An interval full-infinite programming (IFIP) method is developed by introducing a concept of functional intervals into an optimization framework. Since the solutions of the problem should be 'globally' optimal under all possible levels of the associated impact factors, the number of objectives and constraints is infinite. To solve the IFIP problem, it is converted to two interactive semi-infinite programming (SIP) submodels that can be solved by conventional SIP solution algorithms. The IFIP method is applied to a solid waste management system to illustrate its performance in supporting decision-making. Compared to conventional interval linear programming (ILP) methods, the IFIP is capable of addressing uncertainties arising from not only the imprecise information but also complex relations to external impact factors. Compared to SIP that can only handle problems containing infinite constraints, the IFIP approaches are useful for addressing inexact problems with infinite objectives and constraints.
NomenclatureA ± ∈ {R ± } m×n , where R ± denotes a set of intervals A ± (s) ∈ {R ± } m×n , where R ± denotes a set of functional intervals a ± ij = the ith row and j th line element of A ± a ± ij = the ith row and j th line element of A ± (s i )where R ± denotes a set of intervals C ± (s) ∈ {R ± } 1×n , where R ± denotes a set of functional intervals c ± j = the j th element of C ± c ± j (s i ) = the j th element of C ± (s i ) c ± ij k = waste transportation costs from city i to facility j in period k ($/tonne) 710 L. He et al.d ± jk = residue transportation costs from waste-to-energy (WTE) facility j to landfill in period k ($/tonne) EF = energy price ($/m 3 ), an independent variable f ± = system cost f ± opt = the most desirable system cost i = index for cities (i = 1, 2, 3) j = index for facilities (j = 1, 2, 3) k = index for periods (k = 1, 2, 3) m = index for facility capacity expansion type (m = 1, 2, 3) RE ± k = revenue of unit municipal solid waste disposed by WTE facility in period k ($/tonne) RF = residue flow rate from WTE facility to landfill GP = gas price ($/liter), an independent variable TE ± jk = operational costs of facility j in period k ($/tonne) TL ± = existing capacity of the landfill (tonnes) WG ± ik = daily generation amount of solid waste in city i in period k (tonnes/day) WTE ± j = existing capacity of WTE facility j (j = 1, 2) X ± ∈ {R ± } n×1 , where R ± denotes a set of intervals x ± ij k = solid waste flow from city i to facility j in period k (tonnes/day) x − ijk,opt = the lower bound of solid waste flow from city i to facility j in period k ($/tonne)
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