title: A copula-based chance-constrained waste management planning method: An application to the city of Regina, Saskatchewan, Canada.
abstract: This study proposes a copula-based chance-constrained waste management planning (CCWMP) method. The method can effectively reflect the interactions between random parameters of the waste management planning systems, and thus can help analyze the influences of their interactions on the entire systems. In particular, a joint distribution function is established using preestimated marginal distributions of random variables and an optimal copula selected from widely used Gaussian, Student's t, Clayton, Frank, Gumbel, and Ali-Mikhail-Haq copulas. Then a set of joint probabilistic constraints in the chance-constrained programming problems is converted into individual probabilistic constraints using the joint distribution function. Further, this method is applied to residential solid waste management in the city of Regina in Canada for demonstrating its applicability. Nine scenarios based on different joint and marginal probability levels are considered within a multiperiod and multizone context to effectively reflect dynamic, uncertain, and interactive characteristics of the solid waste management systems in the city. The results provide many decision alternatives under these scenarios, including cost-effective and environmentally friendly decision schemes. Moreover, the results indicate that even though the effect of the joint probability levels on the system costs is more significant than that of the marginal probability levels, the effect of marginal probability levels is notable, and there exists a trade-off between the total system cost and the constraint-violation risk. Therefore, the results obtained from the present study would be useful to support the city's long-term solid waste management planning and formulate local policies and regulation concerning the city's waste generation and management.
  
  
  CONCLUSIONS
  The CCWMP method not only can solve chance-constrained problems with unknown probability distributions of random variables in the right-hand sides of constraints, but also can effectively reflect the interactions between the random parameters and thus help analyze the influences of their interactions on the entire systems. The results obtained through applying this method to the city of Regina in Canada can provide many decision alternatives under different joint probability levels and marginal probability levels, and would be useful to support the city's long-term solid waste management planning.
authors.affiliation: a Faculty of Engineering , University of Regina , Regina , Saskatchewan , Canada.
authors.forename: F
authors.initials: F
authors.lastname: Chen
authors.affiliation: b Institute for Energy, Environment and Sustainability Research, UR-NCEPU , University of Regina , Regina , Saskatchewan , Canada.|c Institute for Energy, Environment and Sustainability Research, UR-NCEPU , North China Electric Power University , Beijing , China.
authors.forename: G H
authors.initials: GH
authors.lastname: Huang
authors.affiliation: a Faculty of Engineering , University of Regina , Regina , Saskatchewan , Canada.
authors.forename: Y R
authors.initials: YR
authors.lastname: Fan
authors.affiliation: a Faculty of Engineering , University of Regina , Regina , Saskatchewan , Canada.
authors.forename: S
authors.initials: S
authors.lastname: Wang
mesh_terms: D002947:Cities; D003198:Computer Simulation; D003247:Conservation of Natural Resources; D003657:Decision Making; D004784:Environmental Monitoring; D008962:Models, Theoretical; D012525:Saskatchewan; D012984:Software; D018505:Waste Management / Q000379:methods*