programming to profit maximization with interval coefficients and quantity discount. Appl. Math. Comput, 209(2), 259-265.
2. Huang, W., & Zhu, H. (2021). Performance evaluation and improvement for ZEV credit regulation in a competitive environment. Omega, 102, 102294, https://doi.org/10.1016/j.omega.2020.102294.
3. Napp, T. A., Gambhir, A., Hills, T. P., Florin, N., & Fennell, P. S. (2014). A review of the technologies, economics, and policy instruments for decarbonising energy-intensive manufacturing industries. Renew. Sustain. Energ. Rev, 30, 616-640.
4. Zhang, Q., Tang, W., & Zhang, J. (2018). Who should determine energy efficiency level in a green cost-sharing supply chain with learning effect?. Comput. Ind. Eng., 115, 226-239.
5. Safarzadeh, S., & Rasti-Barzoki, M. (2020). A duopolistic game for designing a comprehensive energy-efficiency scheme regarding consumer features: Which energy policy is the best? J. Clean. Prod., 255, 120195, https://doi.org/10.1016/j.jclepro.2020.120195.
6. Safarzadeh, S., Rasti-Barzoki, M., & Hejazi, S. R. (2020). A review of optimal energy policy instruments on industrial energy efficiency programs, rebound effects, and government policies. Energ. Pol., 139, 111342, https://doi.org/10.1016/j.enpol.2020.111342.
7. Safarzadeh, S., Rasti-Barzoki, M., Hejazi, S. R., & Piran, M. J. (2020). A game-theoretic approach for the duopoly pricing of energy-efficient appliances regarding innovation protection and social welfare. Energy, 200, 117517, https://doi.org/10.1016/j.energy.2020.117517.
8. Liu, K., Li, W., Jia, F., & Lan, Y. (2022). Optimal strategies of green product supply chains based on behavior-based pricing. J. Clean. Prod., 130288, https://doi.org/10.1016/j.jclepro.2021.130288.
9. Nielsen, I. E., Majumder, S., Sana, S. S., & Saha, S. (2019). Comparative analysis of government incentives and game structures on single and two-period green supply chain. J. Clean. Prod., 235, 1371-1398.
10. Mahmoudi, R., & Rasti-Barzoki, M. (2018). Sustainable supply chains under government intervention with a real-world case study: An evolutionary game-theoretic approach. Comput. Ind. Eng., 116, 130-143.
11. Huang, W., Zhou, W., Chen, J., & Chen, X. (2019). The government’s optimal subsidy scheme under Manufacturers’ competition of price and product energy efficiency. Omega, 84, 70-101.
12. Bilgen, S., Keleş, S., Kaygusuz, A., Sarı, A., & Kaygusuz, K. (2008). Global warming and renewable energy sources for sustainable development: a case study in Turkey. Renew. Sustain. Energy Rev., 12(2), 372-396.
13. Zhang, X., Pei, W., Deng, W., Du, Y., Qi, Z., & Dong, Z. (2015). Emerging smart grid technology for mitigating global warming. Int. J. Energy Res., 39(13), 1742-1756.
14. Kirchhoff, H., Kebir, N., Neumann, K., Heller, P. W., & Strunz, K. (2016). Developing mutual success factors and their application to swarm electrification: microgrids with 100% renewable energies in the Global South and Germany. J. Clean. Prod., 128, 190-200.
15. Papageorgiou, A., Ashok, A., Farzad, T. H., & Sundberg, C. (2020). Climate change impact of integrating a solar microgrid system into the Swedish electricity grid. Appl. Energy, 268, 114981, https://doi.org/10.1016/j.apenergy.2020.114981.
16. Yoldaş, Y., Önen, A., Muyeen, S. M., Vasilakos, A. V., & Alan, I. (2017). Enhancing smart grid with microgrids: Challenges and opportunities. Renew. Sustain. Energy Rev., 72, 205-214.
17. Zhang, M., Jiao, Z., Ran, L., & Zhang, Y. (2023). Optimal energy and reserve scheduling in a renewable-dominant power system. Omega, 118, 102848, https://doi.org/10.1016/j.omega.2023.102848.
