Abstract
In this study, a generalized fuzzy integer programming (GFIP) method is developed for planning waste allocation and facility expansion under uncertainty. The developed method can (i) deal with uncertainties expressed as fuzzy sets with known membership functions regardless of the shapes (linear or nonlinear) of these membership functions, (ii) allow uncertainties to be directly communicated into the optimization process and the resulting solutions, and (iii) reflect dynamics in terms of waste-flow allocation and facility-capacity expansion. A stepwise interactive algorithm (SIA) is proposed to solve the GFIP problem and generate solutions expressed as fuzzy sets. The procedures of the SIA method include (i) discretizing the membership function grade of fuzzy parameters into a set ofα-cutlevels; (ii) converting the GFIP problem into an inexact mixed-integer linear programming (IMILP) problem under eachα-cut level; (iii) solving the IMILP problem through an interactive algorithm; and (iv) approximating the membership function for decision variables through statistical regression methods. The developed GFIP method is applied to a municipal solid waste (MSW) management problem to facilitate decision making on waste flow allocation and waste-treatment facilities expansion. The results, which are expressed as discrete or continuous fuzzy sets, can help identify desired alternatives for managing MSW under uncertainty.
Highlights
Municipal solid waste (MSW) management is a priority for many developed and developing countries throughout the world
A stepwise interactive algorithm (SIA) is proposed to solve the generalized fuzzy integer programming (GFIP) problem and generate solutions expressed as fuzzy sets
In detail, (i) the GFIP method can deal with uncertainties expressed as fuzzy sets with known membership functions, regardless of whether these functions are linear or nonlinear; (ii) the proposed GFIP method can allow uncertainties to be directly communicated into the optimization process and the resulting solutions; (iii) the GFIP method can reflect dynamics in terms of waste-flow allocation and facilitycapacity expansion; (iv) compared with other inexact mixedinteger programming approaches (e.g., inexact two-stage mixed-integer linear programming (ITSMILP) by Li and Huang [7]), the GFIP can analyze the inherent interrelationship between the uncertainty of fuzzy parameters (i.e., α-cut levels) and capacity expansion options of waste management facilities, and such analysis can help decision makers make tradeoffs between system reliability and system cost
Summary
Municipal solid waste (MSW) management is a priority for many developed and developing countries throughout the world. In detail, (i) the GFIP method can deal with uncertainties expressed as fuzzy sets with known membership functions, regardless of whether these functions are linear or nonlinear; (ii) the proposed GFIP method can allow uncertainties to be directly communicated into the optimization process and the resulting solutions; (iii) the GFIP method can reflect dynamics in terms of waste-flow allocation and facilitycapacity expansion; (iv) compared with other inexact mixedinteger programming approaches (e.g., ITSMILP by Li and Huang [7]), the GFIP can analyze the inherent interrelationship between the uncertainty of fuzzy parameters (i.e., α-cut levels) and capacity expansion options of waste management facilities, and such analysis can help decision makers make tradeoffs between system reliability and system cost. The results will be used for generating different decision alternatives under various system conditions and for helping identify desired waste management policies
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