Skip to main content
SpringerLink
Log in

Inexact two-stage stochastic partial programming: application to water resources management under uncertainty

  • Original Paper
  • Published:
Stochastic Environmental Research and Risk Assessment Aims and scope Submit manuscript

Abstract

In this study, an inexact two-stage stochastic partial programming (ITSPP) method is developed for tackling uncertainties presented as intervals and partial probability distributions. A scenario-based interactive algorithm is proposed to solve the ITSPP model. This algorithm is implemented through: (i) obtaining extreme points of the linear partial information (LPI); (ii) generating an inexact two-stage stochastic programming (ITSP) model under each extreme point; (iii) solving ITSP models through interactive algorithm proposed by Huang and Loucks (Civil Eng Environ Syst 17:95–118, 2000); (iv) acquiring the interval solutions under each extreme point and the final optimal interval for the objective function. The developed method is applied to a case study for water-resources planning. The modelling results can generate a series of decision alternatives under various system conditions, and thus help decision makers identify the desired water-resources management policies under uncertainty.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  • Abdelaziz FB, Masri H (2005) Stochastic programming with fuzzy linear partial information on probability distribution. Eur J Oper Res 162:619–629

    Article  Google Scholar 

  • Abdelaziz FB, Masri H (2009) Multistage stochastic programming with fuzzy probability distribution. Fuzzy Sets Syst 160:3239–3249

    Article  Google Scholar 

  • Edirisinghe NCP, Ziemba WT (1994) Bounds for two-stage stochastic programs with fixed resources. Math Oper Res 19:292–313

    Article  Google Scholar 

  • Guo P, Huang GH (2009) Two-stage fuzzy chance-constrained programming: application to water resources management under dual uncertainties. Stoch Env Res Risk Assess 23:349–359

    Article  Google Scholar 

  • Guo P, Huang GH, He L, Zhu H (2009) Interval-parameter two-stage stochastic semi-infinite programming: application to water resources management under uncertainty. Water Resour Manag 23(8):1001–1023

    Article  Google Scholar 

  • He L, Wang GQ, Fu XD (2010) Disaggregation model of daily rainfall and its application in the Xiaolihe Watershed, Yellow River. J Environ Inform 16:11–18

    Article  Google Scholar 

  • Huang GH, Loucks DP (2000) An inexact two-stage stochastic programming model for water resources management under uncertainty. Civil Eng Environ Syst 17:95–118

    Article  Google Scholar 

  • Jing L, Chen B (2011) Field investigation and hydrological modelling of a subarctic wetland—the Deer River Watershed. J Environ Inform 17:36–45

    Article  Google Scholar 

  • Kofler E (2001) Linear partial information with applications. Fuzzy Sets Syst 118:167–177

    Article  Google Scholar 

  • Kofler E, Zweifel P (1991) Convolution of fuzzy distributions in decision-making. Stat Papers 32:123–136

    Article  Google Scholar 

  • Li YP, Huang GH (2008) Interval-parameter two-stage stochastic nonlinear programming for water resources management under uncertainty. Water Res Manag 22(6):681–698

    Article  Google Scholar 

  • Li YP, Huang GH, Nie SL (2006) An interval-parameter multi-stage stochastic programming model for water resources management under uncertainty. Adv Water Resour 29(5):776–789

    Article  Google Scholar 

  • Li YP, Huang GH, Nie SL (2007) Mixed interval-fuzzy two-stage integer programming and its application to flood-diversion planning. Eng Optim 39:163–183

    Article  Google Scholar 

  • Li YP, Huang GH, Nie XH, Nie SL (2008) A two-stage fuzzy robust integer programming approach for capacity planning of environmental management systems. Eur J Oper Res 189:399–420

    Article  Google Scholar 

  • Loucks DP, Stedinger JR, Haith DA (1981) Water resource systems planning and analysis. Prentice-Hall, Englewood Cliffs, NJ

    Google Scholar 

  • Lu HW, Huang GH, Zeng GM, Maqsood I, He L (2009) An inexact two-stage fuzzy-stochastic programming model for water resources management. Water Resour Manag 22(8):991–1016

    Article  Google Scholar 

  • Luo B, Maqsood I, Yin YY, Huang GH, Cohen SJ (2003) Adaptation to climate change through water trading under uncertainty—an inexact two-stage nonlinear programming approach. J Environ Inform 2(2):58–68

    Article  Google Scholar 

  • Luo B, Maqsood I, Huang GH (2007) Planning water resources systems with interval stochastic dynamic programming. Water Resour Manag 21(6):997–1014

    Article  Google Scholar 

  • Maqsood I, Huang GH, Yeomans JS (2005) An interval-parameter fuzzy two-stage stochastic program for water resources management under uncertainty. Eur J Oper Res 167:208–225

    Article  Google Scholar 

  • Ping J, Chen Y, Chen B, Howboldt K (2010) A robust statistical analysis approach for pollutant loading in Urban River. J Environ Inform 16:35–42

    Article  Google Scholar 

  • Wagner JM, Shamir U, Marks DH (1994) Containing groundwater contamination: planning models using stochastic programming with recourse. Eur J Oper Res 7:1–26

    Article  Google Scholar 

  • Wu S, Li J, Huang GH (2008) Characterization and evaluation of elevation data uncertainty in water resources modeling with GIS. Water Resour Manag 22(8):959–972

    Article  Google Scholar 

Download references

Acknowledgments

This research was supported by the Major Science and Technology Program for Water Pollution Control and Treatment (2009ZX07104-004) of China. The authors are grateful to the editors and the anonymous reviewers for their insightful comments and suggestions.

Author information

Authors and Affiliations

  1. MOE Key Laboratory of Regional Energy Systems Optimization, S&C Academy of Energy and Environmental Research, North China Electric Power University, Beijing, 102206, China

    Y. R. Fan, G. H. Huang & A. L. Yang

  2. College of Water Conservancy and Civil Engineering, China Agricultural University, Beijing, 100083, China

    P. Guo

Authors
  1. Y. R. Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. H. Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. L. Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. H. Huang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fan, Y.R., Huang, G.H., Guo, P. et al. Inexact two-stage stochastic partial programming: application to water resources management under uncertainty. Stoch Environ Res Risk Assess 26, 281–293 (2012). https://doi.org/10.1007/s00477-011-0504-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00477-011-0504-6

Keywords

Search

Navigation