Planning Water Resources Allocation Under Multiple Uncertainties Through a Generalized Fuzzy Two-Stage Stochastic Programming Method

Abstract

In this study, a generalized fuzzy two-stage stochastic programming (GFTSP) method is developed for planning water resources management systems under uncertainty. The developed GFTSP method can deal with uncertainties expressed as probability distributions, fuzzy sets, as well as fuzzy random variables. With the aid of a robust stepwise interactive algorithm, solutions for GFTSP can be generated by solving a set of deterministic submodels. Furthermore, the possibility information (expressed as fuzzy membership functions) can be reflected in the solutions for the objective function value and decision variables. The developed GFTSP is also applied to a water resources management and planning problem to demonstrate its applicability. Solutions of decision variables and objective function value are expressed as fuzzy membership functions, reflecting the fluctuating ranges of decision alternatives under different plausibilities. Moreover, comparison between solutions obtained through the membership functions derived from GFTSP and interval two-stage stochastic programming (ITSP) method suggests that the possibility information for the objective function value and decision variables is reasonable and robust. And thus the water alternatives can be directly derived from the obtained fuzzy membership functions when the preferred α value is predefined by decision makers.

Inexact Fuzzy Stochastic Chance Constraint Programming for Emergency Evacuation in Qinshan Nuclear Power Plant under Uncertainty

“…The value of μ à (x) va-ries between 0 and 1, indicating the possibility of an element x belonging to Ã. μ à (x) = 1 means that x definitely belongs to the fuzzy set (Ã), while μ à (x) = 0 denotes that x does not belong to Ã. The closer μ à (x) is to 1, the more likely that x belongs to Ã; conversely, the closer μ à (x) is to 0, the less likely x belongs to à (Zimmermann, 1985;Lai andHwang, 1992, Li andFan et al, 2015).…”

A Stochastic Multi-Objective Chance-Constrained Programming Model for Water Supply Management in Xiaoqing River Watershed

“…Previously, many uncertain analysis approaches were developed for dealing with watershed-scale water resource management issues, including stochastic mathematical programming (SMP) [3][4][5][6][7], fuzzy mathematical programming (FMP) [8][9][10][11] and interval mathematical programming (IMP) [12,13], as well as their combinations [14][15][16][17][18]. Among them, stochastic chance-constrained programming (SCCP) was extensively applied in water resource management due to its capacity in evaluating the trade-offs between realization of system objectives and satisfaction degrees of model constraints [19][20][21][22].…”

An Integrated Method for Interval Multi-Objective Planning of a Water Resource System in the Eastern Part of Handan

“…Thirdly, there have been serious contradictions between water supply and demand, water shortage and water pollution, as well as the competition among water users [8]. In addition, water resources systems can be complex with uncertainties which may exist in technical, social, environmental, political, and financial factors [9,10]. For example, there are serious water resource problems in the eastern part of Handa, China: (a) the distribution of water resources is uneven since the main surface water of Handan (Yuecheng and Dongwushi reservoirs) are located in the western part of Handan [11]; (b) the groundwater is seriously over-exploited because it is the most important source for agriculture which is the main industry [12]; (c) transferred water and local water conservancy projects cannot be organically combined, and thus cannot realize the maximum benefit of transferred water [13]; (d) there is a serious competition among different water users [14,15].…”