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

详细信息    查看全文

• 作者：Gaiqiang Yang ; Ping Guo ; Mo Li ; Shiqi Fang ; Liudong Zhang
• 关键词：Interval linear programming ; Interval ; parameter ; Single ; step method ; Two ; step method ; Agricultural water management
• 刊名：Water Resources Management
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：30
• 期：2
• 页码：701-729
• 全文大小：926 KB
• 参考文献：Allahdadi M, Nehi HM (2013) The optimal solution set of the interval linear programming problems. Optim Lett 7(8):1893–1911CrossRef
  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):209–220CrossRef
  Dantzig G (1998) Linear programming and extensions. Princeton University Press, New Jersey
  Dorfman R, Samuelson PA, Solow RM (1987) Linear programming and economic analysis. Dover Publications, New York
  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):1–9CrossRef
  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):1081–1101CrossRef
  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):281–293CrossRef
  Fan YR, Huang GH, Li YP (2012b) Robust interval linear programming for environmental decision making under uncertainty. Eng Optim 44(11):1321–1336CrossRef
  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):4591–4610CrossRef
  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
  Gass SI (2010) Linear programming: methods and applications. Dover Publications, New York
  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):461–470CrossRef
  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):349–359CrossRef
  Guo P, Huang GH (2011) Inexact fuzzy-stochastic quadratic programming approach for waste management under multiple uncertainties. Eng Optim 43(5):525–539CrossRef
  Guo P, Huang GH, Li YP (2008) Interval stochastic quadratic programming approach for municipal solid waste management. J Environ Eng Sci 7(6):569–579CrossRef
  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):521–537CrossRef
  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):1001–1023CrossRef
  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):81–91CrossRef
  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):54–64CrossRef
  Huang GH, Loucks DP (2000) An inexact two-stage stochastic programming model for water resources management under uncertainty. Civ Eng Environ Syst 17(2):95–118CrossRef
  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):17–38CrossRef
  Huang GH, Baetz BW, Patry GG (1995b) Grey integer programming - an application to waste management planning under uncertainty. Eur J Oper Res 83(3):594–620CrossRef
  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):271–283CrossRef
  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):1183–1200CrossRef
  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):764–777CrossRef
  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):875–882CrossRef
  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):188–209CrossRef
  Li YP, Huang GH (2007) Fuzzy two-stage quadratic programming for planning solid waste management under uncertainty. Int J Syst Sci 38(3):219–233CrossRef
  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):96–104CrossRef
  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):5677–5689CrossRef
  Li YP, Huang GH, Nie SL (2011b) Optimization of regional economic and environmental systems under fuzzy and random uncertainties. J Environ Manag 92(8):2010–2020CrossRef
  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):241–260CrossRef
  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):2270–2280CrossRef
  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):353–378CrossRef
  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):868–878CrossRef
  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):1657–1686CrossRef
  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):759–768CrossRef
  Luo J, Li W (2013) Strong optimal solutions of interval linear programming. Linear Algebra Appl 439(8):2479–2493CrossRef
  Mráz F (1998) Calculating the exact bounds of optimal values in LP with interval coefficients. Ann Oper Res 81:51–62CrossRef
  Nie XH, Huang GH, Wang D, Li HL (2008) Robust optimisation for inexact water quality management under uncertainty. Civ Eng Environ Syst 25(2):167–184CrossRef
  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):971–983CrossRef
  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):129–138CrossRef
  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):451–468CrossRef
  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 37:7708–7716CrossRef
  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):620–631CrossRef
  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):1765–1776CrossRef
  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
  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):316–327CrossRef
  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 158:82–98CrossRef
  Zhu H, Huang GH (2011) SLFP: a stochastic linear fractional programming approach for sustainable waste management. Waste Manag 31(12):2612–2619CrossRef
  
• 作者单位：Gaiqiang Yang (1) (2)
  Ping Guo (1) (4)
  Mo Li (1)
  Shiqi Fang (1)
  Liudong Zhang (1) (3)
  
  1. Centre for Agricultural Water Research in China, China Agricultural University, Beijing, 100083, China
  2. Institute of Environmental Science, Taiyuan University of Science and Technology, Taiyuan, Shanxi, 030024, China
  4. College of Water Conservancy and Civil Engineering, China Agricultural University, Beijing, 100083, China
  3. College of Water Conservancy and Hydropower and Architecture Engineering, Yunnan Agricultural University, Kunming, 650201, China
  
• 刊物类别：Earth and Environmental Science
• 刊物主题：Earth sciences
  Hydrogeology
  Geotechnical Engineering
  Meteorology and Climatology
  Civil Engineering
  Environment
  
• 出版者：Springer Netherlands
• ISSN：1573-1650

文摘

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. Keywords Interval linear programming Interval-parameter Single-step method Two-step method Agricultural water management