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A Two-Stage Fuzzy Chance-Constrained Model for Solid Waste Allocation Planning

Y. Xu1*,G. H. Huang1,2,G. H. Cheng2,Y. Liu1,Y. F. Li1

  1. MOE Key Laboratory of Regional Energy and Environmental Systems Optimization, Sino-Canada Resources and Environmental Research Academy, North China Electric Power University, Beijing 102206, China
  2. Faculty of Engineering and Applied Science, University of Regina, Regina, Saskathewan S4S 0A2, Canada

*Corresponding author. Tel: +86-10-61772982 Fax: +86-10-61773889 Email:


A two-stage double-sided fuzzy version of the chance-constrained mixed-integer programming (TDFCCMP) model was developed in this study for supporting municipal solid waste management under multiple uncertainties. TDFCCMP integrates the double-sided fuzzy version of the chance-constrained programming (DFCCP) model and the mixed-integer programming (MIP) model within a two-stage stochastic programming (TSP) framework. It could deal with possibilistic or probabilistic uncertainties and tackle complexities derived from capacity-expansion issues. A hypothetical long-term solid waste management problem was used to demonstrate the applicability of the proposed method. The results indicated that TDFCCMP was useful in assisting the decision makers analyze policy scenarios that were associated with economic penalties within a multi-stage and multi-period context. The model also allowed violation of system constraints at specified confidence-levels under two reliability conditions, leading to solutions with lower costs under acceptable magnitudes of system-failure risk. The generated solutions could help decision makers establish various waste-flow allocation patterns and capacity-expansion plans under complex uncertainties, and gain in-depth insights into the trade-offs between system economy and reliability.

Keywords: fuzzy version of the chance-constrained programming, mixed-integer programming, two-stage stochastic programming, solid waste management, uncertainty

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