# ESG Modeling and Prediction Uncertainty of Electronic Waste

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. E-Waste Collection and Environmental, Social, and Governance (ESG)

## 3. Literature Review

#### 3.1. Grey Forecasting Model

#### 3.2. Optimized Grey Forecasting Models

_{2}emissions. Hu [83] applied a fractional grey prediction model with Fourier series to forecast tourism demand in Taiwan. Hu [84] also developed a grey prediction with Fourier series using Genetic Algorithm for tourism demand forecasting. Jiang et al. [85] analyzed China’s Outward Foreign Direct Investment (OFDI) using a novel multivariate grey prediction model with Fourier series. Nguyen et al. [86] employed Fourier series to improve the prediction accuracy of a univariate nonlinear grey Bernoulli model. Kiran et al. [87] proposed an improved multivariate discrete grey model combining Fourier Transform and an exponential smoothing technique that was used to forecast the in-use stock of mobile phones, televisions, and personal computers considering the Gross Domestic Product and rural and urban populations.

## 4. Methodology

#### 4.1. NBGMFO(1,1)–PSO Integrated with Fourier Series

#### 4.1.1. Grey Model with Fractional Order

#### 4.1.2. Nonlinear Grey Bernoulli Model

#### 4.1.3. Particle Swarm Optimization

#### 4.1.4. Residual Error Modification by Fourier Series

_{2}emissions. Hu [83] applied a fractional grey prediction model with Fourier series to forecast tourism demand in Taiwan. Hu [84] also developed a grey prediction with Fourier series using Genetic Algorithm for tourism demand forecasting. Jiang et al. [85] analyzed China’s Outward Foreign Direct Investment (OFDI) using a novel multivariate grey prediction model with Fourier series. Nguyen et al. [86] employed Fourier series to improve the prediction accuracy of a univariate nonlinear grey Bernoulli model. Kiran et al. [87] proposed an improved multivariate discrete grey model combining Fourier Transform and an exponential smoothing technique that was used to forecast the in-use stock of mobile phones, televisions, and personal computers considering the Gross Domestic Product and rural and urban populations.

_{1}, ε

_{2}, ……, ε

_{n}) denote the sequence of residual values, where:

