Abstract
Due to rapid growth of population and development of economy, water resources allocation problems have aroused wide concern. Therefore, optimization of water resources systems is complex and uncertain, which is a severe challenge faced by water managers. In this paper, a factorial multi-stage stochastic programming with chance constraints approach is developed to deal with the issues of water-resources allocation under uncertainty and risk as well as their interactions. It can deal with uncertainties described as both interval numbers and probability distributions, and can also support the risk assessment within a multistage context. The solutions associated with different risk levels of constraint violation can be obtained, which can help characterize the relationship between the economic objective and the system risk. The inherent interactions between factors at different levels and their effects on total net benefits can be revealed through the analysis of multi-parameter interactions.
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References
Ahmed S, King AJ, Gyana P (2003) A multi-stage stochastic integer programming approach for capacity expansion under uncertainty. J Glob Optim 26(1):3–24
Almiñana M, Escudero LF, Landete M, Monge JF, Rabasa A, Sánchez-Soriano J (2010) WISCHE: a DSS for water irrigation scheduling. Omega 38(6):492–500
Charnes A, Cooper WW, Kirby MJL (1971) Chance-constrained programming: an extension of statistical method. Optimizing methods in statistics. Academic Press, Inc, New York, pp 391–402
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
Fan YR, Huang GH, Huang K, Baetz B (2014) Planning water resources allocation under multiple uncertainties through a generalized fuzzy two-stage stochastic programming method
Guo P, Huang GH (2009) Two-stage fuzzy chance-constrained programming: application to water resources management under dual uncertainties. Stoch Environ Res Risk Assess 23(3):349–359
Housh M, Ostfeld A, Shamir U (2013) Limited multi-stage stochastic programming for managing water supply systems. Environ Model Softw 41:53–64
Huang GH (1998) A hybrid inexact-stochastic water management model. Eur J Oper Res 107(1):137–158
Huang GH, Loucks DP (2000) An inexact two-stage stochastic programming model for water resources management under uncertainty. Civil Eng Syst 17(2):95–118
Hunter JS, Hunter JS, Box G (1978) Statistics for experimenters an introduction to design, data analysis, and model building. Wiley series in probability and mathematical statistics. Wiley, New York
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
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
Li YP, Huang GH (2013) Risk analysis and management for water resources systems. Stoch Environ Res Risk Assess 27(3):593–597
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
Loucks DP, Stedinger JR, Haith DA (1981) Water resource systems planning and analysis. Prentice-Hall, Englewood Cliffs
Montgomery DC (2001) Design and analysis of experiments, 5th edn. Wiley, New York
Montgomery DC (2008) Design and analysis of experiments. Wiley, Hoboken
Pereira MVF, Pinto LM (1991) Multi-stage stochastic optimization applied to energy planning. Math Program 52(1–3):359–375
Syme GJ (2014) Acceptable risk and social values: struggling with uncertainty in Australian water allocation. Stoch Environ Res Risk Assess 28(1):113–121
Taguchi G (1986) Introduction to quality engineering: designing quality into products and processes. The Organization, Tokyo
UN-Water Thematic (2006) Coping with water scarcity: a strategic issue and priority for system-wide action. Retrieved August 11.2009: 2005–2015
Wang S, Huang GH (2011) Interactive two-stage stochastic fuzzy programming for water resources management. J Environ Manag 92(8):1986–1995
Wang S, Huang GH (2014) An integrated approach for water resources decision making under interactive and compound uncertainties. Omega 44:32–40
Wang S, Huang GH (2015) A multi-level Taguchi-factorial two-stage stochastic programming approach for characterization of parameter uncertainties and their interactions: an application to water resources management. Eur J Oper Res 240(2):572–581
Wang L, Fang L, Hipel KW (2008) Basin-wide cooperative water resources allocation. Eur J Oper Res 190(3):798–817
Wang S, Huang GH, Veawab A (2013) A sequential factorial analysis approach to characterize the effects of uncertainties for supporting air quality management. Atmos Environ 67:304–312
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(3):211–230
Zhou Y, Huang GH (2011) Factorial two-stage stochastic programming for water resources management. Stoch Environ Res Risk Assess 25(1):67–78
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This research was supported by the Natural Sciences Foundation (51190095, 51225904), the 111 Project (B14008) and the Natural Science and Engineering Research Council of Canada.
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Liu, X.M., Huang, G.H., Wang, S. et al. Water resources management under uncertainty: factorial multi-stage stochastic program with chance constraints. Stoch Environ Res Risk Assess 30, 945–957 (2016). https://doi.org/10.1007/s00477-015-1143-0
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DOI: https://doi.org/10.1007/s00477-015-1143-0