Skip to main content
SpringerLink
Log in

An inexact programming method for agricultural irrigation systems under parameter uncertainty

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

Abstract

Rapid population growth and economy development have led to increasing reliance on water resources. It is even aggravated for agricultural irrigation systems where more water is necessary to support the increasing population. In this study, an inexact programming method based on two-stage stochastic programming and interval-parameter programming is developed to obtain optimal water-allocation strategies for agricultural irrigation systems. It is capable of handling such problems where two-stage decisions need to be suggested under random- and interval-parameter inputs. An interactive solving procedure derived from conventional interval-parameter programming makes it possible for the impact of lower and upper bounds of interval inputs to be well reflected in the resulting solutions. An agricultural irrigation management problem is then provided to demonstrate the applicability, and reasonable solutions are obtained. Compared to the solutions from a representative interval-parameter programming model where only one decision-stage exists, the interval of optimized objective-function value is narrow, indicating more alternatives could be provided when water-allocation targets are rather high. However, chances of obtaining more benefits exist in association with a risk of paying more penalties; such a relationship becomes apparent when the variation of water availability is much intensive.

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

Similar content being viewed by others

References

  • Abolpour B, Javan M (2007) Optimization model for allocating water in a river basin during a drought. J Irrigation Drainage Eng 133(6):559–572

    Article  Google Scholar 

  • Abrishamchi A, Marino MA, Afshar A (1991) Reservoir planning for irrigation district. J Water Res Plan Manage 117:74–85

    Article  Google Scholar 

  • Bonaccorso B, Cancelliere A, Rossi G (2003) An analytical formulation of return period of drought severity. Stoch Environ Res Risk Assess 17(3):157–174

    Article  Google Scholar 

  • Farmani R, Abadia R, Savic D (2007) Optimum design and management of pressurized branched irrigation networks. J Irrigation Drainage Eng 133(6):528–537

    Article  Google Scholar 

  • Faulkner JW, Steenhuis T, van de Giesen N, Andreini M, Liebe JR (2008) Water use and productivity of two small reservoir irrigation schemes in Ghana's Upper East Region. Irrigation Drainage 57:151–163. doi:10.1002/ird.384

    Article  Google Scholar 

  • Georgiou PE, Papamichail DM, Vougioukas SG (2006) Optimal irrigation reservoir operation and simultaneous multi-crop cultivation area selection using simulated annealing. Irrigation Drainage 55(2):129–144

    Article  Google Scholar 

  • He L, Huang GH, Lu HW et al (2008a) Optimization of surfactant-enhanced aquifer remediation for a laboratory BTEX system under parameter uncertainty. Environ Sci Technol. doi: 10.1021/es071106y

  • He L, Huang GH, Zeng GM et al (2008b) Identifying optimal regional solid waste management strategies through a new inexact integer programming model containing infinite objectives and constraints. Waste Manage. doi: 10.1016/j.wasman.2008.02.003

  • He L, Huang GH, Zeng GM et al (2008c) Identification of the optimal urban solid waste flow schemes under impacts of energy prices. Environ Eng Sci 25(5). doi:10.1089/ees.2007.0078

  • Heidari A, Saghafian B, Maknoon R (2006) Assessment of flood forecasting lead time based on generalized likelihood uncertainty estimation approach. Stoch Environ Res Risk Assess 20(5):363–380

    Article  Google Scholar 

  • Huang GH, Moore RD (1993) Grey linear programming, its solving approach, and its application to water pollution control. Int J Syst Sci 24(1):159–172

    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 

  • Huang GH, Baetz BW, Patry GG (1992) A grey linear programming approach for municipal solid waste management planning under uncertainty. Civil Eng Syst 9:319–335

    Article  CAS  Google Scholar 

  • Huang GH, Sae-Lim N, Liu L et al (2001) An interval-parameter fuzzy-stochastic programming approach for municipal solid waste management and planning. Environ Model Assess 6(4):271–283

    Article  Google Scholar 

  • Kentel E, Aral MM (2004) Probabilistic-fuzzy health risk modeling. Stoch Environ Res Risk Assess 18(5):324–338

