A robust optimization model with two uncertainties applied to supplier selection
Abstract
Under intense industry competition, decision makers must ensure that products demanded by consumers can be quickly produced with minimum production cost. However, because uncertainties are unavoidable and inevitably affect decision makers, numerous studies have discussed how to control uncertainties or minimize their effects. Multiple uncertainties that interact simultaneously may cause a combined effect in actual systems. Therefore, this study presents a robust optimization model with two uncertainties, extending the method of robust optimization with one uncertainty. To demonstrate the applicability of the proposed model with two uncertainties, this study uses the supplier selection problem with component purchase quantity allocation in supply chain management as an analysis case. This considers the reliability of production and transportation and develops a multi-objective robust optimization model with two uncertainties. In addition, a nondominated sorting genetic algorithm is proposed for solving the proposed multi-objective robust optimization model. The relationship between price of robustness and budget parameters is explored by considering the robust optimization model with production and transportation uncertainties proposed in this study. Finally, there is a comparative analysis between the results for price of robustness in the proposed two-uncertainty model and in the one-uncertainty model.
First published online 15 December 2022
Keyword : robust optimization, multiple uncertainties, supplier selection, quantity allocation, supply chain, nondominated sorting genetic algorithm
How to Cite
Che, Z. H., Chiang, T.-A., & Tsai, C.-C. (2023). A robust optimization model with two uncertainties applied to supplier selection. Technological and Economic Development of Economy, 29(1), 165–191. https://doi.org/10.3846/tede.2022.17850
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
Ang, M., Lim, Y. F., & Sim, M. (2012). Robust storage assignment in unit-load warehouses. Management Science, 58(11), 2114–2130. https://doi.org/10.1287/mnsc.1120.1543
Baringo, L., Boffino, L., & Oggioni, G. (2020). Robust expansion planning of a distribution system with electric vehicles, storage and renewable units. Applied Energy, 265, 114679. https://doi.org/10.1016/j.apenergy.2020.114679
Barma, P. S., Dutta, J., Mukherjee, A., & Kar, S. (2021). A multi objective ring star vehicle routing problem for perishable Items. Journal of Ambient Intelligence and Humanized Computing, 13, 2355–2380. https://doi.org/10.1007/s12652-021-03059-2
Ben-Tal, A., & Nemirovski, A. (1999). Robust solutions of uncertain linear programs. Operations Research Letters, 25(1), 1–13. https://doi.org/10.1016/S0167-6377(99)00016-4
Ben-Tal, A., & Nemirovski, A. (2000). Robust solutions of linear programming problems contaminated with uncertain data. Mathematical Programming, 88, 411–424. https://doi.org/10.1007/PL00011380
Bertsimas, D., & Sim, M. (2003). Robust discrete optimization and network flows. Mathematical Programming, 98(1), 49–71. https://doi.org/10.1007/s10107-003-0396-4
Bertsimas, D., & Sim, M. (2004). The price of robustness. Operation Research, 52(1), 35–53. https://doi.org/10.1287/opre.1030.0065
Bohle, C., Maturana, S., & Vera, J. (2010). A robust optimization approach to wine grape harvesting scheduling. European Journal of Operational Research, 200(1), 245–252. https://doi.org/10.1016/j.ejor.2008.12.003
Chatterjee, K., & Kar, S. (2018). Supplier selection in telecom supply chain management, A fuzzy-rasch based COPRAS-G method. Technological and Economic Development of Economy, 24(2), 765–791. https://doi.org/10.3846/20294913.2017.1295289
Che, Z. H. (2017). A multi-objective optimization algorithm for solving the supplier selection problem with assembly sequence planning and assembly line balancing. Computers & Industrial Engineering, 105, 247–259. https://doi.org/10.1016/j.cie.2016.12.036
Che, Z. H., Chiang, T. A., & Lin, T. T. (2021). A multi-objective genetic algorithm for assembly planning and supplier selection with capacity constraints. Applied Soft Computing, 101, 107030. https://doi.org/10.1016/j.asoc.2020.107030
Che, Z. H., Chiang, T. A., & Luo, Y. J. (2022). Multiobjective optimization for planning the service areas of smart parcel locker facilities in logistics last mile delivery. Mathematics, 10(3), 422. https://doi.org/10.3390/math10030422
Chu, J., Huang, K., & Thiele, A. (2019). A robust optimization approach to model supply and demand uncertainties in inventory systems. Journal of the Operational Research Society, 70(11), 1885–1899. https://doi.org/10.1080/01605682.2018.1507424
Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182–197. https://doi.org/10.1109/4235.996017
Dutta, J., Barma, P. S., Mukherjee, A., Kar, S., & De, T. (2020). A multi-objective open set orienteering problem. Neural Computing and Applications, 32, 13953–13969. https://doi.org/10.1007/s00521-020-04798-7
Fonseca, C. M., & Fleming, P. J. (1993). Genetic algorithms for multi-objective optimization: Formulation, discussion and generalization. In S. Forrest (Ed.), Proceedings of the ICGA-93: Fifth International Conference on Genetic Algorithms (pp. 416–423). San Mateo.