## 5. Case Study in WMP Predictions

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

X_{i}^{(0)} | Original data series |

X_{i}^{(1)} | Accumulated data series |

n | Total number of data series |

r | Fractional order value |

b_{i} | Model parameters |

u | Grey control parameter |

z_{i} | Background value |

p | Background value coefficient |

B | Input matrix |

Y | Output vector |

m | Exponential coefficient |

RMSE | Root Mean Square Error |

w | Inertia weight |

V | Velocity of a particle |

c_{1}, c_{2} | Learning factors |

$\mathsf{\epsilon}$ | Residual values |

P | Input matrix in Fourier series |

C | Output vector in Fourier series |

## References

- Forti, V.; Balde, C.P.; Kuehr, R.; Bel, G. The Global E-Waste Monitor 2020: Quantities, Flows and the Circular Economy Potential; United Nations University/United Nations Institute for Training and Research: Bonn, Germany; International Telecommunication Union: Geneva, Switzerland; International Solid Waste Association: Rotterdam, The Netherlands, 2020. [Google Scholar]
- Alshibli, M.; El Sayed, A.; Tozanli, O.; Kongar, E.; Sobh, T.M.; Gupta, S.M. A decision maker-centered end-of-life product recovery system for robot task sequencing. J. Intell. Robot. Syst.
**2018**, 91, 603–616. [Google Scholar] [CrossRef] - Saha, L.; Kumar, V.; Tiwari, J.; Rawat, S.; Singh, J.; Bauddh, K. Electronic waste and their leachates impact on human health and environment: Global ecological threat and management. Environ. Technol. Innov.
**2021**, 24, 102049. [Google Scholar] - Zhao, G.; Wang, Z.; Dong, M.H.; Rao, K.; Luo, J.; Wang, D.; Zha, J.; Huang, S.; Xu, Y.; Ma, M. PBBs, PBDEs, and PCBs levels in hair of residents around e-waste disassembly sites in Zhejiang Province, China, and their potential sources. Sci. Total Environ.
**2008**, 397, 46–57. [Google Scholar] [CrossRef] - Pietrelli, L.; Ferro, S.; Vocciante, M. Eco-friendly and cost-effective strategies for metals recovery from printed circuit boards. Renew. Sustain. Energy Rev.
**2019**, 112, 317–323. [Google Scholar] [CrossRef] - Kumar, A.; Holuszko, M.; Espinosa, D.C.R. E-waste: An overview on generation, collection, legislation and recycling practices. Resour. Conserv. Recycl.
**2017**, 122, 32–42. [Google Scholar] [CrossRef] - Namias, J. The Future of Electronic Waste Recycling in the United States: Obstacles and Domestic Solutions; Columbia University: New York, NY, USA, 2013. [Google Scholar]
- Yao, P.; Gupta, S.M. Invasive Weed Optimization Algorithm for Solving Multi-Objective Sequence-Dependent U-Shaped Disassembly Line Balancing Problem. Int. J. Res. Eng. Sci.
**2022**, 10, 1705–1716. [Google Scholar] - Murthy, V.; Ramakrishna, S. A Review on Global E-Waste Management: Urban Mining towards a Sustainable Future and Circular Economy. Sustainability
**2022**, 14, 647. [Google Scholar] [CrossRef] - Robinson, B.H. E-waste: An assessment of global production and environmental impacts. Sci. Total Environ.
**2009**, 408, 183–191. [Google Scholar] [CrossRef] - Perkins, D.N.; Drisse, M.-N.B.; Nxele, T.; Sly, P.D. E-waste: A global hazard. Ann. Glob. Health
**2014**, 80, 286–295. [Google Scholar] [CrossRef] - Patil, R.A.; Ghisellini, P.; Ramakrishna, S. Towards sustainable business strategies for a circular economy: Environmental, social and governance (ESG) performance and evaluation. In An Introduction to Circular Economy; Springer: Singapore, 2021; pp. 527–554. [Google Scholar]
- Lundgren, K. The Global Impact of E-Waste: Addressing the Challenge; International Labour Organization: Geneva, Switzerland, 2012. [Google Scholar]
