This paper proposes a grey fuzzy quadratic programming (GFQP) approach
as a means for optimization analysis under uncertainty. The method co
mbines the ideas of grey fuzzy linear programming (GFLP) and fuzzy qua
dratic programming (FQP) within a general optimization framework. It i
mproves upon the previous GFLP method by using n grey control variable
s, x (lambda(i))(i = 1, 2,...,n), for n constraints instead of one x (
lambda) for n constraints in order to incorporate the independent prop
erties of the stipulation uncertainties; it also improves upon the FQP
method by further introducing grey numbers for coefficients in A and
C to effectively reflect the lefthand side uncertainties. Compared wit
h the GFLP method, the GFQP approach is helpful for better satisfying
model objective/constraints and providing grey solutions with higher s
ystem certainty and lower system cost; compared with the FQP method, m
ore information of the independent uncertain features of not only the
stipulations but also the lefthand side coefficients are effectively r
eflected in the GFQP method. The GFQP modelling approach is applied to
a hypothetical case study of waste flow allocation planning under unc
ertainty, with the input model stipulations fluctuating within wide in
tervals and having independent uncertain characteristics. The results
indicated that reasonable solutions have been generated. Comparisons b
etween the GFQP and FQP/GFLP solutions are also provided, which demons
trate that the GFQP method could better reflect system uncertainties a
nd provide more realistic and applicable solutions with lower system u
ncertainties and higher system benefits.