    Article  Google Scholar 

  • Kipkorir EC, Raes D, Labadie J (2001) Optimal allocation of short-term irrigation supply. Irrigation Drainage Syst 15(3):247–267

    Article  Google Scholar 

  • Lejano RP (2006) Optimizing the layout and design of branched pipeline water distribution systems. Irrigation Drainage Syst 20(1):125–137

    Article  Google Scholar 

  • Lin YP, Huang GH, Lu HW, et al (2008) Modeling of substrate degradation and oxygen consumption in waste composting processes. Waste Manage 28(8):1375–1385. doi:10.1016/j.wasman.2007.09.016

    Article  CAS  Google Scholar 

  • Llamas MR, Custodio E (eds) (2003) Intensive use of groundwater: challenges and opportunities. Taylor & Francis Group, London

    Google Scholar 

  • Loaiciga HA, Marino MA (1987) The inverse problem and ground water management. Stoch Environ Res Risk Assess 1(3):161–168

    Google Scholar 

  • Lu HW, Huang GH, Zeng GM, et al (2007a) An inexact two-stage fuzzy-stochastic programming model for water resources management. Water Res Manage. doi:10.1007/s11269-007-9206-8

  • Lu HW, Huang GH, He L, et al (2007b) An inexact dynamic optimization model for municipal solid waste management in association with greenhouse gas emission control. J Environ Manage. doi:10.1016/j.jenvman.2007.10.011

  • Lu HW, Huang GH, Liu L, et al (2008) An interval-parameter fuzzy-stochastic programming approach for air quality management under uncertainty. Environ Eng Sci 25(6):895–910. doi:10.1089/ees.2007.0165

    Article  CAS  Google Scholar 

  • Maqsood I, Huang GH, Huang YF et al (2005) ITOM: an interval-parameter two-stage optimization model for stochastic planning of water resources systems. Stoch Environ Res Risk Assess 19:125–133

    Article  Google Scholar 

  • Montazar A, Rahimikob A (2008) Optimal water productivity of irrigation networks in arid and semi-arid regions. Irrigation Drainage. doi: 10.1002/ird.376

  • Onta PR, Loof R, Banskota M (1995) Performance based irrigation planning under water shortage. Irrigation Drainage Syst 9(2):143–162

    Article  Google Scholar 

  • Paudyal GN, Gupta AD (1990) Irrigation management by multilevel optimization. J Irrigation Drainage Eng 116:273–291

    Article  Google Scholar 

  • Sahoo B, Lohani AK, Sahu RK (2006) Fuzzy multiobjective and linear programming based management models for optimal land-water-crop system. Water Res Manage 20(6):931–948

    Article  Google Scholar 

  • Spiliotis M, Tsakiris G (2007) Minimum cost irrigation network design using interactive fuzzy integer programming. J Irrigation Drainage Eng 133(3):242–248

    Article  Google Scholar 

  • Tsakiris G, Spiliotis M (2006) Cropping pattern planning under water supply from multiple sources. Irrigation Drainage Systems 20:57–68

    Article  Google Scholar 

Download references

Acknowledgments

This research was supported by the Major State Basic Research Development Program of MOST (2005CB724200 and 2006CB403307) and the Natural Science and Engineering Research Council of Canada. The authors are grateful to the editor and the anonymous reviewers for their insightful comments and suggestions.

Author information

Authors and Affiliations

  1. Environmental Systems Engineering, Faculty of Engineering, University of Regina, Regina, SK, S4S 0A2, Canada

    H. W. Lu, G. H. Huang & L. He

  2. Chinese Research Academy of Environmental Science, North China Electric Power University, 100012-102206, Beijing, China

    G. H. Huang

Authors
  1. H. W. Lu
    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. L. He
    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

Lu, H.W., Huang, G.H. & He, L. An inexact programming method for agricultural irrigation systems under parameter uncertainty. Stoch Environ Res Risk Assess 23, 759–768 (2009). https://doi.org/10.1007/s00477-008-0256-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00477-008-0256-0

Keywords

Search

Navigation