- Grant, K.; Goldizen, F.C.; Sly, P.D.; Brune, M.-N.; Neira, M.; van den Berg, M.; Norman, R.E. Health consequences of exposure to e-waste: A systematic review. Lancet Glob. Health
**2013**, 1, e350–e361. [Google Scholar] [CrossRef] [Green Version] - Heacock, M.; Kelly, C.B.; Asante, K.A.; Birnbaum, L.S.; Bergman, Å.L.; Bruné, M.-N.; Buka, I.; Carpenter, D.O.; Chen, A.; Huo, X. E-waste and harm to vulnerable populations: A growing global problem. Environ. Health Perspect.
**2016**, 124, 550–555. [Google Scholar] [CrossRef] [Green Version] - Ikhlayel, M. An integrated approach to establish e-waste management systems for developing countries. J. Clean. Prod.
**2018**, 170, 119–130. [Google Scholar] [CrossRef] - Bisschop, L. Is it all going to waste? Illegal transports of e-waste in a European trade hub. Crime Law Soc. Chang.
**2012**, 58, 221–249. [Google Scholar] [CrossRef] [Green Version] - Chen, Y.; Wu, T.-H. Effective E-Waste Management—The Role of International Cooperation and Fragementation. 2010. Available online: https://mpra.ub.uni-muenchen.de/25902/1/MPRA_paper_25902.pdf (accessed on 30 May 2023).
- Erhun, F.; Kraft, T.; Wijnsma, S. Sustainable Triple—A Supply Chains. Prod. Oper. Manag.
**2021**, 30, 644–655. [Google Scholar] [CrossRef] - Kim, S.T.; Lee, H.-H.; Lim, S. The Effects of Green SCM Implementation on Business Performance in SMEs: A Longitudinal Study in Electronics Industry. Sustainability
**2021**, 13, 11874. [Google Scholar] [CrossRef] - Cotta, B. What goes around, comes around? Access and allocation problems in Global North–South waste trade. Int. Environ. Agreem. Politics Law Econ.
**2020**, 20, 255–269. [Google Scholar] [CrossRef] - Abd-Mutalib, H.; Muhammad Jamil, C.Z.; Mohamed, R.; Shafai, N.A.; Nor-Ahmad, S.N.H.J.N. Firm and Board Characteristics, and E-Waste Disclosure: A Study in the Era of Digitalisation. Sustainability
**2021**, 13, 10417. [Google Scholar] [CrossRef] - Achillas, C.; Vlachokostas, C.; Moussiopoulos, Ν.; Banias, G. Decision support system for the optimal location of electrical and electronic waste treatment plants: A case study in Greece. Waste Manag.
**2010**, 30, 870–879. [Google Scholar] [CrossRef] - Ayvaz, B.; Bolat, B.; Aydın, N. Stochastic reverse logistics network design for waste of electrical and electronic equipment. Resour. Conserv. Recycl.
**2015**, 104, 391–404. [Google Scholar] [CrossRef] - Gomes, M.I.; Barbosa-Povoa, A.P.; Novais, A.Q. Modelling a recovery network for WEEE: A case study in Portugal. Waste Manag.
**2011**, 31, 1645–1660. [Google Scholar] [CrossRef] - Guarnieri, P.; Sobreiro, V.A.; Nagano, M.S.; Marques Serrano, A.L. The challenge of selecting and evaluating third-party reverse logistics providers in a multicriteria perspective: A Brazilian case. J. Clean. Prod.
**2015**, 96, 209–219. [Google Scholar] [CrossRef] - Kilic, H.S.; Cebeci, U.; Ayhan, M.B. Reverse logistics system design for the waste of electrical and electronic equipment (WEEE) in Turkey. Resour. Conserv. Recycl.
**2015**, 95, 120–132. [Google Scholar] [CrossRef] - Li, R.C.; Tee, T.J.C. A Reverse Logistics Model For Recovery Options of E-waste Considering the Integration of the Formal and Informal Waste Sectors. Procedia Soc. Behav. Sci.
**2012**, 40, 788–816. [Google Scholar] [CrossRef] [Green Version] - Prakash, C.; Barua, M.K.; Pandya, K.V. Barriers Analysis for Reverse Logistics Implementation in Indian Electronics Industry using Fuzzy Analytic Hierarchy Process. Procedia Soc. Behav. Sci.
