Skip to main content
SpringerLink
Log in

An Improved Solving Approach for Interval-Parameter Programming and Application to an Optimal Allocation of Irrigation Water Problem

  • Published:
Water Resources Management Aims and scope Submit manuscript

Abstract

In this study, an improved single-step method (SSM) is developed based on two-step method (TSM) to solve the interval-parameter linear programming (ILP) model of which the right-hand sides are highly uncertain. Two numerical examples are presented to ascertain appropriate value of λ in SSM. The risk preference degree of λ could be 0.8 for maximum objective function type. To demonstrate the applicability of the developed method, an agricultural water management problem has been provided in the case study section. The results show that SSM is more effective than TSM for complete solutions. There is only partial solution obtained from the first submodel of TSM, because the right-hand side of the wheat output constraint is highly uncertain. Finally, local farmers’ net benefit reaches to [8.949, 12.442] × 108 RMB (the unit of Chinese currency). The priority order of crops that are needed to be irrigated by surface water is maize > wheat > cotton.

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

Similar content being viewed by others

References

  • Allahdadi M, Nehi HM (2013) The optimal solution set of the interval linear programming problems. Optim Lett 7(8):1893–1911

    Article  Google Scholar 

  • Cai YP, Huang GH, Li CH, Tan Q (2011) Identifying optimal strategies for environmental management in the mixed fuzzy stochastic environment. International Conference on Environmental Pollution and Public Health 2011. Engineering Information Institute, China

  • Chinneck JW, Ramadan K (2000) Linear programming with interval coefficients. J Oper Res Soc 51(2):209–220

    Article  Google Scholar 

  • Dantzig G (1998) Linear programming and extensions. Princeton University Press, New Jersey

    Google Scholar 

  • Dorfman R, Samuelson PA, Solow RM (1987) Linear programming and economic analysis. Dover Publications, New York

    Google Scholar 

  • Fan YR, Huang GH (2012) A robust Two-Step method for solving interval linear programming problems within an environmental management context. J Environ Inform 19(1):1–9

    Article  Google Scholar 

  • Fan YR, Huang GH, Li YP, Cao MF, Cheng GH (2009) A fuzzy linear programming approach for municipal solid-waste management under uncertainty. Eng Optim 41(12):1081–1101

    Article  Google Scholar 

  • Fan YR, Huang GH, Guo P, Yang AL (2012a) Inexact two-stage stochastic partial programming: application to water resources management under uncertainty. Stoch Env Res Risk A 26(2):281–293

    Article  Google Scholar 

  • Fan YR, Huang GH, Li YP (2012b) Robust interval linear programming for environmental decision making under uncertainty. Eng Optim 44(11):1321–1336

    Article  Google Scholar 

  • Fu DZ, Li YP, Huang GH (2013) A factorial-based dynamic analysis method for reservoir operation under fuzzy-stochastic uncertainties. Water Resour Manag 27(13):4591–4610

    Article  Google Scholar 

  • Fu Y, Li M, Guo P (2014) Optimal allocation of water resources model for different growth stages of crops under uncertainty. Am Soc Civ Eng 140(6):1272–1273

    Google Scholar 

  • Gass SI (2010) Linear programming: methods and applications. Dover Publications, New York

    Google Scholar 

  • Guo P, Huang GH (2009a) Inexact fuzzy-stochastic mixed-integer programming approach for long-term planning of waste management - part a: methodology. J Environ Manag 91(2):461–470

    Article  Google Scholar 

  • Guo P, Huang GH (2009b) Two-stage fuzzy chance-constrained programming: application to water resources management under dual uncertainties. Stoch Env Res Risk A 23(3):349–359

    Article  Google Scholar 

  • Guo P, Huang GH (2011) Inexact fuzzy-stochastic quadratic programming approach for waste management under multiple uncertainties. Eng Optim 43(5):525–539

    Article  Google Scholar 

  • Guo P, Huang GH, Li YP (2008) Interval stochastic quadratic programming approach for municipal solid waste management. J Environ Eng Sci 7(6):569–579

    Article  Google Scholar 

  • Guo P, Huang GH, He L, Li HL (2009a) Interval-parameter fuzzy-stochastic semi-infinite mixed-integer linear programming for waste management under uncertainty. Environ Model Assess 14(4):521–537

