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Journal of Environmental Accounting and Management
António Mendes Lopes (editor), Jiazhong Zhang(editor)
António Mendes Lopes (editor)

University of Porto, Portugal

Email: aml@fe.up.pt

Jiazhong Zhang (editor)

School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi Province 710049, China

Fax: +86 29 82668723 Email: jzzhang@mail.xjtu.edu.cn


A Risk-averse Two-Stage Stochastic Optimization Model for Water Resources Allocation under Uncertainty

Journal of Environmental Accounting and Management 6(1) (2018) 71--82 | DOI:10.5890/JEAM.2018.03.006

Ye Xu$^{1}$, Sha Li$^{1}$, Feng Liu$^{2}$, Jinping Qian$^{3}$, Yanpeng Cai$^{4}$, Guanhui Cheng$^{5}$

$^{1}$ MOE Key Laboratory of Regional Energy and Environmental Systems Optimization, College of Environmental Science and Engineering, North China Electric Power University, Beijing 102206, China

$^{2}$ School of Materials and Metallurgy, University of Science and Technology Liaoning, Anshan 114051, China

$^{3}$ College of Resources and Environmental Sciences, Hebei Normal University, No.20 Road East. 2nd Ring South, Yuhua District, Shijiazhuang, Hebei, 050024 China

$^{4}$ State Key Laboratory of Water Environment Simulation, School of Environment, Beijing Normal University, Beijing 100875, China

$^{5}$ Faculty of Engineering, University of Regina, Regina, Saskatchewan, Canada S4S 0A2

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Abstract

The water resource shortage has caused intense contradictions among various water users; moreover, unfair and irrational water allocation may result in the economic loss, even the social instability. A risk-averse twostage stochastic programming model (RATSP) are developed for tackling this issue. The significant contribution made by the RATSP model is that it concerns the importance of the financial risk under each scenario, where the risk is expressed as the probability of occurrence in that benefit generated under each scenario is lower than predefined target profit. It can avoid possible suboptimal solutions caused by only considering the maximization of the expected value for all scenarios as an objective function. Moreover, the risk measure is incorporated into the objective function, leading a variety of solutions under various weight coefficients and target levels, which is suitable in analyzing the trade-off between the system economy and reliability. A case of water resources management system is used to reflect the applicability and feasibility of this model. The obtained results demonstrate that the RATSP model can help decision makers gain in-depth insights into potential system risk, analyze the trade-off between system economy and stability, generate the stable water allocation schemes, and avoid the contradictions among users.

Acknowledgments

This research was supported by the Natural Sciences Foundation of China (71303017), National Key Research and Development Plan (2016YFE0102400) and Fundamental Research Funds for the Central Universities (2017MS050).

References

  1. [1]  Barbaro, A. and Bagajewicz, M.J. (2004), Managing financial risk in planning under uncertainty, Process Systems Engineering 50, 963-989.
  2. [2]  Birge, J.R. and Louveaux, F.V. (1988), A multicut algorithm for two-stage stochastic linear programs, European Journal of Operational Research 34, 384-392.
  3. [3]  Fattahi, P. and Fayyaz, S. (2010), A compromise programming model to integrated urban water management, Water Resource Management 24, 1211-1227.
  4. [4]  Feng, Z.M., Yang, Y.Z. and You, Z. (2014), Research on the water resources restriction on population distribution in China, Journal of Natural Resources 29(10), 1637-1648. (In Chinese)
  5. [5]  Han, Y., Xu, S.G. and Xu, X.Z. (2008), Modeling multisource multiuser water resources allocation, Water Resource Management 22, 911-923.
  6. [6]  Howe, B., Maier, D. and Baptista, A. (2003), A language for spatial data manipulation, Journal of Environmental Informatics 2, 23-37.
  7. [7]  Huang, G.H. (1996), IPWM: An interval-parameter water quality management model, Engineering Optimization 26, 79-103.
  8. [8]  Huang, G.H. and Loucks, D.P. (2000), An inexact two-stage stochastic programming model for water resources management under uncertainty, Civil Engineering and Environmental Systems 17, 95-118.
  9. [9]  Jenkins, M.W. and Lund, J.R. (2000), Integrating yield and shortage management under multiple uncertainties, Journal of Water Resources Planning and Management 126(5), 288-297.
  10. [10]  Jia, Y. and Culver, T.B. (2006), Robust optimization for total maximum daily load allocations, Water Resources Research 42, W02412.
  11. [11]  Li, C.Y. and Zhang, L. (2015), An inexact two-stage allocation model for water resources management under uncertainty, Water Resources Management 29(6), 1823-1841.
  12. [12]  Li, W., Liu, M., Wu, S.Z. and Xu, Y. (2015), An inexact optimization model associated with two robust programming approaches for water resources management, International Journal of Environmental Science and Technology 12(7), 2401-2414.
  13. [13]  Li, Y.P. and Huang, G.H. (2007), Inexact multistage stochastic quadratic programming method for planning water resources systems under uncertainty, Environmental Engineering Science 24(10), 1361-1377.
  14. [14]  Liu D., Liu, W.T., Fu, Q., Zhang, Y.J., Li, T.Q., Imran, K.M. and Abrar, F.M. (2017), Two-stage multi-water sources allocation model in regional water resources management under uncertainty, Water Resources Management, 31(2), 1-19.
  15. [15]  Liu, Y., Guo, H.C., Zhou, F. and Qin, X.S. (2007), An inexact chance-constrained linear programming model for optimal water pollution management at the watershed scale, Journal of Water Resources Planning and Management (ASCE) 134, 347-356.
  16. [16]  Maqsood, I., Huang, G.H. and Yeomans, J.S. (2005), An interval-parameter fuzzy two-stage stochastic program for water resources management under uncertainty, European Journal of Operational Research 167, 208-225.
  17. [17]  Qin, X.S., Huang, G.H., Zeng, G.M., Chakma, A. and Huang, Y.F. (2007), An interval-parameter fuzzy nonlinear optimization model for stream water quality management under uncertainty, European Journal of Operational Research 180(3), 1331-1357.
  18. [18]  Song, X.S., Shi, P.J. and Jin, R. (2005), Analysis on the contradiction between supply and demand of water resources in China owing to uneven regional distribution, Arid Zone Research 22(2), 163-166. (In Chinese)
  19. [19]  Wagner, J.M., Shamir, U. and Marks, D.H. (1994), Containing groundwater contamination: Planning models using stochastic programming with recourse, European Journal of Operational Research 7, 1-26.
  20. [20]  Wilchfort, O. and Lund, J.R. (1997), Shortage management modeling for urban water supply systems, Journal of Water Resources Planning and Management 123(4), 250-258.
  21. [21]  Xu, Y., Huang, G.H. and Qin, X.S. (2009), An inexact two-stage stochastic robust optimization model for water resources management under uncertainty, Environmental Engineering Science 26, 1765-1776.
  22. [22]  Xu, Y., Huang, G.H. and Xu, T.Y. (2012), Inexact management modeling for urban water Supply systems, Journal of Environmental Informatics 20(1), 34-43. Xu, Y. and Huang, G.H. (2016), A risk-based interval two-Stage programming model for agricultural system management under uncertainty, Mathematical Problems in Engineering 7438913.
  23. [23]  Xu, Y., Li, W. and Ding, X.W. (2017), A stochastic multi-objective chance-constrained programming model for water supply management in Xiaoqing river watershed, Water 14(2), 171-183.