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Two-stage fuzzy chance-constrained programming: application to water resources management under dual uncertainties

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Abstract

In this study, a two-stage fuzzy chance-constrained programming (TFCCP) approach is developed for water resources management under dual uncertainties. The concept of distribution with fuzzy probability (DFP) is presented as an extended form for expressing uncertainties. It is expressed as dual uncertainties with both stochastic and fuzzy characteristics. As an improvement upon the conventional inexact linear programming for handling uncertainties in the objective function and constraints, TFCCP has advantages in uncertainty reflection and policy analysis, especially when the input parameters are provided as fuzzy sets, probability distributions and DFPs. TFCCP integrates the two-stage stochastic programming (TSP) and fuzzy chance-constrained programming within a general optimization framework. TFCCP incorporates the pre-regulated water resources management policies directly into its optimization process to analyze various policy scenarios; each scenario has different economic penalty when the promised amounts are not delivered. TFCCP is applied to a water resources management system with three users. Solutions from TFCCP provide desired water allocation patterns, which maximize both the system’s benefits and feasibility. The results indicate that reasonable solutions were generated for objective function values and decision variables, thus a number of decision alternatives can be generated under different levels of stream flows, α-cut levels and fuzzy dominance indices.

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Acknowledgments

This research was supported by the Major State Basic Research Development Program (2005CB724200 and 2006CB403307) and the Natural Science and Engineering Research Council of Canada.

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Authors and Affiliations

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

    P. Guo

  2. Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    G. H. Huang

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  1. P. Guo
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  2. G. H. Huang
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Correspondence to G. H. Huang.

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Guo, P., Huang, G.H. Two-stage fuzzy chance-constrained programming: application to water resources management under dual uncertainties. Stoch Environ Res Risk Assess 23, 349–359 (2009). https://doi.org/10.1007/s00477-008-0221-y

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