    Article  Google Scholar 

  • Guo P, Huang GH, He L, Zhu H (2009b) Interval-parameter two-stage stochastic semi-infinite programming: application to water resources management under uncertainty. Water Resour Manag 23(5):1001–1023

    Article  Google Scholar 

  • Guo P, Huang GH, Li YP (2010) An inexact fuzzy-chance-constrained two-stage mixed-integer linear programming approach for flood diversion planning under multiple uncertainties. Adv Water Resour 33(1):81–91

    Article  Google Scholar 

  • Hladık M (2010) Linear programming-new frontiers in theory and applications. Nova Science, New York

  • Huang GH, Cao MF (2011) Analysis of solution methods for interval linear programming. J Environ Inform 17(2):54–64

    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(2):95–118

    Article  Google Scholar 

  • Huang GH, Baetz BW, Park SW (1995a) Grey fuzzy integer programming - an application to regional waste management planning under uncertainty. Socio Econ Plan Sci 29(1):17–38

    Article  Google Scholar 

  • Huang GH, Baetz BW, Patry GG (1995b) Grey integer programming - an application to waste management planning under uncertainty. Eur J Oper Res 83(3):594–620

    Article  Google Scholar 

  • Huang GH, Sae-Lim N, Liu L, Chen Z (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 

  • Jansson C (1988) A self-validating method for solving linear programming problems with interval input data. Springer Vienna, USA

  • Jin L, Huang G, Fan Y, Nie X, Cheng G (2012) A hybrid dynamic dual interval programming for irrigation water allocation under uncertainty. Water Resour Manag 26(5):1183–1200

    Article  Google Scholar 

  • Khare D, Jat MK, Ediwahyunan X (2006) Assessment of counjunctive use planning options: a case study of sapon irrigation command area of Indonesia. J Hydrol 328(3,4):764–777

    Article  Google Scholar 

  • Kim HK, Jang TI, Im SJ, Park SW (2009) Estimation of irrigation return flow from paddy fields considering the soil moisture. Agric Water Manag 96(5):875–882

    Article  Google Scholar 

  • Li YP, Huang GH (2006) An inexact two-stage mixed integer linear programming method for solid waste management in the City of Regina. J Environ Manag 81(3):188–209

    Article  Google Scholar 

  • Li YP, Huang GH (2007) Fuzzy two-stage quadratic programming for planning solid waste management under uncertainty. Int J Syst Sci 38(3):219–233

    Article  Google Scholar 

  • Li YP, Huang GH, Xiao HN (2008) Municipal solid waste management under uncertainty: an interval-fuzzy Two-stage stochastic programming approach. J Environ Inform 12(2):96–104

    Article  Google Scholar 

  • Li MW, Li YP, Huang GH (2011a) An interval-fuzzy two-stage stochastic programming model for planning carbon dioxide trading under uncertainty. Energy 36(9):5677–5689

    Article  Google Scholar 

  • Li YP, Huang GH, Nie SL (2011b) Optimization of regional economic and environmental systems under fuzzy and random uncertainties. J Environ Manag 92(8):2010–2020

    Article  Google Scholar 

  • Li M, Guo P, Yang GQ, Fang SQ (2014) IB-ICCMSP: an integrated irrigation water optimal allocation and planning model based on inventory theory under uncertainty. Water Resour Manag 28(1):241–260

    Article  Google Scholar 

  • Lin QG, Huang GH (2010) An inexact two-stage stochastic energy systems planning model for managing greenhouse gas emission at a municipal level. Energy 35(5):2270–2280

    Article  Google Scholar 

  • Lin QG, Huang GH (2011) Interval-fuzzy stochastic optimization for regional energy systems planning and greenhouse-gas emission management under uncertainty-a case study for the Province of Ontario, Canada. Clim Chang 104(2):353–378

    Article  Google Scholar 

  • Lin QG, Huang GH, Bass B, Qin XS (2009) IFTEM: an interval-fuzzy two-stage stochastic optimization model for regional energy systems planning under uncertainty. Energ Policy 37(3):868–878

    Article  Google Scholar 

  • Liu Y, Huang G, Cai Y, Dong C (2011) An inexact Mix-Integer Two-Stage linear programming model for supporting the management of a Low-Carbon energy system in china. Energies 4(10):1657–1686

    Article  Google Scholar 

  • Lu HW, Huang GH, He L (2009) An inexact programming method for agricultural irrigation systems under parameter uncertainty. Stoch Env Res Risk A 23(6):759–768