**2015**, 189, 91–102. [Google Scholar] [CrossRef] [Green Version] - Safdar, N.; Khalid, R.; Ahmed, W.; Imran, M. Reverse logistics network design of e-waste management under the triple bottom line approach. J. Clean. Prod.
**2020**, 272, 122662. [Google Scholar] [CrossRef] - Sarkis, J.; Helms, M.M.; Hervani, A.A. Reverse logistics and social sustainability. Corp. Soc. Responsib. Environ. Manag.
**2010**, 17, 337–354. [Google Scholar] [CrossRef] - Bal, A.; Satoglu, S.I. A goal programming model for sustainable reverse logistics operations planning and an application. J. Clean. Prod.
**2018**, 201, 1081–1091. [Google Scholar] [CrossRef] - Duman, G.M.; Kongar, E.; Gupta, S.M. Estimation of electronic waste using optimized multivariate grey models. Waste Manag.
**2019**, 95, 241–249. [Google Scholar] [CrossRef] - United Nations. Transforming Our World: The 2030 Agenda for Sustainable Development. Available online: https://sdgs.un.org/2030agenda (accessed on 30 May 2023).
- Shittu, O.S.; Williams, I.D.; Shaw, P.J. Global E-waste management: Can WEEE make a difference? A review of e-waste trends, legislation, contemporary issues and future challenges. Waste Manag.
**2021**, 120, 549–563. [Google Scholar] [CrossRef] - Forti, V.; Baldé, C.P.; Kuehr, R.; Bel, G. The Global E-Waste Monitor 2020; United Nations University (UNU): Bonn, Germany; International Telecommunication Union (ITU): Geneva, Switzerland; International Solid Waste Association (ISWA): Rotterdam, The Netherlands, 2020. [Google Scholar]
- National Conference of State Legislatures. Electronic Waste Recycling. Available online: https://www.ncsl.org/research/environment-and-natural-resources/e-waste-recycling-legislation.aspx (accessed on 30 May 2023).
- Jaunich, M.K.; DeCarolis, J.; Handfield, R.; Kemahlioglu-Ziya, E.; Ranjithan, S.R.; Moheb-Alizadeh, H. Life-cycle modeling framework for electronic waste recovery and recycling processes. Resour. Conserv. Recycl.
**2020**, 161, 104841. [Google Scholar] [CrossRef] - Schumacher, K.A.; Agbemabiese, L. Towards comprehensive e-waste legislation in the United States: Design considerations based on quantitative and qualitative assessments. Resour. Conserv. Recycl.
**2019**, 149, 605–621. [Google Scholar] [CrossRef] - Ongondo, F.O.; Williams, I.D.; Cherrett, T.J. How are WEEE doing? A global review of the management of electrical and electronic wastes. Waste Manag.
**2011**, 31, 714–730. [Google Scholar] [CrossRef] [PubMed] - Duman, G.M.; Kongar, E.; Gupta, S.M. Predictive analysis of electronic waste for reverse logistics operations: A comparison of improved univariate grey models. Soft Comput.
**2020**, 24, 15747–15762. [Google Scholar] [CrossRef] - Gui, L.; Atasu, A.; Ergun, Ö.; Toktay, L.B. Implementing extended producer responsibility legislation: A multi-stakeholder case analysis. J. Ind. Ecol.
**2013**, 17, 262–276. [Google Scholar] [CrossRef] - Noon, M.S.; Lee, S.-J.; Cooper, J.S. A life cycle assessment of end-of-life computer monitor management in the Seattle metropolitan region. Resour. Conserv. Recycl.
**2011**, 57, 22–29. [Google Scholar] [CrossRef] - Templeton, N.J. Dark Side of Recycling and Reusing Electronics: Is Washington’s E-Cycle Program Adequate. Seattle J. Soc. Just.
**2008**, 7, 763. [Google Scholar] - EPA Management of Electronic Waste in the United States Approach Two. Available online: https://nepis.epa.gov/Exe/ZyPURL.cgi?Dockey=P100BC9O.TXT (accessed on 18 September 2018).
- EPA Electronics Waste Management in the United States: Approach I. Available online: https://nepis.epa.gov/Exe/ZyPURL.cgi?Dockey=P1001FPK.TXT (accessed on 18 September 2018).
