Dual inexact fuzzy chance-constrained programming for planning waste management systems

Abstract

This study develops a dual inexact fuzzy chanceconstrained programming (DIFCCP) method for planning municipal solid waste (MSW) management systems. The concept of random boundary interval (RBI) is introduced to address the high uncertain parameters in the studied system. Fuzzy flexible programming and chance-constrained programming are also introduced to take into account the uncertainties of RBIs and various uncertainties in MSW management system. Compared with the existing methods, the developed method could deal with the uncertainty without simplification and thus is more robust. Moreover, the potential system-failure risks in MSW management system due to the existing uncertainties could be quantified by means of violation levels and satisfaction levels in DIF-CCP. The developed method then is applied to a MSW management system. The obtained solutions could be used for generating efficient management schemes. The values of violation and satisfaction levels could help decision makers understand the tradeoffs between system cost and systemfailure risk, and identify desired strategy according to the practical economic and environmental situation.

A dual-inexact fuzzy stochastic model for water resources management and non-point source pollution mitigation under multiple uncertainties

“…In order to further demonstrate that the method DIFSP is more applicable than ICCP in dealing with water resources and farmland use management problems under uncertainty, a comparable study was conducted between the generated solutions from these two optimization methods. Letting the lower and upper bounds of RBIs equal their mid-values, the model would be simplified into a conventional inexact chance-constrained programming (ICCP) problem (Cao et al, 2010). The system benefits obtained through ICCP and DIFSP are presented in Table 8, which indicates that the results of DIFSP are much more robust than those of ICCP, meaning that the solution width of DIFSP is tighter and less uncertain.…”

“…Instead, the obtained data can be presented as a random boundary interval (RBI) with its lower and upper bounds being random variables (Cao et al, 2010). Specifically, the parametersB − i andB + i on the right-hand side of constraints can be formulated as follows: (u 1 , v 1 ), (u 2 , v 2 ),.…”

“…Since parameters on the left-hand side are intervals, an interval chance-constrained linear programming (ICCP) can be developed (Huang et al, 1992(Huang et al, , 1995. As Z i is a random variable with known distribution function, model (1) can be converted into the following (Cao et al, 2010;Cai et al, 2007Cai et al, , 2009a:…”

“…For example, the availabilities of various water resources are sensitive to geographical conditions and climate, technology selection and utilization efficiency, as well as water-saving consciousness, causing difficulties to related data acquisition, even the determination of interval numbers, when the lower and upper bounds are correlated. In the past decades, little work has been conducted to handle this type of uncertainty (dual uncertainty) existing in the processes of water and farmland use planning, which might result in missed information and thus impractical decision support (Cao et al, 2010). Therefore, in this study, a concept of random boundary interval (RBI) will be introduced to reflect such dual uncertainty.…”

Compromising economic cost and air pollutant emissions of municipal solid waste management strategies by fuzzy multiobjective optimization model

“…Fuzzy mathematical programming (FMP), which employs fuzzy set theory, is generally applied to deal with multiobjective functions or right-side uncertainties of the constraints in the DMP model Li and Huang, 2007;Li et al, 2008;Minciardi et al, 2008;Fan et al, 2009;Galante et al, 2010;Srivastava and Nema, 2011). Several studies also incorporated fuzzy sets theory into IMP to develop interval fuzzy mathematical programming (IFMP) models for the MSWM system (Huang et al, 1993;Chang and Wang, 1996;Nie et al, 2009;Cao et al, 2010;Sun et al, 2011;. Some studies further incorporated probability theory into IFMP to deal with right-side uncertainties of the constraints (Li et al, 2006;He et al, 2008;Li et al, 2009;Guo and Huang, 2011;Wang et al, 2012).…”