D- and I-optimal design of mixture experiments in the presence of ingredient availability constraints

Mixture experiments usually involve various constraints on the proportions of the ingredients of the mixture under study. In this paper, inspired by the fact that the available stock of certain ingredients is often limited, we focus on a new type of constraint, which we refer to as an ingredient availability constraint. This type of constraint substantially complicates the search for optimal designs for mixture experiments. One difficulty, for instance, is that the optimal number of experimental runs is not known a priori. We show that the optimal design problem in the presence of ingredient availabililty constraints is a nonlinear multidimensional knapsack problem and propose a variable neighborhood descent algorithm to identify D- and I-optimal designs for mixture experiments in case there is a limited stock of certain ingredients.