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

Constructing $K-$optimal designs for different Scheff\'{e} models