- Brunner, P.H.; Rechberger, H. Handbook of Material Flow Analysis: For Environmental, Resource, and Waste Engineers; CRC Press: Boca Raton, FL, USA, 2016. [Google Scholar]
- Lau, W.K.-Y.; Chung, S.-S.; Zhang, C. A material flow analysis on current electrical and electronic waste disposal from Hong Kong households. Waste Manag.
**2013**, 33, 714–721. [Google Scholar] [CrossRef] [PubMed] - Steubing, B.; Böni, H.; Schluep, M.; Silva, U.; Ludwig, C. Assessing computer waste generation in Chile using material flow analysis. Waste Manag.
**2010**, 30, 473–482. [Google Scholar] [CrossRef] - Oguchi, M.; Kameya, T.; Yagi, S.; Urano, K. Product flow analysis of various consumer durables in Japan. Resour. Conserv. Recycl.
**2008**, 52, 463–480. [Google Scholar] [CrossRef] - Althaf, S.; Babbitt, C.W.; Chen, R. Forecasting electronic waste flows for effective circular economy planning. Resour. Conserv. Recycl.
**2019**, 151, 104362. [Google Scholar] [CrossRef] - Matthews, H.S.; McMichael, F.C.; Hendrickson, C.T.; Hart, D.J. Disposition and end-of-life options for personal computers. In Carnegie Mellon University Green Design Initiative Technical Report; 1997; Available online: https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=83f0ce7279333cc05eb7af08cb6c225a9e05e681 (accessed on 30 May 2023).
- Jain, A.; Sareen, R. E-waste assessment methodology and validation in India. J. Mater. Cycles Waste Manag.
**2006**, 8, 40–45. [Google Scholar] [CrossRef] - Yang, Y.; Williams, E. Logistic model-based forecast of sales and generation of obsolete computers in the U.S. Technol. Forecast. Soc. Chang.
**2009**, 76, 1105–1114. [Google Scholar] [CrossRef] - Petridis, N.E.; Stiakakis, E.; Petridis, K.; Dey, P. Estimation of computer waste quantities using forecasting techniques. J. Clean. Prod.
**2016**, 112, 3072–3085. [Google Scholar] [CrossRef] [Green Version] - Albuquerque, C.; Mello, C.; Paes, V.; Balestrassi, P.; Souza, L. Electronic Junk: Best Practice of Recycling and Production Forecast Case Study in Brazil. In New Global Perspectives on Industrial Engineering and Management; Springer: Berlin/Heidelberg, Germany, 2019; pp. 127–134. [Google Scholar]
- Deng, J.L. Introduction to Grey system theory. J. Grey Syst.
**1989**, 1, 1–24. [Google Scholar] - Chen, C.I. Application of the novel nonlinear grey Bernoulli model for forecasting unemployment rate. Chaos Solitons Fractals
**2008**, 37, 278–287. [Google Scholar] [CrossRef] - Chen, C.I.; Chen, H.L.; Chen, S.-P. Forecasting of foreign exchange rates of Taiwan’s major trading partners by novel nonlinear Grey Bernoulli model NGBM(1,1). Commun. Nonlinear Sci. Numer. Simul.
**2008**, 13, 1194–1204. [Google Scholar] [CrossRef] - Wang, Z.X.; Hipel, K.W.; Wang, Q.; He, S.-W. An optimized NGBM(1,1) model for forecasting the qualified discharge rate of industrial wastewater in China. Appl. Math. Model.
**2011**, 35, 5524–5532. [Google Scholar] [CrossRef] - Pao, H.-T.; Fu, H.-C.; Tseng, C.-L. Forecasting of CO
_{2}emissions, energy consumption and economic growth in China using an improved grey model. Energy**2012**, 40, 400–409. [Google Scholar] [CrossRef] - Wu, L.; Liu, S.; Yao, L.; Yan, S.; Liu, D. Grey system model with the fractional order accumulation. Commun. Nonlinear Sci. Numer. Simul.