Gülpinar, N., & Pachamanova, D. (2013). A robust optimization approach to asset-liability management under time-varying investment opportunities. Journal of Banking & Finance, 37(6), 2031–2041. https://doi.org/10.1016/j.jbankfin.2013.01.025
Hajela, P., & Lin, C. Y. (1992). Genetic search strategies in multi-criteria optimal design. Structural Optimization, 4, 99–107. https://doi.org/10.1007/BF01759923
Hnaien, F., & Afsar, H. M. (2017). Robust single-item lot-sizing problems with discrete-scenario lead time. International Journal of Production Economics, 185, 223–229. https://doi.org/10.1016/j.ijpe.2017.01.008
Holland, J. H. (1992). Adaptation in natural and artificial systems: An introductory analysis with applications to biology, control, and artificial intelligence (2nd ed.). University of Michigan Press, Ann Arbor. https://doi.org/10.7551/mitpress/1090.001.0001
Izadpanahi, E., Downward, A., Arthanari, T., & Liu, Y. (2022). Robust optimization for energy transition planning in manufacturing firms: An integrated model addressing economic and environmental issues. Journal of Cleaner Production, 334, 130237. https://doi.org/10.1016/j.jclepro.2021.130237
Leung, S. C. H., Tsang, S. O. S., Ng, W. L., & Wu, Y. (2007). A robust optimization model for multi-site production planning problem in an uncertain environment. European Journal of Operational Research, 181(1), 224–238. https://doi.org/10.1016/j.ejor.2006.06.011
Li, C., & Liu, S. (2013). A robust optimization approach to reduce the bullwhip effect of supply chains with vendor order placement lead time delays in an uncertain environment. Applied Mathematical Modelling, 37(3), 707–718. https://doi.org/10.1016/j.apm.2012.02.033
Li, S., Murat, A., & Huang, W. (2009). Selection of contract suppliers under price and demand uncertainty in a dynamic market. European Journal of Operational Research, 198(3), 830–847. https://doi.org/10.1016/j.ejor.2008.09.038
Li, Z., & Ierapetritou, M. G. (2008). Robust optimization for process scheduling under uncertainty. Industrial and Engineering Chemistry Research, 47(12), 4148–4157. https://doi.org/10.1021/ie071431u
Lin, Y. K., & Yeh, C. T. (2012). Multi-objective optimization for stochastic computer networks using NSGA-II and TOPSIS. European Journal of Operational Research, 218(3), 735–746. https://doi.org/10.1016/j.ejor.2011.11.028
Liu, B., Zhang, Q., & Yuan, Z. (2021). Two-stage distributionally robust optimization for maritime inventory routing. Computers & Chemical Engineering, 149, 107307. https://doi.org/10.1016/j.compchemeng.2021.107307
Majewski, D. E., Lampe, M., Voll, P., & Bardow, A. (2017a). TRusT: A two-stage robustness trade-off approach for the design of decentralized energy supply systems. Energy, 118, 590–599. https://doi.org/10.1016/j.energy.2016.10.065
Majewski, D. E., Wirtz, M., Lampe, M., & Bardow, A. (2017b). Robust multi-objective optimization for sustainable design of distributed energy supply systems. Computers & Chemical Engineering, 102, 26–39. https://doi.org/10.1016/j.compchemeng.2016.11.038
Majumder, S., Kar, S., & Pal, T. (2019). Uncertain multi-objective Chinese postman problem. Soft Computing, 23, 11557–11572. https://doi.org/10.1007/s00500-018-03697-3
Majumder, S., Kar, M. B., Kar, S., & Pal, T. (2020). Uncertain programming models for multi-objective shortest path problem with uncertain parameters. Soft Computing, 24, 8975–8996. https://doi.org/10.1007/s00500-019-04423-3
