Inexact two-stage stochastic partial programming: application to water resources management under uncertainty

Abstract

In this study, an inexact two-stage stochastic partial programming (ITSPP) method is developed for tackling uncertainties presented as intervals and partial probability distributions. A scenario-based interactive algorithm is proposed to solve the ITSPP model. This algorithm is implemented through: (i) obtaining extreme points of the linear partial information (LPI); (ii) generating an inexact two-stage stochastic programming (ITSP) model under each extreme point; (iii) solving ITSP models through interactive algorithm proposed by Huang and Loucks (Civil Eng Environ Syst 17: 2000); (iv) acquiring the interval solutions under each extreme point and the final optimal interval for the objective function. The developed method is applied to a case study for waterresources planning. The modelling results can generate a series of decision alternatives under various system conditions, and thus help decision makers identify the desired water-resources management policies under uncertainty.

A stochastic programming with imprecise probabilities model for planning water resources systems under multiple uncertainties

“…Over the past decades, a large number of inexact optimization methodologies have been proposed for tackling water resources management problems (Karamouz and Houck 1987;Reca et al 2001;Luo et al 2003;Huang and Chang 2003;Maqsood et al 2005;Xevi and Khan 2005;Ganji et al 2008;Li et al 2010;Fan et al 2012;He et al 2012;Shen et al 2012;Chen et al 2013;Tan et al 2013;Huang 2014, 2015). Among these approaches, two-stage stochastic programming (TSP) is an effective approach for addressing uncertainties expressed as random variables with known probability distributions.…”

Mathematical modeling for air quality management under stochastic and interval uncertainties

“…Previously, a significant number of optimization techniques were developed for dealing with environmental management problems, including stochastic mathematical programming (SMP), fuzzy mathematical programming (FMP) and interval mathematical programming (IMP), as well as their integrations (Macchiato et al 1994;Teng and Tzeng 1994;Lejano et al 1997;Liu et al 2003;Zhu et al 2009;Cao et al 2010;Qin et al 2010;Xu et al 2010a;Fan et al 2012;Hu et al 2012;lv et al 2012;Xu et al 2012;Li et al 2014). For example, Liu et al (2003) developed a hybrid fuzzy-stochastic robust programming method for regional air quality management where the random and fuzzy variables are tackled by stochastic chance-constrained programming and fuzzy robust programming, respectively.…”

An Inexact Two-Stage Stochastic Programming Model for Sustainable Utilization of Water Resource in Dalian City

“…For example, TSP can handle uncertain problems presented as probability density functions (PDFs) and account for economic "penalties" with recourse against infeasibility, but it is hard to deal with uncertain coefficients in constraints' left side. In addition, as the data for producing PDFs are always insufficient, probabilistic specifications for parameters under uncertainty could not be very realistic in many practical problems [14].So how to define the PDFs and degree of confidence level that closer to the objective world will need to be further studied [15]. To deal with these uncertain problems with the TSP method, the inexact twostage stochastic programming (ITSP) model has already attracted widespread attentions over the past decades [16][17][18][19].…”