18. Wang, G., Zhang, Q., Li, H., McLellan, B. C., Chen, S., Li, Y., & Tian, Y. (2017). Study on the promotion impact of demand response on distributed PV penetration by using non-cooperative game theoretical analysis. Appl. Energy, 185, 1869-1878.
19. Tushar, M. H. K., Zeineddine, A. W., & Assi, C. (2017). Demand-side management by regulating charging and discharging of the EV, ESS, and utilizing renewable energy. IEEE Trans. Ind. Inform., 14(1), 117-126.
20. Van Ackooij, W., De Boeck, J., Detienne, B., Pan, S., & Poss, M. (2018). Optimizing power generation in the presence of micro-grids. Eur. J. Oper. Res., 271(2), 450-461.
21. Fang, Y., Wei, W., Liu, F., Mei, S., Chen, L., & Li, J. (2019). Improving solar power usage with electric vehicles: Analyzing a public-private partnership cooperation scheme based on evolutionary game theory. J. Clean. Prod., 233, 1284-1297.
22. Akbari-Dibavar, A., Nojavan, S., Mohammadi-Ivatloo, B., & Zare, K. (2020). Smart home energy management using hybrid robust-stochastic optimization. Comput. Ind. Eng., 143, 106425, https://doi.org/10.1016/j.cie.2020.106425.
23. Dai, Y., Qi, Y., Li, L., Wang, B., & Gao, H. (2021). A dynamic pricing scheme for electric vehicle in photovoltaic charging station based on Stackelberg game considering user satisfaction. Comput. Ind. Eng., 154, 107117, https://doi.org/10.1016/j.cie.2021.107117.
24. Lin, Q., Liu, L. J., Yuan, M., Ge, L. J., Wang, Y. H., & Zhang, M. (2021). Choice of the distributed photovoltaic power generation operating mode for a manufacturing enterprise: Surrounding users vs a power grid. J. Clean. Prod., 293, 126199, https://doi.org/10.1016/j.jclepro.2021.126199.
25. Erol, Ö., & Filik, Ü. B. (2022). A Stackelberg game approach for energy sharing management of a microgrid providing flexibility to entities. Appl. Energy, 316, 118944, https://doi.org/10.1016/j.apenergy.2022.118944.
26. Luo, X., Shi, W., Jiang, Y., Liu, Y., & Xia, J. (2022). Distributed peer-to-peer energy trading based on game theory in a community microgrid considering ownership complexity of distributed energy resources. J. Clean. Prod., 351, 131573, https://doi.org/10.1016/j.jclepro.2022.131573.
27. Zhou, W., & Huang, W. (2016). Contract designs for energy-saving product development in a monopoly. Eur. J. Oper. Res., 250(3), 902-913.
28. Zhou, W., Huang, W., & Zhou, S. X. (2017). Energy performance contracting in a competitive environment. Decis. Sci. J., 48(4), 723-765.
29. Safarzadeh, S., & Rasti-Barzoki, M. (2019). A game-theoretic approach for pricing policies in a duopolistic supply chain considering energy productivity, industrial rebound effect, and government policies. Energy, 167, 92-105.
30. Safarzadeh, S., & Rasti-Barzoki, M. (2019). A game-theoretic approach for assessing residential energy-efficiency program considering rebound, consumer behavior, and government policies. Appl. Energ., 233, 44-61.
31. uit het Broek, M. A., Van der Heide, G., & Van Foreest, N. D. (2020). Energy-saving policies for temperature-controlled production systems with state-dependent setup times and costs. Eur. J. Oper. Res., 287(3), 916-928.
32. Rasti-Barzoki, M., & Moon, I. (2020). A game-theoretic approach for car pricing and its energy efficiency level versus governmental sustainability goals by considering rebound effect: A case study of South Korea. Appl. Energ., 271, 115196.