Mirzapour Al-e-hashem, S. M. J., Malekly, H., & Aryanezhad, M. B. (2011). A multi-objective robust optimization model for multi-product multi-site aggregate production planning in a supply chain under uncertainty. International Journal of Production Economics, 134(1), 28–42. https://doi.org/10.1016/j.ijpe.2011.01.027
Moret, S., Babonneau, F., Bierlaire, M., & Maréchal, F. (2020). Decision support for strategic energy planning: A robust optimization framework. European Journal of Operational Research, 280(2), 539–554. https://doi.org/10.1016/j.ejor.2019.06.015
Mulvey, J. M., Vanderbei, R. J., & Zenios, S. A. (1995). Robust optimization of large scale systems. Operation Research, 43(2), 264–281. https://doi.org/10.1287/opre.43.2.264
Omrani, H. (2013). Common weights data envelopment analysis with uncertain data: A robust optimization approach. Computers & Industrial Engineering, 66(4), 1163–1170. https://doi.org/10.1016/j.cie.2013.07.023
Pan, F., & Nagi, R. (2010). Robust supply chain design under uncertain demand in agile manufacturing. Computers & Operations Research, 37(4), 668–683. https://doi.org/10.1016/j.cor.2009.06.017
Rezaei, J., & Davoodi, M. (2011). Multi-objective models for lot-sizing with supplier selection. International Journal of Production Economics, 130(1), 77–86. https://doi.org/10.1016/j.ijpe.2010.11.017
Rojas, I., Gonzalez, J., Pomares, H., Merelo, J. J., Castillo, P. A., & Romero, G. (2002). Statistical analysis of the main parameters involved in the design of a genetic algorithm. IEEE Transactions on Systems, Man and Cybernetics, Part C, 32(1), 31–37. https://doi.org/10.1109/TSMCC.2002.1009128
Schaffer, J. D. (1985). Multiple objective optimization with vector evaluated genetic algorithms. In J. J. Grefenstette (Ed.), Proceedings of the First International Conference on Genetic Algorithms and Their Applications (pp. 93–100). Lawrence Erlbaum, Hillsdale, New Jersey.
Soyster, A. L. (1973). Convex programming with set-inclusive constraints and applications to inexact linear programming. Operation Research, 21(5), 1154–1157. https://doi.org/10.1287/opre.21.5.1154
Srinivas, N., & Deb, K. (1994). Multi-objective optimization using nondominated sorting in genetic algorithms. Evolutionary Computation, 2(3), 221–248. https://doi.org/10.1162/evco.1994.2.3.221
Thevenin, S., Ben-Ammar, O., & Brahimi, N. (2022). Robust optimization approaches for purchase planning with supplier selection under lead time uncertainty. European Journal of Operational Research, 303(3), 1199–1215. https://doi.org/10.1016/j.ejor.2022.03.029
Thorsen, A., & Yao, T. (2017). Robust inventory control under demand and lead time uncertainty. Annals of Operations Research, 257(1–2), 207–236. https://doi.org/10.1007/s10479-015-2084-1
Veldhuizen, D. Van, & Lamont, G. (1999). Multi-objective evolutionary algorithm test suites. In Proceedings of the 1999 ACM Symposium on Applied Computing (pp. 351–357). New York. https://doi.org/10.1145/298151.298382
Wang, H. F., & Hsu, H. W. (2010). A closed-loop logistic model with a spanning-tree based genetic algorithm. Computers & Operations Research, 37(2), 376–389. https://doi.org/10.1016/j.cor.2009.06.001
Wu, Q. H., & Cao, Y. J. (1997, April). Stochastic optimization of control parameters in genetic algorithms. In Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC ‘97) (pp. 77–80). Indianapolis, IN, USA. IEEE. https://doi.org/10.1109/ICEC.1997.592272
Yusoff, Y., Ngadiman, M. S., & Zain, A. M. (2011). Overview of NSGA-II for optimizing machining process parameters. Procedia Engineering, 15, 3978–3983. https://doi.org/10.1016/j.proeng.2011.08.745