**2013**, 18, 1775–1785. [Google Scholar] [CrossRef] - Wu, L.; Liu, S.; Fang, Z.; Xu, H. Properties of the GM(1,1) with fractional order accumulation. Appl. Math. Comput.
**2015**, 252, 287–293. [Google Scholar] [CrossRef] - Wu, L.; Liu, S.; Yao, L.; Xu, R.; Lei, X. Using fractional order accumulation to reduce errors from inverse accumulated generating operator of grey model. Soft Comput.
**2015**, 19, 483–488. [Google Scholar] [CrossRef] - Shili, F.; Lifeng, W.; Liang, Y.; Zhigeng, F. Using fractional GM(1,1) model to predict maintenance cost of weapon system. In Proceedings of the 2013 IEEE International Conference on Grey Systems and Intelligent Services (GSIS), Macao, China, 15–17 November 2013; IEEE: Piscataway, NJ, USA, 2013; pp. 177–181. [Google Scholar]
- Duan, H.; Lei, G.R.; Shao, K. Forecasting Crude Oil Consumption in China Using a Grey Prediction Model with an Optimal Fractional-Order Accumulating Operator. Complexity
**2018**, 2018, 3869619. [Google Scholar] [CrossRef] - Li, S.; Meng, W.; Xie, Y. Forecasting the Amount of Waste-Sewage Water Discharged into the Yangtze River Basin Based on the Optimal Fractional Order Grey Model. Int. J. Environ. Res. Public Health
**2017**, 15, 20. [Google Scholar] [CrossRef] [Green Version] - Wu, L.; Zhao, H. Discrete grey model with the weighted accumulation. Soft Comput.
**2019**, 23, 12873–12881. [Google Scholar] [CrossRef] - Xie, Q.; Xie, Y. Forecast of Regional Gross National Product Based on Grey Modelling Optimized by Genetic Algorithm. In Proceedings of the 2009 International Conference on E-Learning, E-Business, Enterprise Information Systems, and E-Government, Hong Kong, China, 5–6 December 2009; IEEE: Piscataway, NJ, USA, 2009; pp. 3–5. [Google Scholar]
- Xie, Y.; Li, M. Research on gray prediction modeling optimized by genetic algorithm for energy consumption demand. In Proceedings of the 2009 International Conference on Industrial Mechatronics and Automation, Chengdu, China, 15–16 May 2009; IEEE: Piscataway, NJ, USA, 2009; pp. 289–291. [Google Scholar]
- Wang, C.H.; Hsu, L.-C. Using genetic algorithms grey theory to forecast high technology industrial output. Appl. Math. Comput.
**2008**, 195, 256–263. [Google Scholar] [CrossRef] - Hsu, L.-C. A genetic algorithm based nonlinear grey Bernoulli model for output forecasting in integrated circuit industry. Expert Syst. Appl.
**2010**, 37, 4318–4323. [Google Scholar] [CrossRef] - Hsu, L.-C. Forecasting the output of integrated circuit industry using genetic algorithm based multivariable grey optimization models. Expert Syst. Appl.
**2009**, 36, 7898–7903. [Google Scholar] [CrossRef] - Hu, Y.-C. A multivariate grey prediction model with grey relational analysis for bankruptcy prediction problems. Soft Comput.
**2020**, 24, 4259–4268. [Google Scholar] [CrossRef] - Wang, F.X.; Zhang, L.-S. Combination Gray Forecast Model Based on the Ant Colony Algorithm. Math. Pract. Theory
**2009**, 14, 017. [Google Scholar] - Zhao, H.; Guo, S. An optimized grey model for annual power load forecasting. Energy
**2016**, 107, 272–286. [Google Scholar] [CrossRef] - Zhao, H.; Zhao, H.; Guo, S. Using GM(1,1) optimized by MFO with rolling mechanism to forecast the electricity consumption of inner mongolia. Appl. Sci.
**2016**, 6, 20. [Google Scholar] [CrossRef] [Green Version] - Zhou, J.; Fang, R.; Li, Y.; Zhang, Y.; Peng, B. Parameter optimization of nonlinear grey Bernoulli model using particle swarm optimization. Appl. Math. Comput.
**2009**, 207, 292–299. [Google Scholar] [CrossRef] - Li, K.; Liu, L.; Zhai, J.; Khoshgoftaar, T.M.; Li, T. The improved grey model based on particle swarm optimization algorithm for time series prediction. Eng. Appl. Artif. Intell.
**2016**, 55, 285–291. [Google Scholar] [CrossRef] - Liu, L.; Wang, Q.; Wang, J.; Liu, M. A rolling grey model optimized by particle swarm optimization in economic prediction. Comput. Intell.