    Article  Google Scholar 

  • Luo J, Li W (2013) Strong optimal solutions of interval linear programming. Linear Algebra Appl 439(8):2479–2493

    Article  Google Scholar 

  • Mráz F (1998) Calculating the exact bounds of optimal values in LP with interval coefficients. Ann Oper Res 81:51–62

    Article  Google Scholar 

  • Nie XH, Huang GH, Wang D, Li HL (2008) Robust optimisation for inexact water quality management under uncertainty. Civ Eng Environ Syst 25(2):167–184

    Article  Google Scholar 

  • Reeb JE, Leavengood SA, Others (1998) Using the graphical method to solve linear programs. Oregon State University, USA

  • Sahinidis NV (2004) Optimization under uncertainty: state-of-the-art and opportunities. Comput Chem Eng 28(6):971–983

    Article  Google Scholar 

  • Sengupta A, Pal TK, Chakraborty D (2001) Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming. Fuzzy Sets Syst 119(1):129–138

    Article  Google Scholar 

  • Sun Y, Li Y, Huang G (2010) Development of a Fuzzy-Queue-Based interval linear programming model for municipal solid waste management. Environ Eng Sci 27(6):451–468

    Article  Google Scholar 

  • Tan Q, Huang GH, Cai YP (2008) Planning of municipal solid waste management systems under mixed fuzzy and stochastic environment. Annual Conference of the Canadian Society for Civil Engineering 2008 Canadian Society for Civil Engineering, Canada

  • Tong F, Guo P (2013) Simulation and optimization for crop water allocation based on crop water production functions and climate factor under uncertainty. Appl Math Model 37:7708–7716

    Article  Google Scholar 

  • Xi BD, Su J, Huang GH, Qin XS, Jiang YH, Huo SL, Ji DF, Yao B (2010) An integrated optimization approach and multi-criteria decision analysis for supporting the waste-management system of the City of Beijing, China. Eng Appl Artif Intell 23(4):620–631

    Article  Google Scholar 

  • Xu Y, Huang G, Qin X (2009a) Inexact Two-Stage stochastic robust optimization model for water resources management under uncertainty. Environ Eng Sci 26(12):1765–1776

    Article  Google Scholar 

  • Xu Y, Huang GH, Qin XS, Huang Y (2009b) SRFILP: a stochastic robust fuzzy interval linear programming model for municipal solid waste management under uncertainty. J Environ Inform 14(2):74–82

    Google Scholar 

  • Xu Y, Huang GH, Qin XS, Cao MF, Sun Y (2010) An interval-parameter stochastic robust optimization model for supporting municipal solid waste management under uncertainty. Waste Manag 30(2):316–327

    Article  Google Scholar 

  • Yang G, Guo P, Huo L, Ren C (2015) Optimization of the irrigation water resources for Shijin irrigation district in north China. Agric Water Manag 158:82–98

    Article  Google Scholar 

  • Zhu H, Huang GH (2011) SLFP: a stochastic linear fractional programming approach for sustainable waste management. Waste Manag 31(12):2612–2619

    Article  Google Scholar 

Download references

Acknowledgments

This research was supported by the Government Public Research Funds for Projects of Ministry of Agriculture (No. 201203077), International Science & Technology Cooperation Program of China (2013DFG70990), and the National Natural Science Foundation of China (No. 51321001).

Author information

Authors and Affiliations

  1. Centre for Agricultural Water Research in China, China Agricultural University, Beijing, 100083, China

    Gaiqiang Yang, Ping Guo, Mo Li, Shiqi Fang & Liudong Zhang

  2. Institute of Environmental Science, Taiyuan University of Science and Technology, Taiyuan, Shanxi, 030024, China

    Gaiqiang Yang

  3. College of Water Conservancy and Hydropower and Architecture Engineering, Yunnan Agricultural University, Kunming, 650201, China

    Liudong Zhang

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

    Ping Guo

Authors
  1. Gaiqiang Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ping Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mo Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shiqi Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Liudong Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ping Guo.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, G., Guo, P., Li, M. et al. An Improved Solving Approach for Interval-Parameter Programming and Application to an Optimal Allocation of Irrigation Water Problem. Water Resour Manage 30, 701–729 (2016). https://doi.org/10.1007/s11269-015-1186-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11269-015-1186-5

Keywords

Search

Navigation