Zeferino, J. A., Cunha, M. C., & Antunes, A. P. (2012). Robust optimization approach to regional wastewater system planning. Journal of Environmental Management, 109, 113–122. https://doi.org/10.1016/j.jenvman.2012.05.008
Zhao, B., Ren, J., Chen, J., Lin, D., & Qin, R. (2020). Tri-level robust planning-operation co-optimization of distributed energy storage in distribution networks with high PV penetration. Applied Energy, 279, 115768. https://doi.org/10.1016/j.apenergy.2020.115768
Baringo, L., Boffino, L., & Oggioni, G. (2020). Robust expansion planning of a distribution system with electric vehicles, storage and renewable units. Applied Energy, 265, 114679. https://doi.org/10.1016/j.apenergy.2020.114679
Barma, P. S., Dutta, J., Mukherjee, A., & Kar, S. (2021). A multi objective ring star vehicle routing problem for perishable Items. Journal of Ambient Intelligence and Humanized Computing, 13, 2355–2380. https://doi.org/10.1007/s12652-021-03059-2
Ben-Tal, A., & Nemirovski, A. (1999). Robust solutions of uncertain linear programs. Operations Research Letters, 25(1), 1–13. https://doi.org/10.1016/S0167-6377(99)00016-4
Ben-Tal, A., & Nemirovski, A. (2000). Robust solutions of linear programming problems contaminated with uncertain data. Mathematical Programming, 88, 411–424. https://doi.org/10.1007/PL00011380
Bertsimas, D., & Sim, M. (2003). Robust discrete optimization and network flows. Mathematical Programming, 98(1), 49–71. https://doi.org/10.1007/s10107-003-0396-4
Bertsimas, D., & Sim, M. (2004). The price of robustness. Operation Research, 52(1), 35–53. https://doi.org/10.1287/opre.1030.0065
Bohle, C., Maturana, S., & Vera, J. (2010). A robust optimization approach to wine grape harvesting scheduling. European Journal of Operational Research, 200(1), 245–252. https://doi.org/10.1016/j.ejor.2008.12.003
Chatterjee, K., & Kar, S. (2018). Supplier selection in telecom supply chain management, A fuzzy-rasch based COPRAS-G method. Technological and Economic Development of Economy, 24(2), 765–791. https://doi.org/10.3846/20294913.2017.1295289
Che, Z. H. (2017). A multi-objective optimization algorithm for solving the supplier selection problem with assembly sequence planning and assembly line balancing. Computers & Industrial Engineering, 105, 247–259. https://doi.org/10.1016/j.cie.2016.12.036
Che, Z. H., Chiang, T. A., & Lin, T. T. (2021). A multi-objective genetic algorithm for assembly planning and supplier selection with capacity constraints. Applied Soft Computing, 101, 107030. https://doi.org/10.1016/j.asoc.2020.107030
Che, Z. H., Chiang, T. A., & Luo, Y. J. (2022). Multiobjective optimization for planning the service areas of smart parcel locker facilities in logistics last mile delivery. Mathematics, 10(3), 422. https://doi.org/10.3390/math10030422
Chu, J., Huang, K., & Thiele, A. (2019). A robust optimization approach to model supply and demand uncertainties in inventory systems. Journal of the Operational Research Society, 70(11), 1885–1899. https://doi.org/10.1080/01605682.2018.1507424
Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182–197. https://doi.org/10.1109/4235.996017
Dutta, J., Barma, P. S., Mukherjee, A., Kar, S., & De, T. (2020). A multi-objective open set orienteering problem. Neural Computing and Applications, 32, 13953–13969. https://doi.org/10.1007/s00521-020-04798-7
Fonseca, C. M., & Fleming, P. J. (1993). Genetic algorithms for multi-objective optimization: Formulation, discussion and generalization. In S. Forrest (Ed.), Proceedings of the ICGA-93: Fifth International Conference on Genetic Algorithms (pp. 416–423). San Mateo.
