  To avoid multicollinearity in regression analysis, Ye and Zhou(2013) proposed
$K-$optimality criterion. By far the most popular models for modeling the
response of a mixture experiment are the Scheff\'{e} models. However, there
have been no reports about constructing $K-$optimal designs for mixture models.
The paper constructs $K-$optimal designs for first-order and second-order
Scheff\'{e} models. The analytical solutions for first-order and second-order
Scheff\'{e} models are obtained. A series of numerical results and examples are
given to illustrate the theory.
