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An Inexact Chance-constrained Quadratic Programming Model for Stream Water Quality Management

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  • X. Qin
  • G. Huang

Abstract

Water quality management is complicated with a variety of uncertainties and nonlinearities. This leads to difficulties in formulating and solving the resulting inexact nonlinear optimization problems. In this study, an inexact chance-constrained quadratic programming (ICCQP) model was developed for stream water quality management. A multi-segment stream water quality (MSWQ) simulation model was provided for establishing the relationship between environmental responses and pollution-control actions. The relationship was described by transformation matrices and vectors that could be used directly in a multi-point-source waste reduction (MWR) optimization model as water-quality constraints. The interval quadratic polynomials were employed to reflect the nonlinearities and uncertainties associated with wastewater treatment costs. Uncertainties associated with the water-quality parameters were projected into the transformation matrices and vectors through Monte Carlo simulation. Uncertainties derived from water quality standards were characterized as random variables with normal probability distributions. The proposed ICCQP model was applied to a water quality management problem in the Changsha section of the Xiangjiang River in China. The results demonstrated that the proposed optimization model could effectively communicate uncertainties into the optimization process, and generate inexact solutions containing a spectrum of wastewater treatment options. Decision alternatives could then be obtained by adjusting different combinations of the decision variables within their solution intervals. Solutions from the ICCQP model could be used to analyze tradeoffs between the wastewater treatment cost and system-failure risk due to inherent uncertainties. The results are valuable for supporting decision makers in seeking cost-effective water management strategies. Copyright Springer Science+Business Media B.V. 2009

Suggested Citation

  • X. Qin & G. Huang, 2009. "An Inexact Chance-constrained Quadratic Programming Model for Stream Water Quality Management," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 23(4), pages 661-695, March.
    • Handle: RePEc:spr:waterr:v:23:y:2009:i:4:p:661-695
    DOI: 10.1007/s11269-008-9294-0
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    4. Yao Ji & Guo Huang & Wei Sun, 2015. "Nonpoint-Source Water Quality Management Under Uncertainty Through an Inexact Double-Sided Chance-Constrained Model," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(9), pages 3079-3094, July.
    5. Qi Liu & Gengzhong Feng & Giri Kumar Tayi & Jun Tian, 2021. "Managing Data Quality of the Data Warehouse: A Chance-Constrained Programming Approach," Information Systems Frontiers, Springer, vol. 23(2), pages 375-389, April.
    6. Li, Y.P. & Huang, G.H. & Nie, S.L. & Chen, X., 2011. "A robust modeling approach for regional water management under multiple uncertainties," Agricultural Water Management, Elsevier, vol. 98(10), pages 1577-1588, August.
    7. Sun, Wei & Huang, Guo H. & Lv, Ying & Li, Gongchen, 2013. "Inexact joint-probabilistic chance-constrained programming with left-hand-side randomness: An application to solid waste management," European Journal of Operational Research, Elsevier, vol. 228(1), pages 217-225.
    8. Feifei Dong & Yong Liu & Han Su & Zhongyao Liang & Rui Zou & Huaicheng Guo, 2016. "Uncertainty-Based Multi-Objective Decision Making with Hierarchical Reliability Analysis Under Water Resources and Environmental Constraints," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(2), pages 805-822, January.
    9. Maryam Zavareh & Viviana Maggioni, 2018. "Application of Rough Set Theory to Water Quality Analysis: A Case Study," Data, MDPI, vol. 3(4), pages 1-15, November.
    10. Xu, Y. & Huang, G.H. & Qin, X.S. & Cao, M.F., 2009. "SRCCP: A stochastic robust chance-constrained programming model for municipal solid waste management under uncertainty," Resources, Conservation & Recycling, Elsevier, vol. 53(6), pages 352-363.
    11. Ping-Feng Pai & Fong-Chuan Lee, 2010. "A Rough Set Based Model in Water Quality Analysis," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(11), pages 2405-2418, September.
    12. M. Islam & Rehan Sadiq & Manuel Rodriguez & Homayoun Najjaran & Alex Francisque & Mina Hoorfar, 2013. "Evaluating Water Quality Failure Potential in Water Distribution Systems: A Fuzzy-TOPSIS-OWA-based Methodology," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(7), pages 2195-2216, May.
    13. D. Fu & Y. Li & G. Huang, 2013. "A Factorial-based Dynamic Analysis Method for Reservoir Operation Under Fuzzy-stochastic Uncertainties," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(13), pages 4591-4610, October.
    14. Li, Y.P. & Huang, G.H. & Zhang, N. & Nie, S.L., 2011. "An inexact-stochastic with recourse model for developing regional economic-ecological sustainability under uncertainty," Ecological Modelling, Elsevier, vol. 222(2), pages 370-379.
    15. M. Li & P. Guo & G. Yang & S. Fang, 2014. "IB-ICCMSP: An Integrated Irrigation Water Optimal Allocation and Planning Model Based on Inventory Theory under Uncertainty," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(1), pages 241-260, January.
    16. Feifei Dong & Yong Liu & Han Su & Zhongyao Liang & Rui Zou & Huaicheng Guo, 2016. "Uncertainty-Based Multi-Objective Decision Making with Hierarchical Reliability Analysis Under Water Resources and Environmental Constraints," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(2), pages 805-822, January.

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