Gülpinar, N., & Pachamanova, D. (2013). A robust optimization approach to asset-liability management under time-varying investment opportunities. Journal of Banking & Finance, 37(6), 2031–2041. https://doi.org/10.1016/j.jbankfin.2013.01.025
Hajela, P., & Lin, C. Y. (1992). Genetic search strategies in multi-criteria optimal design. Structural Optimization, 4, 99–107. https://doi.org/10.1007/BF01759923
Hnaien, F., & Afsar, H. M. (2017). Robust single-item lot-sizing problems with discrete-scenario lead time. International Journal of Production Economics, 185, 223–229. https://doi.org/10.1016/j.ijpe.2017.01.008
Holland, J. H. (1992). Adaptation in natural and artificial systems: An introductory analysis with applications to biology, control, and artificial intelligence (2nd ed.). University of Michigan Press, Ann Arbor. https://doi.org/10.7551/mitpress/1090.001.0001
Izadpanahi, E., Downward, A., Arthanari, T., & Liu, Y. (2022). Robust optimization for energy transition planning in manufacturing firms: An integrated model addressing economic and environmental issues. Journal of Cleaner Production, 334, 130237. https://doi.org/10.1016/j.jclepro.2021.130237
Leung, S. C. H., Tsang, S. O. S., Ng, W. L., & Wu, Y. (2007). A robust optimization model for multi-site production planning problem in an uncertain environment. European Journal of Operational Research, 181(1), 224–238. https://doi.org/10.1016/j.ejor.2006.06.011
Li, C., & Liu, S. (2013). A robust optimization approach to reduce the bullwhip effect of supply chains with vendor order placement lead time delays in an uncertain environment. Applied Mathematical Modelling, 37(3), 707–718. https://doi.org/10.1016/j.apm.2012.02.033
Li, S., Murat, A., & Huang, W. (2009). Selection of contract suppliers under price and demand uncertainty in a dynamic market. European Journal of Operational Research, 198(3), 830–847. https://doi.org/10.1016/j.ejor.2008.09.038
Li, Z., & Ierapetritou, M. G. (2008). Robust optimization for process scheduling under uncertainty. Industrial and Engineering Chemistry Research, 47(12), 4148–4157. https://doi.org/10.1021/ie071431u
Lin, Y. K., & Yeh, C. T. (2012). Multi-objective optimization for stochastic computer networks using NSGA-II and TOPSIS. European Journal of Operational Research, 218(3), 735–746. https://doi.org/10.1016/j.ejor.2011.11.028
Liu, B., Zhang, Q., & Yuan, Z. (2021). Two-stage distributionally robust optimization for maritime inventory routing. Computers & Chemical Engineering, 149, 107307. https://doi.org/10.1016/j.compchemeng.2021.107307
Majewski, D. E., Lampe, M., Voll, P., & Bardow, A. (2017a). TRusT: A two-stage robustness trade-off approach for the design of decentralized energy supply systems. Energy, 118, 590–599. https://doi.org/10.1016/j.energy.2016.10.065
Majewski, D. E., Wirtz, M., Lampe, M., & Bardow, A. (2017b). Robust multi-objective optimization for sustainable design of distributed energy supply systems. Computers & Chemical Engineering, 102, 26–39. https://doi.org/10.1016/j.compchemeng.2016.11.038
Majumder, S., Kar, S., & Pal, T. (2019). Uncertain multi-objective Chinese postman problem. Soft Computing, 23, 11557–11572. https://doi.org/10.1007/s00500-018-03697-3
Majumder, S., Kar, M. B., Kar, S., & Pal, T. (2020). Uncertain programming models for multi-objective shortest path problem with uncertain parameters. Soft Computing, 24, 8975–8996. https://doi.org/10.1007/s00500-019-04423-3
Mirzapour Al-e-hashem, S. M. J., Malekly, H., & Aryanezhad, M. B. (2011). A multi-objective robust optimization model for multi-product multi-site aggregate production planning in a supply chain under uncertainty. International Journal of Production Economics, 134(1), 28–42. https://doi.org/10.1016/j.ijpe.2011.01.027
