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It is clear that, sometimes decision of using substitution and simultaneous ordering is not affordable and it depends on values of problem parameters, so we analyzed this too.
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Let denote the optimal values of problems and, respectively, that is.
In addition, the global optimal values of problems (P) and (Q) are equal.
The optimal values of problems ( P ) and ( D ) are denoted by v ( P ) and v ( D ), respectively.
Moreover, it is easy to see that the global optimal values of problems (FP) and (FP2) are equal.
The minimal objective function values of problems (P) and (P1) are equal, i.e., (f(x^{ast})=G y^{ast})).
New formulation of possibilistic programming method is developed which is able to minimize the total mean and risk values of problems with possibilistic-based uncertainty.
Let (V(mathrm{P}(D))) and (V(mathrm{Q}(D))) be the optimal values of problems (mathrm{P}(D)) and (mathrm{Q}(D)), respectively.
Let (v(P)), (v tilde{P})) and (v(D)) denote the optimal values of problems (P), ((tilde{P})) and (D), respectively.
In other words, the optimal objective value of problem (AP) is less than or equal to the optimal objective value of problem (DCLFP).
For convenience, let τ to be the target value of problem (8) and problem (9).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com