**2016**, 32, 391–419. [Google Scholar] [CrossRef] - Zeng, B.; Li, C. Improved multi-variable grey forecasting model with a dynamic background-value coefficient and its application. Comput. Ind. Eng.
**2018**, 118, 278–290. [Google Scholar] [CrossRef] - Jiang, H.; Kong, P.; Hu, Y.-C.; Jiang, P. Forecasting China’s CO
_{2}emissions by considering interaction of bilateral FDI using the improved grey multivariable Verhulst model. Environ. Dev. Sustain.**2021**, 23, 225–240. [Google Scholar] [CrossRef] [Green Version] - Hu, Y.-C. Forecasting tourism demand using fractional grey prediction models with Fourier series. Ann. Oper. Res.
**2021**, 300, 467–491. [Google Scholar] [CrossRef] - Hu, Y.-C. Developing grey prediction with Fourier series using genetic algorithms for tourism demand forecasting. Qual. Quant.
**2021**, 55, 315–331. [Google Scholar] [CrossRef] - Jiang, H.; Hu, Y.-C.; Lin, J.-Y.; Jiang, P. Analyzing China’s OFDI using a novel multivariate grey prediction model with Fourier series. Int. J. Intell. Comput. Cybern.
**2019**, 12, 352–371. [Google Scholar] [CrossRef] - Nguyen, N.T.; Phan, V.T.; Malara, Z. Using Fourier series to improve the prediction accuracy of nonlinear Grey Bernoulli model. In Proceedings of the ACIIDS 2019: Intelligent Information and Database Systems, Yogyakarta, Indonesia, 8–11 April 2019; Springer: Berlin/Heidelberg, Germany, 2019; pp. 363–372. [Google Scholar]
- Kiran, M.; Shanmugam, P.V.; Mishra, A.; Mehendale, A.; Sherin, H.N. A multivariate discrete grey model for estimating the waste from mobile phones, televisions, and personal computers in India. J. Clean. Prod.
**2021**, 293, 126185. [Google Scholar] [CrossRef] - Wang, F.; Yu, L.; Wu, A. Forecasting the electronic waste quantity with a decomposition-ensemble approach. Waste Manag.
**2021**, 120, 828–838. [Google Scholar] [CrossRef] [PubMed] - Ye, J.; Dang, Y.; Yang, Y. Forecasting the multifactorial interval grey number sequences using grey relational model and GM(1,N) model based on effective information transformation. Soft Comput.
**2019**, 24, 5255–5269. [Google Scholar] [CrossRef] - Ene, S.; Öztürk, N. Grey modelling based forecasting system for return flow of end-of-life vehicles. Technol. Forecast. Soc. Chang.
**2017**, 115, 155–166. [Google Scholar] [CrossRef] - Chen, C.I.; Hsin, P.-H.; Wu, C.-S. Forecasting Taiwan’s major stock indices by the Nash nonlinear grey Bernoulli model. Expert Syst. Appl.
**2010**, 37, 7557–7562. [Google Scholar] [CrossRef] - Wang, Z.-X.; Li, Q. Modelling the nonlinear relationship between CO
_{2}emissions and economic growth using a PSO algorithm-based grey Verhulst model. J. Clean. Prod.**2019**, 207, 214–224. [Google Scholar] [CrossRef] - Eberhart, R.; Kennedy, J. A new optimizer using particle swarm theory. In Proceedings of the Sixth International Symposium on Micro Machine and Human Science, Nagoya, Japan, 4–6 October 1995; pp. 39–43. [Google Scholar]
- Ozsut Bogar, Z.; Gungor, A. Forecasting Waste Mobile Phone (WMP) Quantity and Evaluating the Potential Contribution to the Circular Economy: A Case Study of Turkey. Sustainability
**2023**, 15, 3104. [Google Scholar] [CrossRef] - Wang, Z.X. An optimized Nash nonlinear grey Bernoulli model for forecasting the main economic indices of high technology enterprises in China. Comput. Ind. Eng.
**2013**, 64, 780–787. [Google Scholar] [CrossRef] - Zhang, L.; Zheng, Y.; Wang, K.; Zhang, X.; Zheng, Y. An optimized Nash nonlinear grey Bernoulli model based on particle swarm optimization and its application in prediction for the incidence of Hepatitis B in Xinjiang, China. Comput. Biol. Med.
**2014**, 49, 67–73. [Google Scholar] [CrossRef]

