Abstract
Uncertainties exist in the water resources system, while traditional two-stage stochastic programming is risk-neutral and compares the random variables (e.g., total benefit) to identify the best decisions. To deal with the risk issues, a risk-aversion inexact two-stage stochastic programming model is developed for water resources management under uncertainty. The model was a hybrid methodology of interval-parameter programming, conditional value-at-risk measure, and a general two-stage stochastic programming framework. The method extends on the traditional two-stage stochastic programming method by enabling uncertainties presented as probability density functions and discrete intervals to be effectively incorporated within the optimization framework. It could not only provide information on the benefits of the allocation plan to the decision makers but also measure the extreme expected loss on the second-stage penalty cost. The developed model was applied to a hypothetical case of water resources management. Results showed that that could help managers generate feasible and balanced risk-aversion allocation plans, and analyze the trade-offs between system stability and economy.
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References
Claessens S, Kreuser J (2004) A framework for strategic foreign reserves risk management. In: Risk management for Central Bank foreign reserves. European Central Bank, Frankfurt, pp 47–74
Ganji A, Khalili D, Karamouz M, Ponnambalam K, Javan M (2008) A fuzzy stochastic dynamic Nash game analysis of policies for managing water allocation in a reservoir system. Water Resour Manag 22:51–66
Haneveld WKK, vander Vlerk (2006) Integrated chance constraints: reduced forms and an algorithm. Comput Manag Sci 3:245–269
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
Karamouz M, Houck MH (1987) Comparison of stochastic and deterministic dynamic programming for reservoir operating rule generation. J Am Water Resour Association 23:1–9
Kramer B (2012) CVaR Optimization of Real Estate Portfolios in an ALM Context. OFRC Applied Paper No. 2011–05
Li YP, Huang GH (2008) Interval-parameter two-stage stochastic nonlinear programming for water resources management under uncertainty. Water Resour Manag 22:681–698
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
Li W, Li YP, Li CH, Huang GH (2010) An inexact two-stage water management model for planning agricultural irrigation under uncertainty. Agric Water Manag 97:1905–1914
Li YP, Li W, Huang GH (2012) Two-stage inexact-probabilistic programming model for water quality management. Environ Eng Sci 29:713–725
Lu HW, Huang GH, He L (2011) An inexact rough-interval fuzzy linear programming method for generating conjunctive water-allocation strategies to agricultural irrigation systems. Appl Math Model 35:4330–4340
Luo B, Maqsood I, Yin YY, Huang GH, Cohen SJ (2003) Adaptation to climate change through water trading under uncertainty—an inexact two-stage nonlinear programming approach. J Environ Informat 2:58–68
Maqsood I, Huang GH (2003) A two-stage interval-stochastic programming model for waste management under uncertainty. J Air Waste Manag Assoc 53:540–552
Maqsood I, Huang GH, Huang YF (2005) ITOM: an interval-parameter two-stage optimization model for stochastic planning of water resources systems. Stochast Environ Res Risk Assess 19:125–133
Özelkan EC, Galambosi Á, Fernández-Gaucherand E, Duckstein L (1997) Linear quadratic dynamic programming for water reservoir management. Appl Math Model 21:591–598
Piantadosia J, Metcalfe AV, Howlett PG (2008) Stochastic dynamic programming (SDP) with a conditional value-at-risk (CVaR) criterion for management of storm-water. J Hydrol 348:320–329
Reca J, Roldán J, Alcaide M, López R, Camacho E (2001) Optimization model for water allocation in deficit irrigation systems: I. Description Model Agric Water Manag 48:103–116
Rockafellar RT, Uryasev S (2000) Optimization of conditional value-at-risk. J Risk 2:21–41
Shao LG, Luan SJ (2010) A CVaR-based nonlinear stochastic model for water resources management. Presented at the Conference on Environmental Pollution and Public Health, Wuhan, China
Shao LG, Qin XS, Xu Y (2011) A conditional value-at-risk based inexact water allocation model. Water Resour Manag 25:2125–2145
Topaloglou N (2004) A stochastic programming framework for international portfolio management. Dissertation, School of Economics and Management, University of Cyprus
Xevi E, Khan S (2005) A multi-objective optimization approach to water management. J Environ Manag 77:269–277
Xu Y, Huang GH, Qin XS (2009) Inexact two-stage stochastic robust optimization model for water resources management under uncertainty. Environ Eng Sci 26:1765–1776
Xu JY, Li YP, Huang GH (2013) A hybrid interval–robust optimization model for water quality management. Environ Eng Sci 30:248–263
Zeng GM, Li YP, Qin XS, Huang GH, Li JB, Jiang R (2004) Optimum municipal wastewater treatment plant design with consideration of uncertainty. J Environ Sci 16:126–131
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Li, W., Wang, B., Xie, Y.L. et al. An inexact mixed risk-aversion two-stage stochastic programming model for water resources management under uncertainty. Environ Sci Pollut Res 22, 2964–2975 (2015). https://doi.org/10.1007/s11356-014-3547-7
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DOI: https://doi.org/10.1007/s11356-014-3547-7