Skip to main content
SpringerLink
Log in

An inexact joint-probabilistic programming method for risk assessment in water resources allocation

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

Abstract

In this study, an inexact joint probabilistic programming (IJPP) approach is developed for risk assessment and uncertainty reflection in water resources management systems. IJPP can dominate random parameters in the model’s left- and right-hand sides of constraints and interval parameters in the objective function. It can also help examine the risk of violating joint probabilistic constraints, which allows an increased robustness in controlling system risk in the optimization process. Moreover, it can facilitate analyses of various policy scenarios that are associated with different levels of economic consequences when the promised targets are violated within a multistage context. The IJPP method is then applied to a case study of planning water resources allocation within a multi-reservoir and multi-period context. Solutions of system benefit, economic penalty, water shortage, and water-allocation pattern vary with different risks of violating water-demand targets from multiple competitive users. Results also demonstrate that different users possess different water-guarantee ratios and different water-allocation priorities. The results can be used for helping water resources managers to identify desired system designs against water shortage and for risk control, and to determine which of these designs can most efficiently accomplish optimizing the system objective 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
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  • Abdelaziz FB, Aouni B, Fayedh RE (2007) Multi-objective stochastic programming for portfolio selection. Eur J Oper Res 177:1811–1823

    Article  Google Scholar 

  • Andrieu L, Henrion R, Römisch W (2010) A model for dynamic chance constraints in hydro power reservoir management. Eur J Oper Res 207:579–589

    Article  Google Scholar 

  • Birge JR (1985) Decomposition and partitioning methods for multistage stochastic linear programs. Oper Res 33:989–1007

    Article  Google Scholar 

  • Charnes A, Cooper WW (1959) Chance constrained programming. Manag Sci 6:73–79

    Article  Google Scholar 

  • Charnes A, Cooper WW (1983) Response to decision problems under risk and chance constrained programming: dilemmas in the transitions. Manag Sci 29:750–753

    Article  Google Scholar 

  • Fayaed SS, El-Shafie A, Jaafar O (2013) Reservoir-system simulation and optimization techniques. Stoch Environ Res Risk Assess 27(7):1751–1772

    Article  Google Scholar 

  • Gibbs MS, Dandy GC, Maier HR (2014) Assessment of the ability to meet environmental water requirements in the upper south east of south Australia. Stoch Environ Res Risk Assess 28(1):39–56

    Article  Google Scholar 

  • Housh M, Ostfeld A, Shamir U (2013) Limited multi-stage stochastic programming for managing water supply systems. Environ Model Softw 41:53–64

    Article  Google Scholar 

  • Huang GH (1998) A hybrid inexact-stochastic water management model. Eur J Oper Res 107:137–158

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Kasiviswanathan KS, Sudheer KP (2013) Quantification of the predictive uncertainty of artificial neural network based river flow forecast models. Stoch Environ Res Risk Assess 27(1):137–146

    Article  Google Scholar 

  • Kriauciuniene J, Jakimavicius D, Sarauskiene D, Kaliatka T (2013) Estimation of uncertainty sources in the projections of Lithuanian river runoff. Stoch Environ Res Risk Assess 27(4):769–784

    Article  Google Scholar 

  • Lejeune MA, Prekopa A (2005) Approximations for and convexity of probabilistic constrained problems with random right-hand sides. Rutcor Res, Report 17

    Google Scholar 

  • Li YP, Huang GH (2009) Fuzzy-stochastic-based violation analysis method for planning water resources management systems with uncertain information. Inf Sci 179:4261–4276

    Article  Google Scholar 

  • Li YP, Huang GH (2013) Risk analysis and management for water resources systems. Stoch Environ Res Risk Assess 27(3):593–597

    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 29:776–789

    Article  Google Scholar 

  • Li YP, Huang GH, Nie SL, Liu L (2008) Inexact multistage stochastic integer programming for water resources management under uncertainty. J Environ Manag 88:93–107

    Article  CAS  Google Scholar 

  • Li YP, Huang GH, Nie SL (2009) Water resources management and planning under uncertainty: an inexact multistage joint-probabilistic programming method. Water Resour Manag 23:2515–2538

    Article  Google Scholar 

  • Loucks DP, Stedinger JR, Haith DAH (1981) Water resources systems planning and analysis. Prentice Hall, Englewood Cliffs

    Google Scholar 

  • Mahiny AS, Clarke KC (2013) Simulating hydrologic impacts of urban growth using SLEUTH, multi criteria evaluation and runoff modeling. J Environ Inform 22(1):27–38

    Article  Google Scholar 

  • Miller BL, Wager HM (1965) Chance constrained programming with joint constraints. Oper Res 13(6):930–945

    Article  Google Scholar 

  • Morgan DR, Eheart JW, Valocchi AJ (1993) Aquifer remediation design under uncertainty using a new chance constrained programming technique. Water Resour Res 29:551–568

    Article  CAS  Google Scholar 

  • Sun W, Huang GH, Lv Y, Li GC (2013) Inexact joint-probabilistic chance-constrained programming with left-hand-side randomness: an application to solid waste management. Eur J Oper Res 228:217–225

    Article  Google Scholar 

  • Suo MQ, Li YP, Huang GH (2013) Electric power system planning under uncertainty using inexact inventory nonlinear programming method. J Environ Inf 22(1):49–67

    Article  Google Scholar 

  • Syme GJ (2014) Acceptable risk and social values: struggling with uncertainty in Australian water allocation. Stoch Environ Res Risk Assess 28(1):113–121

    Article  Google Scholar 

  • Tilmant A, Pinte D, Goor Q (2008) Assessing marginal water values in multipurpose multireservoir systems via stochastic programming. Water Resour Res 44:W12431

    Google Scholar 

  • Watkins DW, McKinney DC, Lasdon LS, Nielsen SS, Martin QW (2000) A scenario-based stochastic programming model for water supplies from the highland lakes. Int Trans Oper Res 7:211–230

    Article  Google Scholar 

  • Xu TY, Qin XS (2013) Solving water quality management problem through combined genetic algorithm and fuzzy simulation. J Environ Inf 22(1):39–48

    Article  Google Scholar 

  • Zhang Y, Monder D, Forbes JF (2002) Real-time optimization under parametric uncertainty: a probability constrained approach. J Process Control 12:373–389

    Article  CAS  Google Scholar 

  • Zhang GQ, Shang J, Li WL (2011) Collaborative production planning of supply chain under price and demand uncertainty. Eur J Oper Res 215:590–603

    Article  Google Scholar 

Download references

Acknowledgments

This research was supported by the National Natural Sciences Foundation (51225904 and 51190095), the National High-tech R&D (863) Program (2012AA091103), the 111Project (B14008), and the Program for Innovative Research Team in University (IRT1127). 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, Sino-Canada Resources and Environmental Research Academy, North China Electric Power University, Beijing, 102206, China

    X. W. Zhuang, Y. P. Li, G. H. Huang & X. T. Zeng

Authors
  1. X. W. Zhuang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Y. P. Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. H. Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. X. T. Zeng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Y. P. Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhuang, X.W., Li, Y.P., Huang, G.H. et al. An inexact joint-probabilistic programming method for risk assessment in water resources allocation. Stoch Environ Res Risk Assess 29, 1287–1301 (2015). https://doi.org/10.1007/s00477-014-1008-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00477-014-1008-y

Keywords

Search

Navigation