**Figure 2.**Waste mobile phone (WMP) data [94].

**Table 1.**Waste mobile phone (WMP) data [94].

Year | WMP Quantity |
---|---|

2001 | 1,515,539 |

2002 | 1,661,498 |

2003 | 1,851,941 |

2004 | 2,127,025 |

2005 | 2,580,265 |

2006 | 3,140,099 |

2007 | 4,026,068 |

2008 | 5,146,729 |

2009 | 6,097,611 |

2010 | 6,602,838 |

2011 | 7,098,585 |

2012 | 7,688,849 |

2013 | 7,919,715 |

2014 | 8,180,400 |

2015 | 8,419,223 |

2016 | 8,761,059 |

2017 | 9,024,298 |

2018 | 9,192,462 |

2019 | 9,136,731 |

2020 | 9,286,120 |

Population | 30 | Learning factor 1 | 1 | |

Maximum iteration | 300 | Learning factor 2 | 1 | |

Inertia value | 0.8 | Range for p | (0 < p < 1) | |

Range for m | (0 < m < 1) | Range for r | (0 < r < 1) | |

Results | ||||

Method | RMSE | p | m | r |

NBGMFO(1,1) | 537,926.78 | 0.9615 | 0.6035 | 0.1047 |

**Table 3.**Estimated values of generated e-waste via NBGMFO(1,1)–PSO and NBGMC(1,1)–PSO with Fourier Series.

Year | NBGMFO(1,1)–PSO Estimates | NBGMFO(1,1)–PSO with Fourier Series Estimates |
---|---|---|

2001 | 1,515,539 | 1,515,539 |

2002 | 1,992,497 | 1,644,780 |

2003 | 2,551,513 | 1,868,659 |

2004 | 3,140,572 | 2,110,307 |

2005 | 3,738,236 | 2,596,983 |

2006 | 4,330,556 | 3,123,381 |

2007 | 4,907,595 | 4,042,786 |

2008 | 5,462,248 | 5,130,011 |

2009 | 5,989,585 | 6,114,329 |

2010 | 6,486,393 | 6,586,120 |

2011 | 6,950,802 | 7,115,303 |

2012 | 7,381,991 | 7,672,131 |

2013 | 7,779,947 | 7,936,433 |

2014 | 8,145,260 | 8,163,682 |

2015 | 8,478,967 | 8,435,941 |

2016 | 8,782,418 | 8,744,341 |

2017 | 9,057,175 | 9,041,016 |

2018 | 9,304,931 | 9,175,744 |

2019 | 9,527,444 | 9,153,449 |

2020 | 9,726,488 | 9,269,402 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Duman, G.M.; Kongar, E.
ESG Modeling and Prediction Uncertainty of Electronic Waste. *Sustainability* **2023**, *15*, 11281.
https://doi.org/10.3390/su151411281

**AMA Style**

Duman GM, Kongar E.
ESG Modeling and Prediction Uncertainty of Electronic Waste. *Sustainability*. 2023; 15(14):11281.
https://doi.org/10.3390/su151411281

**Chicago/Turabian Style**

Duman, Gazi Murat, and Elif Kongar.
2023. "ESG Modeling and Prediction Uncertainty of Electronic Waste" *Sustainability* 15, no. 14: 11281.
https://doi.org/10.3390/su151411281