33. Yan, J., Deng, D., Lu, F., & Zhang, Z. (2020). A new efficient energy-preserving finite volume element scheme for the improved Boussinesq equation. Appl. Math. Model., 87, 20-41.
34. Wang, W., Du, W., Cheng, C., Lu, X., & Zou, W. (2022). Output feedback control for energy-saving asymmetric hydraulic servo system based on desired compensation approach. Appl. Math. Model., 101, 360-379.
35. Chargui, K., Zouadi, T., Sreedharan, V. R., El Fallahi, A., & Reghioui, M. (2023). A novel robust exact decomposition algorithm for berth and quay crane allocation and scheduling problems considering uncertainty and energy efficiency. Omega, 118, 102868, https://doi.org/10.1016/j.omega.2023.102868.
36. Bai, Q., Chen, J., & Xu, J. (2023). Energy conservation investment and supply chain structure under cap-and-trade regulation for a green product. Omega, 119, 102886, https://doi.org/10.1016/j.omega.2023.102886.
37. Fatemi, Z., Sadjadi, S. J., Jabbarzadeh, A., & Makui, A. (2023). Investments in energy efficiency with government environmental sensitiveness: An application of geometric programming and game theory. Sci. Iran., 10.24200/sci.2023.60289.6706.
38. Diaby, M., Cruz, J. M., & Nsakanda, A. L. (2013). Shortening cycle times in multi-product, capacitated production environments through quality level improvements and setup reduction. Eur. J. Oper. Res., 228(3), 526-535.
39. Duffin, R. J., & Peterson, E. L. (1973). Geometric programming with signomials. J. Optim. Theor. Appl., 11(1), 3-35.
40. Shen, P., Zhu, Z., & Chen, X. (2019). A practicable contraction approach for the sum of the generalized polynomial ratios problem. Eur. J. Oper. Res., 278(1), 36-48.
41. Sadjadi, S. J., Oroujee, M., & Aryanezhad, M. B. (2005). Optimal production and marketing planning. Comput. Optim. Appl ., 30, 195-203.
42. Sadjadi, S. J., Ghazanfari, M., & Yousefli, A. (2010). Fuzzy pricing and marketing planning model: A possibilistic geometric programming approach. Expert Syst. Appl., 37(4), 3392-3397.
43. Sadjadi, S. J., Yazdian, S. A., & Shahanaghi, K. (2012). Optimal pricing, lot-sizing and marketing planning in a capacitated and imperfect production system. Comput. Ind. Eng., 62(1), 349-358.
44. Lim, S. (2013). A joint optimal pricing and order quantity model under parameter uncertainty and its practical implementation. Omega, 41(6), 998-1007.
45. Ruby, R., Zhong, S., Ng, D. W. K., Wu, K., & Leung, V. C. (2019). Enhanced energy-efficient downlink resource allocation in green non-orthogonal multiple access systems. Comput. Commun., 139, 78-90.
46. Yaghin, R. G. (2020). Enhancing supply chain production-marketing planning with geometric multivariate demand function (a case study of textile industry). Comput. Ind. Eng., 140, 106220.
47. Hayhoe, M., Barreras, F., & Preciado, V. M. (2021). Multitask learning and nonlinear optimal control of the COVID-19 outbreak: A geometric programming approach. Annu. Rev. Control., 52, 495-507.
48. Liu, Z., Zhu, H., Yuan, Y., Chan, K. Y., Yang, Y., & Guan, X. (2022). Maximizing lower bound of energy efficiency in multi-tier heterogeneous cellular network via stochastic geometry. Comput. Commun., 184, 64-72.
49. Boyd, S., Kim, S. J., Vandenberghe, L., & Hassibi, A. (2007). A tutorial on geometric programming. Optim. Eng., 8(1), 67-127.
50. Islam, S. (2008). Multi-objective marketing planning inventory model: a geometric programming approach. Appl. Math. Comput., 205(1), 238-246.
51. Liu, S. T. (2009). Using geometric programming to profit maximization with interval coefficients and quantity discount. Appl. Math. Comput, 209(2), 259-265.