Moret, S., Babonneau, F., Bierlaire, M., & Maréchal, F. (2020). Decision support for strategic energy planning: A robust optimization framework. European Journal of Operational Research, 280(2), 539–554. https://doi.org/10.1016/j.ejor.2019.06.015
Mulvey, J. M., Vanderbei, R. J., & Zenios, S. A. (1995). Robust optimization of large scale systems. Operation Research, 43(2), 264–281. https://doi.org/10.1287/opre.43.2.264
Omrani, H. (2013). Common weights data envelopment analysis with uncertain data: A robust optimization approach. Computers & Industrial Engineering, 66(4), 1163–1170. https://doi.org/10.1016/j.cie.2013.07.023
Pan, F., & Nagi, R. (2010). Robust supply chain design under uncertain demand in agile manufacturing. Computers & Operations Research, 37(4), 668–683. https://doi.org/10.1016/j.cor.2009.06.017
Rezaei, J., & Davoodi, M. (2011). Multi-objective models for lot-sizing with supplier selection. International Journal of Production Economics, 130(1), 77–86. https://doi.org/10.1016/j.ijpe.2010.11.017
Rojas, I., Gonzalez, J., Pomares, H., Merelo, J. J., Castillo, P. A., & Romero, G. (2002). Statistical analysis of the main parameters involved in the design of a genetic algorithm. IEEE Transactions on Systems, Man and Cybernetics, Part C, 32(1), 31–37. https://doi.org/10.1109/TSMCC.2002.1009128
Schaffer, J. D. (1985). Multiple objective optimization with vector evaluated genetic algorithms. In J. J. Grefenstette (Ed.), Proceedings of the First International Conference on Genetic Algorithms and Their Applications (pp. 93–100). Lawrence Erlbaum, Hillsdale, New Jersey.
Soyster, A. L. (1973). Convex programming with set-inclusive constraints and applications to inexact linear programming. Operation Research, 21(5), 1154–1157. https://doi.org/10.1287/opre.21.5.1154
Srinivas, N., & Deb, K. (1994). Multi-objective optimization using nondominated sorting in genetic algorithms. Evolutionary Computation, 2(3), 221–248. https://doi.org/10.1162/evco.1994.2.3.221
Thevenin, S., Ben-Ammar, O., & Brahimi, N. (2022). Robust optimization approaches for purchase planning with supplier selection under lead time uncertainty. European Journal of Operational Research, 303(3), 1199–1215. https://doi.org/10.1016/j.ejor.2022.03.029
Thorsen, A., & Yao, T. (2017). Robust inventory control under demand and lead time uncertainty. Annals of Operations Research, 257(1–2), 207–236. https://doi.org/10.1007/s10479-015-2084-1
Veldhuizen, D. Van, & Lamont, G. (1999). Multi-objective evolutionary algorithm test suites. In Proceedings of the 1999 ACM Symposium on Applied Computing (pp. 351–357). New York. https://doi.org/10.1145/298151.298382
Wang, H. F., & Hsu, H. W. (2010). A closed-loop logistic model with a spanning-tree based genetic algorithm. Computers & Operations Research, 37(2), 376–389. https://doi.org/10.1016/j.cor.2009.06.001
Wu, Q. H., & Cao, Y. J. (1997, April). Stochastic optimization of control parameters in genetic algorithms. In Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC ‘97) (pp. 77–80). Indianapolis, IN, USA. IEEE. https://doi.org/10.1109/ICEC.1997.592272
Yusoff, Y., Ngadiman, M. S., & Zain, A. M. (2011). Overview of NSGA-II for optimizing machining process parameters. Procedia Engineering, 15, 3978–3983. https://doi.org/10.1016/j.proeng.2011.08.745
Zeferino, J. A., Cunha, M. C., & Antunes, A. P. (2012). Robust optimization approach to regional wastewater system planning. Journal of Environmental Management, 109, 113–122. https://doi.org/10.1016/j.jenvman.2012.05.008
Zhao, B., Ren, J., Chen, J., Lin, D., & Qin, R. (2020). Tri-level robust planning-operation co-optimization of distributed energy storage in distribution networks with high PV penetration. Applied Energy, 279, 115768. https://doi.org/10.1016/j.apenergy.2020.115768